High School Music: Theory, Listening & Performance

The twelfth fret problem

Take a guitar. Pluck the thinnest string open and let it ring. Now press that same string down at the twelfth fret, exactly halfway along its sounding length, and pluck again. The second note is higher, obviously. But it is not just higher. It is somehow the same note. Sing the first, then the second, and your voice does not feel like it has moved to a different letter of the alphabet. It feels like it has moved to the same place upstairs.

Nothing about that is obvious. If you press the string at the seventh fret you get a genuinely different note. At the fifth fret, a different note again. Only at the halfway point does the string hand back something the ear files under the same name. Why should cutting a string in half be special?

That question is the whole lesson, and answering it will hand you three things you will use for the rest of the course: what pitch physically is, why the letters A to G run out and start again, and why every piano on earth is very slightly out of tune on purpose.

What is actually moving

A plucked string swings back and forth. Each swing shoves the air beside it, and that shove passes outward as a travelling squeeze of air pressure at roughly 343 metres per second in a room at 20 degrees Celsius. When the squeezes reach your eardrum they push it in and out at the same rate the string is swinging. Your ear counts that rate.

The rate is called the frequency, measured in hertz (Hz), which just means swings per second. Faster swinging is heard as higher pitch. A healthy young ear picks up roughly 20 Hz at the bottom to roughly 20,000 Hz at the top, and the ceiling drops as you get older. The lowest note on a piano, A0, swings 27.5 times a second, slow enough that you half feel it as a flutter in your chest. The top note, C8, swings 4,186 times a second.

Two other things about the wave matter, and neither is pitch. How hard the string shoves, its amplitude, is heard as loudness. The particular mixture of wobbles riding on top of the main swing is heard as timbre, the difference between a flute and a fuzz guitar. Keep these apart in your head. A note high on the staff is faster, not louder.

Four hundred and forty times a second, by agreement

Go to an orchestral concert and the last thing you hear before the music is the oboe playing one long note, with everybody tuning to it. That note is A4, the A above middle C, and by international agreement it swings 440 times a second. An international conference in London in 1939 recommended the figure, and it later became the standard A440, published by the International Organization for Standardization as ISO 16.

Agreement is the point. Nothing in physics prefers 440. Plenty of ensembles do not use it: many European orchestras tune a shade brighter, around 442 or 443 Hz, and groups playing Baroque music on period instruments often drop to A = 415 Hz, about a semitone below modern pitch, which is why a Bach cantata on period instruments can sound startlingly low if you know the tune. A tuner app on your phone assumes 440 unless you tell it otherwise.

Key idea: Pitch is a number of swings per second, and standard pitch is a human decision about which number to call A. The physics is fixed; the reference point is a convention that has moved before and could move again.

One string is never playing one note

Here is the fact that unlocks the twelfth fret. A real string does not swing in one simple arc. It swings as a whole and, at the same time and more quietly, in halves, in thirds, in quarters, and on up. Each of those smaller sections swings faster, in exact whole-number multiples of the main rate. The whole stack is called the harmonic series, and the components above the bottom one are overtones.

Put numbers on it. Tune a string to A2, the A two octaves below the oboe's tuning note, at 110 Hz. Every harmonic it produces is a whole-number multiple of 110:

Read down the third column. A, A, E, A, C sharp, E, an outsider, A. The letter A keeps coming back, at harmonics 1, 2, 4 and 8, which are exactly the doublings. Everything the Western note system treats as consonant is sitting in the low end of this list, in the order the list gives it.

Why the octave answers the twelfth fret problem

Halving the string doubles the frequency. That is what the twelfth fret does, and it is what harmonic 2 is. The doubled note is called the octave, and the ear treats the two as versions of one thing, an effect called octave equivalence.

The harmonic series explains why. When you play A2 at 110 Hz, the sound already contains 220, 440 and 880 Hz. When you then play A3 at 220 Hz, its own harmonics are 220, 440, 660, 880 and so on. The two notes share a huge fraction of their content. They are not similar by convention; they physically overlap. A perfect fifth, the 3:2 relationship between harmonics 2 and 3, overlaps a good deal too, which is why fifths sound stable and why so many instruments are tuned in fifths.

That is also why letter names run out at seven and start again. Every doubling brings you back to a note that sounds like home, so music only needs names for the distances inside one doubling. A4 at 440 and A5 at 880 get the same letter with a different number, and the whole staff you will learn next lesson is built on that repetition.

The fifth, and the trouble it causes

Now build a keyboard using only pure ratios and watch it fail. Start at some low C and go up by pure fifths, each one exactly 3/2 of the last: C, G, D, A, E, B, F sharp, C sharp, G sharp, D sharp, A sharp, E sharp. Twelve fifths and, in letter names, you are back on C. You have also gone up seven octaves. So twelve pure fifths ought to equal seven octaves.

They do not. Multiply 3/2 by itself twelve times and you get about 129.746. Seven octaves is 2 to the power of 7, which is exactly 128. The gap, about 1.4 percent, is the Pythagorean comma, and it is roughly a quarter of a semitone: small enough to look like a rounding error, large enough that the last fifth in the chain howls.

For centuries this was managed by tuning some intervals pure and shoving the error into keys nobody used. That works until a composer wants to start in C and end up in A flat.

Equal temperament: everyone slightly out, on purpose

Equal temperament solves it by refusing to keep any interval pure except the octave. Divide the octave into twelve steps of exactly the same size, so that each step multiplies the frequency by the twelfth root of two, about 1.0595. Twelve of those steps multiply out to exactly 2, so the octaves are perfect and every key is identical in tuning to every other. The cost is paid by everything in between: measured in cents, where a semitone is 100, the pure fifth is 702 and the tempered fifth is 700, so fifths are two cents narrow, which nobody notices. The pure major third is 386 cents and the tempered major third is 400, so every major third on a piano is about 14 cents sharp, which trained ears do notice and which good singers and string players quietly correct in performance. The upshot: equal temperament trades a small permanent error on thirds for the freedom to play in all twenty-four keys on one instrument, and that trade is why a guitar and a piano can play together at all.

Why a flute and a violin at A4 do not sound the same

Both are swinging 440 times a second, so both are A4. What differs is the recipe of harmonics above that. A flute produces a strong fundamental and relatively weak upper harmonics, which is heard as round and pure. A violin, bowed, keeps many upper harmonics alive, which the ear hears as bright and complex. A clarinet's tube favours the odd-numbered harmonics, which gives it that hollow, woody low register. Timbre is not a vague word for mood. It is a measurable balance inside the harmonic stack you just read in the table.

Listen for it

Three pieces make this audible. First, a bugle. A bugle has no valves, so it can only sound the harmonics of one tube: roughly harmonics 3 to 6, four notes. The call known as Taps, in use in the United States Army since 1862, is built entirely from those four, and it is the harmonic series played as a tune.

Second, the opening of Also sprach Zarathustra, written in 1896 by Richard Strauss. In the first half minute, under a low rumble, the trumpets play three rising notes: C, then G, then C. Those are harmonics 2, 3 and 4. The most famous orchestral opening of the nineteenth century is a harmonic series with the lights on. The score is at IMSLP.

Third, if you play guitar: rest a finger lightly on the string directly over the twelfth fret without pressing down, pluck, and lift. You get a clear bell tone an octave above the open string. That is you silencing the whole-string swing and letting harmonic 2 through on its own. Do the same over the seventh fret for harmonic 3, an octave and a fifth up. You are not playing new notes. You are filtering the ones that were already there.

Common misconceptions

• Higher does not mean louder. Frequency and amplitude are separate. A piccolo playing quietly is high and soft; a bass drum is low and enormous.
• Bach did not write The Well-Tempered Clavier for equal temperament. Well tempered meant that every key was usable, not that every semitone was mathematically identical. Several unequal tunings of the period met that test, and scholars still argue about which one Bach preferred. Equal temperament became the keyboard default later.
• A440 is not a law of nature. It is a published standard, chosen in the twentieth century, and orchestras depart from it on purpose.
• The overtones are not optional extras. You do not hear them as separate notes, but remove them and the instrument stops sounding like itself. A pure single frequency with no harmonics sounds like a hearing test, not like music.

Try it: work the numbers

Do these with a calculator and check each answer before moving on.

1. The oboe sounds A4 at 440 Hz. What is the frequency of the A one octave below, and the A two octaves below? Answer: 220 Hz and 110 Hz. Each octave down halves the frequency.

2. A tuner tells you a string is sounding 330 Hz while a 110 Hz string rings beside it. Which harmonic of the low string is that, and what interval are you hearing? Answer: 330 divided by 110 is 3, so it is harmonic 3, and the interval is an octave plus a perfect fifth.

3. An equal-tempered semitone multiplies frequency by about 1.0595. Start at 440 Hz and take three semitones up. Roughly what frequency do you land on, and what note is it? Answer: 440 times 1.0595 three times over is about 523 Hz, which is C5. Three semitones above A is C.

4. A Baroque ensemble tunes to A = 415 Hz. Is their A higher or lower than yours, and by roughly how much? Answer: lower, by close to one semitone, since 440 divided by about 1.0595 is around 415.

What to carry forward

Pitch is a count of swings per second. Doubling that count produces the octave, the one interval everybody agrees sounds like the same note twice, because the two sounds physically share most of their harmonics. Every other interval in Western music is a smaller step inside that doubling, and the twelve steps on a modern keyboard are made exactly equal so that no key is out of bounds, at the price of thirds that are all slightly sharp.

You now have the reason the alphabet of notes only runs from A to G before repeating, which is the fact the next lesson builds on when it puts those letters onto five lines. Keep the harmonic table in mind as you go: fifths, fourths and thirds will keep turning up in the order the series gave them, and the ear's preference for them is not taste, it is arithmetic you can hear.

Sources

1. Schmidt-Jones, C. (n.d.). Acoustics for music theory. In Understanding Basic Music Theory. Humanities LibreTexts. human.libretexts.org
2. Schmidt-Jones, C. (n.d.). Standing waves and musical instruments. In Understanding Basic Music Theory. Humanities LibreTexts. human.libretexts.org
3. Hutchinson, R. (n.d.). Pitch. In Music Theory for the 21st-Century Classroom. University of Puget Sound. musictheory.pugetsound.edu
4. Wikipedia contributors. (n.d.). Equal temperament. en.wikipedia.org

One printed note, two right answers

Draw a single notehead on the middle line of a five-line staff and hand the page to two players. The violinist plays B, the one just above middle C. The double bass player, reading the same dot in the same place, plays D, more than two octaves lower. Neither of them is guessing and neither is wrong.

The dot alone does not name a pitch. It names a position. A small symbol at the far left of the staff, the clef, declares which pitch one particular line stands for, and every other line and space follows from that one anchor. Change the clef and the whole page re-reads itself. This lesson works one line of music from left to right, then changes the clef and works it again, so you can watch that happen.

Five lines, four spaces, counted from the bottom

The staff is five parallel lines with four spaces between them. A notehead either has a line running through its middle, in which case it is a line note, or it sits in the gap, in which case it is a space note. Higher on the page is higher in pitch, for the reason you met last lesson: the vertical axis is frequency.

Lines and spaces are numbered upward. The bottom line is the first line; the bottom space is the first space. Say "third line" to any musician anywhere and their eye lands on the same place. Moving from a line to the next space, or a space to the next line, is one step of the musical alphabet. Since the alphabet runs A B C D E F G and then starts again, nine staff positions cover a ninth, a little over an octave, which is why five lines and not six or four.

The treble clef is a G, and the bass clef is an F

Both clefs began life as letters, drawn so ornately that the letter disappeared.

The treble clef is a decorated G. Its inner curl wraps around the second line from the bottom, and that line is therefore G4, the G above middle C. From that one fact everything else follows by stepping: the lines from bottom to top are E, G, B, D, F, and the spaces from bottom to top spell F, A, C, E. Flutes, violins, trumpets, right hands at a piano, and most singers read it.

The bass clef is a decorated F. Its two dots sit above and below the fourth line from the bottom, and that line is F3, the F below middle C. The lines from bottom to top are G, B, D, F, A, and the spaces are A, C, E, G. Cellos, double basses, bassoons, trombones, tubas, bass guitars and left hands at a piano read it.

Mnemonics help for a few weeks and then become a bottleneck, because spelling out "Every Good Boy Deserves Fruit" takes a second and a half per note. Use them to get started, then drop them. The way fluency actually arrives is by learning two or three landmark notes cold, middle C, treble G on the second line, bass F on the fourth line, and counting one or two steps out from whichever landmark is nearest.

The grand staff, and the note in the middle

Piano and harp music uses both staves at once, joined by a brace: the treble staff above, the bass staff below. That pair is the grand staff, and the gap between them is not empty. It holds exactly one note, middle C (C4, about 262 Hz), which sits on a short added line one step below the treble staff and, equivalently, one step above the bass staff.

Notice what the diagram shows about range. The bottom line of the treble staff is E4 and the top line of the bass staff is A3, so the two staves nearly meet, with middle C as the one rung between them. That is why a pianist can read both at a glance and why a note can be written either way depending on which hand plays it.

Ledger lines

Music regularly needs pitches outside the five lines. A ledger line is a short segment added above or below the staff, one per pitch, extending the ladder only as far as needed. Above the treble staff: the space above the top line is G5, the first ledger line is A5, the space above it B5, the second ledger line C6. Below the treble staff: the space below the bottom line is D4, the first ledger line is middle C.

One or two ledger lines read instantly. Five or six stop even professionals, which is why engravers switch clefs or write a mark meaning "sound this an octave higher" instead of stacking a tower of little lines.

Worked example: decode eight notes

Here is a line of music given as staff positions rather than a picture. Read it in treble clef and name each note.

G G C C D D C A. Sing it and you will recognise the shape of the nursery tune usually sung to the alphabet: two repeated notes, a jump up, two more repeats, a step higher, then a walk back down. The traditional melody is often attributed to an eighteenth-century French tune, and Mozart wrote twelve keyboard variations on it, K. 265, whose score is on IMSLP.

Change one symbol and every note moves

Now change nothing on the page except the clef. Same eight positions, read in bass clef:

B B E E F F E C. The tune is the same shape, because the positions did not move, but it now lives almost two octaves lower and it is in a different key. Remember: the staff stores relative shape; the clef supplies the absolute pitch. Learners who think of note names as glued to positions get stuck the first time a piece uses a clef they did not expect.

The keyboard, half steps, and the three accidentals

Look at a piano. Eighty-eight keys, fifty-two white and thirty-six black, black ones grouped in twos and threes so your hand can find its place without looking. The white keys spell A B C D E F G over and over. The distance from any key to the very next key, black or white, is a half step, also called a semitone, and two half steps make a whole step.

Two places on the keyboard have no black key between the white ones: between E and F, and between B and C. Those two pairs are already only a half step apart. This single irregularity causes most of the confusion in the next three lessons, so look at a keyboard and see it now rather than taking it on trust.

An accidental is a sign placed immediately to the left of a notehead that shifts it:

• A sharp raises the note by one half step. F sharp is the black key just right of F.
• A flat lowers the note by one half step. B flat is the black key just left of B.
• A natural cancels a previous sharp or flat and returns the note to its plain white-key self.
• Double sharps and double flats move two half steps, and you will meet them in a year or two.

An accidental applies for the rest of the bar it appears in, and to that pitch in that octave only. In the next bar, it is gone unless rewritten.

Because the black key between F and G can be reached from below or above, it has two spellings: F sharp and G flat. Notes that sound the same but are spelled differently are enharmonic. They are not interchangeable on the page. Which spelling is correct depends on the key and on where the note is heading, and getting it right is what separates a legible score from a puzzle.

How loud: the dynamic markings

Everything so far tells a player which pitch. The marks below the staff tell them how loud, and they are Italian because Italian printers dominated early music publishing.

Two long wedge signs handle change: opening wider means crescendo, get louder; closing means diminuendo or decrescendo, get quieter. These are relative, not absolute. A forte on a solo recorder and a forte in a brass band are wildly different numbers of decibels; what the mark fixes is the relationship to the surrounding music.

For the single most famous use of a dynamic in the repertoire, listen to the second movement of Haydn's Symphony No. 94 of 1791. A plain tune is played twice, very quietly, and then at roughly 0:25 to 0:30 the entire orchestra plus timpani hits one fortissimo chord. Haydn wrote the joke into the score; a recording is on Wikimedia Commons.

How each note is attacked: articulation

Articulation marks sit on or near the notehead and control how a note starts, how long it is held, and how it joins to its neighbour.

Slur and tie look identical and mean different things, which is the single most common misreading on this page. If the two notes under the curve are at different heights, it is a slur and you play both smoothly. If they are the same pitch, it is a tie and you play once and hold.

Mozart's Eine kleine Nachtmusik, K. 525, of 1787 opens with the contrast in the first ten seconds: the rising figure is played detached and punchy, and the answering phrase immediately after is smooth and joined. Same instruments, same volume, completely different character, and the only thing that changed is articulation.

How fast: tempo marks

At the top left sits a word, a number, or both. The Italian words are approximate and always have been; the numbers are exact. A metronome mark such as "quarter note = 120" means 120 beats a minute, one every half second. Rough ranges, on which sources genuinely disagree by ten or twenty beats:

• Largo, broad and slow, around 40-60
• Adagio, slow and easy, around 66-76
• Andante, walking pace, around 76-108
• Moderato, moderate, around 108-120
• Allegro, fast and cheerful, around 120-168
• Presto, very fast, around 168-200

Words that modify: poco (a little), molto (very), ma non troppo (but not too much), ritardando (gradually slowing), a tempo (back to the original speed).

Common misconceptions

• A note high on the staff is not louder. Height is pitch. Loudness lives in the dynamic marks underneath.
• Sharp does not mean black key. Sharp means one half step higher. E sharp is F, and B sharp is C, because those pairs have no black key between them.
• An accidental does not last for the whole piece. It lasts to the end of its bar, at that pitch, in that octave.
• Bass clef is not "treble clef moved down". It anchors a different line to a different letter. You cannot convert by counting a fixed number of steps in your head without knowing the anchor.
• A curved line is not always a slur. Same pitch on both ends means a tie, and a tie is a duration instruction, not an articulation.

Try it: read and re-read

Work these on paper, then check.

1. A note sits in the first space of the treble staff. Name it, then name the note two steps higher. Answer: F4; two steps up is A4, the second space, because steps alternate space, line, space.

2. A note sits on the first ledger line below the treble staff. Name it. Where is the identical pitch written on the bass staff? Answer: middle C, C4. On the bass staff it is the first ledger line above.

3. A bar begins with an F sharp on the top line of the treble staff. Three notes later the same line appears again with no accidental. What do you play? Answer: F sharp again. The accidental holds for the rest of the bar at that pitch.

4. Name the enharmonic equivalent of D sharp, and of C flat. Answer: E flat, and B. C flat is a half step below C, which on a keyboard is the white key B.

5. A passage is marked mp with an opening wedge leading to ff, and each note carries a dot. Describe how it sounds. Answer: it starts moderately quiet and grows steadily to very loud, with every note clipped short and separated rather than joined.

Putting it together

A clef anchors one line to one pitch; the staff supplies everything else by stepping. Ledger lines extend the ladder. Accidentals nudge individual notes by a half step and expire at the bar line. Dynamics say how loud relative to the surroundings, articulation says how each note starts and ends, and the tempo mark says how fast the beats go past.

What matters here: none of these symbols mean anything on their own. They are instructions to a person holding an instrument, and every one of them exists because a composer heard something specific and had no other way to ask for it. When you read a page from now on, read it as a set of requests rather than a code to be decrypted. The next module gives the horizontal axis its own attention: how long each of these notes lasts, and how the beats underneath them are grouped.

Sources

1. Hamm, C., and Gotham, M. (n.d.). Notation of notes, clefs, and ledger lines. In Open Music Theory (2nd ed.). VIVA Open Publishing. viva.pressbooks.pub
2. Gotham, M., et al. (n.d.). Other aspects of notation. In Open Music Theory (2nd ed.). VIVA Open Publishing. viva.pressbooks.pub
3. musictheory.net. (n.d.). The staff, clefs, and ledger lines. musictheory.net
4. musictheory.net. (n.d.). Steps and accidentals. musictheory.net
5. Hutchinson, R. (n.d.). Accidentals. In Music Theory for the 21st-Century Classroom. University of Puget Sound. musictheory.pugetsound.edu

Six claps in a bar of four

A student is counting a simple part in 4/4. First bar, four quarter notes: one, two, three, four. Fine. Second bar has four eighth notes followed by two quarter notes, and the student counts one, two, three, four, five, six, gets to the end early, and the whole group falls apart.

The reasoning behind the mistake is perfectly sensible: count one number per note. It is also the single most common rhythm error there is, and everything in this lesson exists to replace it. Numbers do not belong to notes. Numbers belong to beats, and a note takes up as many beats, or as small a fraction of one, as its shape says.

What a note value actually measures

A note value is a proportion, not a stopwatch reading. The whole system is built by repeated halving, and nothing else:

Two names exist for each value, and both are in daily use, so learn the pairs now:

Notice that the word "quarter" tells you nothing about the clock. A quarter note at Largo can last a second and a half; a quarter note at Presto can last a third of a second. It is always a quarter of a whole note, and in 4/4 it is always one beat. Tempo decides how long a beat is; the note value decides how many beats the note occupies.

Stems, flags and beams

A stem is the vertical line. Below the middle line of the staff, stems point up from the right side of the head; on or above the middle line, they point down from the left. That is a rule of engraving, not of sound, and it exists so that stems do not run off the page.

A flag is the little tail on an eighth or sixteenth note. When several such notes occur in a row, engravers replace the flags with beams, the thick horizontal bars joining the stems, and beams are grouped to show where the beats are. This is genuinely helpful rather than decorative: in 4/4, four eighth notes are usually beamed in two pairs rather than one group of four, so your eye sees beat one and beat two immediately. If you ever find a rhythm hard to read, check the beaming first; it is a map of the beats.

Rests: the silences are written too

Every note value has a matching rest of identical length. Silence is not the absence of notation. It is notated as precisely as sound, because an ensemble needs to know exactly when to stop.

The whole rest and the half rest are easy to confuse, and the memory hook is worth the ten seconds it takes: the whole rest is heavier, so it hangs down from the line; the half rest is lighter, so it sits on top. One more convention: a whole rest also means a whole bar of silence in any time signature. In a bar of 3/4 a whole rest means three beats of nothing, not four.

Counting out loud, and why it is not optional

Every beat in a bar gets its number: one, two, three, four. Then you keep saying those numbers at a steady speed whatever the notes do. Subdivisions get syllables:

• Quarter notes: 1 - 2 - 3 - 4
• Eighth notes: 1 and 2 and 3 and 4 and
• Sixteenth notes: 1 e and a 2 e and a 3 e and a 4 e and a, spoken "one ee and uh"

Say it out loud. Not in your head. Counting silently lets your count drift to match your mistake, which is exactly the failure mode you are trying to catch; an audible count is a witness. Professionals count out loud in rehearsal constantly, and the habit is worth building now rather than at sixteen when it feels embarrassing.

There are other systems. Some teachers use a syllable system where a quarter is "ta" and two eighths are "ti-ti", which is excellent for young children and for folk players. Others use the Kodaly or Gordon systems. Use whichever your teacher or your app uses, and use one of them consistently. Switching systems in mid-piece is how people get lost.

Back to the bug

Return to the student's bar: four eighth notes, then two quarter notes, in 4/4. Count the beats, not the notes.

Six notes, four beats. The four eighth notes use up beats 1 and 2 between them, two notes per beat, and each quarter note occupies one whole beat on its own. The point: the number of claps and the number of beats are different quantities, and a bar is measured in beats. Once you count the grid first and fit the notes onto it, the bar cannot come out long or short.

Clap these, then check

All five are in 4/4. Clap on each note, say the count out loud at a steady sixty beats a minute, and hold the silences.

1. quarter, quarter, half. Count: clap on 1, clap on 2, clap on 3 and hold through 4. Three claps, four beats.

2. two eighths, quarter, two eighths, quarter. Count: 1 and, 2, 3 and, 4. Six claps: on 1, the and of 1, 2, 3, the and of 3, and 4.

3. quarter, quarter rest, quarter, quarter rest. Count: clap on 1, silence through 2, clap on 3, silence through 4. Two claps, four beats, and the silences are the hard part: most people rush into beat 3.

4. four sixteenths, quarter, half. Count: 1 e and a, 2, 3 and hold 4. Six claps: the four sixteenths all sit inside beat 1.

5. half, two eighths, quarter. Count: clap on 1 and hold through 2, then clap on 3 and on the and of 3, then clap on 4. Four claps, four beats.

If any of these came out wrong, do not replay it faster. Slow the metronome to forty, count aloud through the whole bar including the beats where nothing happens, and only then add the claps.

The number under the tempo mark

How fast the beats themselves go past is tempo, and a metronome mark states it exactly: "quarter note = 60" means one beat per second. Johann Maelzel patented the mechanical metronome in 1815, and Beethoven was among the first composers to publish metronome marks for his own works, in 1817. Before that, tempo was a word and a tradition.

Your phone has a metronome, and it is the most useful practice tool you own. Set it to 60, clap quarters, then eighths, then sixteenths, then back to quarters without the pulse shifting. That single exercise, five minutes a day, fixes more rhythm problems than any amount of reading about rhythm.

Common misconceptions

• One note does not equal one count. Counts belong to beats. A half note takes two counts and a pair of eighths shares one.
• A quarter note has no fixed duration in seconds. It is a quarter of a whole note. Tempo converts proportions into time.
• Rests are not optional. A rest is an instruction to stop sounding at a precise moment, and in an ensemble the ends of notes matter as much as the beginnings.
• Beaming is not a style choice. Beams are grouped to reveal the beats. Four eighths beamed as two pairs and four eighths beamed as one group sound identical but the first is readable.
• Faster practice does not fix rhythm. If a bar is wrong at 120, it is wrong at 60 too, and at 60 you can hear where.

Summing up

Note values are proportions produced by halving: whole, half, quarter, eighth, sixteenth, each one twice the speed of the last. Rests do the same job for silence. Beats, not notes, carry the counting, and the syllables one, one-and, and one-e-and-a give you a grid fine enough for almost everything you will meet this year.

In short: count the grid first, then place the notes on it. The student who counted to six was not bad at rhythm; they were counting the wrong thing. Next lesson puts a fence around these beats and asks how many go in each bar, which is where time signatures come in, and where the difference between 6/8 and 3/4 finally stops being mysterious.

Sources

1. Hamm, C. (n.d.). Notating rhythm. In Open Music Theory (2nd ed.). VIVA Open Publishing. viva.pressbooks.pub
2. musictheory.net. (n.d.). Note duration. musictheory.net
3. musictheory.net. (n.d.). Rest duration. musictheory.net
4. Hutchinson, R. (n.d.). Basics of rhythm. In Music Theory for the 21st-Century Classroom. University of Puget Sound. musictheory.pugetsound.edu

Six eighth notes, two completely different bars

Write six eighth notes in a row and draw a bar line after the last one. You have written nothing yet about how the bar goes, because six eighth notes can be grouped two ways and the two ways produce different kinds of music.

Group them 2 + 2 + 2 and you get three beats, each split in half. That is a waltz. Count one-and, two-and, three-and, and you are counting the tune of The Blue Danube, written by Johann Strauss II in 1866, where the bass note falls on beat one and two light chords answer on beats two and three.

Group the very same six notes 3 + 3 and you get two beats, each split into three. That is a jig, and it lopes rather than spins. Count one-and-a, two-and-a, and you are counting the traditional jig rhythm that fiddlers have played for three hundred years.

Identical note values. Identical number of eighth notes per bar. Completely different music. The thing that decides which one you are reading is the pair of numbers at the start of the piece, and that pair is the subject of this lesson.

What the two numbers say

A time signature is two numbers stacked at the left of the first staff, after the clef and key signature. It is not a fraction and there is no line between them.

• In a simple metre, the top number counts the beats in a bar and the bottom number names the note value that gets one beat. So 3/4 is three beats a bar, quarter note gets the beat.
• In a compound metre, the top number counts the divisions in a bar and the bottom number names the division note. So 6/8 holds six eighth-note divisions, which group into two beats of three.

That change of meaning between simple and compound is what catches people out, and it is worth saying slowly. In 3/4 the top number is a beat count. In 6/8 the top number is not a beat count; it counts the small notes. Nobody conducts six beats in a bar of 6/8 at ordinary speed. They conduct two.

The bottom number is written as the denominator of the fraction of a whole note: 2 means half note, 4 means quarter note, 8 means eighth note, 16 means sixteenth note.

Simple metre: beats that divide in two

If the beat splits naturally into two equal halves, the metre is simple. Three sizes cover nearly everything:

• Simple duple, two beats a bar: 2/4, 2/2. Marches live here. John Philip Sousa wrote The Stars and Stripes Forever in 1896 in 2/4, and you can feel the left-right of walking in it; the score is on IMSLP.
• Simple triple, three beats a bar: 3/4, 3/8, 3/2. Waltzes, minuets, and a great deal of folk song.
• Simple quadruple, four beats a bar: 4/4. The default of pop, rock, hip-hop, hymns and most of what you hear on any given day.

Compound metre: beats that divide in three

If the beat splits naturally into three, the metre is compound. The beat is then a dotted note, because only a dotted note divides into three.

• Compound duple, two beats a bar: 6/8. Jigs, barcarolles, and a great many ballads.
• Compound triple, three beats a bar: 9/8.
• Compound quadruple, four beats a bar: 12/8. Slow blues and doo-wop ballads almost all sit here, and so does the closing movement of "Spring" from Vivaldi's The Four Seasons, published in 1725. Put on a recording of that third movement, for instance the public-domain performance on Wikimedia Commons, and tap only the four slow beats while the strings rock in threes underneath. It is the clearest demonstration of compound quadruple you can get in twenty seconds.

The comparison, side by side

Read the row marked "Eighth notes per bar". Both 3/4 and 6/8 contain six. That is why the two look interchangeable on paper and are not interchangeable in the ear. Why this matters: metre is about grouping, not about arithmetic. Two bars can contain the same total duration and still be different bars, because the listener is told where the strong pulses land.

Counting compound metre out loud

The mistake almost everybody makes with 6/8 is counting six. Try it at speed and you will hear the music turn into a scramble. Count the beats instead and let the threes fill in underneath:

• 6/8 slow, for learning: 1 2 3, 4 5 6, with weight on 1 and 4.
• 6/8 at real speed: 1 and a, 2 and a, two beats only.
• 9/8: 1 and a, 2 and a, 3 and a.
• 12/8: 1 and a, 2 and a, 3 and a, 4 and a.

The syllables "and a" are doing the work here. In simple metre "and" splits a beat in two; in compound metre "and a" splits it in three. Once you can flip between saying "1 and 2 and" and "1 and a 2 and a" over the same metronome click, compound metre stops being strange.

How a conductor shows it

A conductor beats patterns in the air, and the pattern depends on the number of beats, not on whether the metre is simple or compound. Two beats a bar is a down-up motion; three is down, out to the side, up; four is down, across to the left, out to the right, up. So a conductor in 6/8 uses the same two-beat pattern as in 2/4, and the players supply the threes. Watch any orchestra on video with the sound off and count the shapes; you can usually name the metre before you hear a note.

Shorthand, pickups and the awkward metres

Two symbols survive from medieval notation. A large C means common time and is simply another way of writing 4/4. A C with a vertical line through it means cut time or alla breve, which is 2/2: the bar still holds four quarter notes but you feel two half-note beats, which is how fast marches are notated so the page does not fill with beams.

Many tunes do not start on beat one. A partial bar at the very beginning is an anacrusis, also called a pickup or upbeat. "Happy Birthday" is the standard example: the first syllable arrives before the bar line, on the last beat of an incomplete bar, and the word "birth" lands on a downbeat. When a piece has a pickup, the final bar is usually short by the same amount, so the two together make one complete bar.

Not everything is two, three or four. Gustav Holst wrote "Mars, the Bringer of War", the opening movement of The Planets, in 5/4 between 1914 and 1916, and the lurching, unbalanced pulse is the whole point of the piece. "Take Five", composed by Paul Desmond and recorded by the Dave Brubeck Quartet in 1959, is also in 5/4, and it became one of the best-selling jazz singles ever made, which tells you audiences adapt faster than people assume. Balkan dance traditions have used 7/8 and 11/8 for centuries. Count fives as 3 + 2 or 2 + 3, and sevens as 2 + 2 + 3, and they become easy.

Common misconceptions

• 6/8 is not "3/4 with faster notes". The two have different beat counts and different strong-beat placement. 6/8 has two beats; 3/4 has three.
• The top number is not always the beat count. In compound metres it counts divisions. Divide the top number by three to get the beats.
• The time signature is not a fraction. There is no line, and 4/4 does not equal 2/2 even though the arithmetic looks the same; the felt pulse differs.
• A bar line is not a breath mark. It marks where the strong beat falls. Plenty of phrases run straight across bar lines.
• Odd metres are not harder. They are unfamiliar. Grouped as 3 + 2 or 2 + 2 + 3 they are as countable as anything else.

Try it: identify and count

1. A piece is in 9/8. How many beats does the conductor show, and what note value gets a beat? Answer: three beats, each a dotted quarter note, since nine eighths group as 3 + 3 + 3.

2. A bar of 2/2 contains how many quarter notes, and how many beats do you feel? Answer: four quarter notes, but two beats, because the half note gets the beat.

3. You hear a tune where the bass plays on one strong pulse and the guitar strums two lighter chords after it, over and over. Simple or compound, and how many beats? Answer: simple triple, three beats a bar, almost certainly 3/4. That is the waltz accompaniment pattern.

4. A slow blues rocks in a long-short, long-short pattern with three small notes inside every beat. What time signature is it most likely written in? Answer: 12/8, compound quadruple, four beats each divided into three.

5. A song begins on the word "Should" before the first bar line. What is that partial bar called? Answer: an anacrusis, or pickup.

What to remember

The top number counts beats in simple metre and divisions in compound metre; the bottom number names the note value that unit stands for. Ask one question of any piece and the metre falls out: does the beat split into two or into three? Two means simple and the beat is an ordinary note value; three means compound and the beat is a dotted note.

Worth holding on to: the notes on the page do not by themselves tell you the metre. Six eighth notes are six eighth notes. The time signature is the composer telling you where to feel the weight, and that single instruction is the difference between a waltz and a jig. Next lesson keeps the metre fixed and starts fighting against it, which is where syncopation, ties and the backbeat come from.

Sources

1. Gotham, M., and Hamm, C. (n.d.). Simple meter and time signatures. In Open Music Theory (2nd ed.). VIVA Open Publishing. viva.pressbooks.pub
2. Gotham, M., and Hamm, C. (n.d.). Compound meter and time signatures. In Open Music Theory (2nd ed.). VIVA Open Publishing. viva.pressbooks.pub
3. musictheory.net. (n.d.). Simple and compound meter. musictheory.net
4. Hutchinson, R. (n.d.). Time signature. In Music Theory for the 21st-Century Classroom. University of Puget Sound. musictheory.pugetsound.edu

Sedalia, Missouri, 1899

A piano player named Scott Joplin walks into John Stark's music shop with a piece he has been playing at the Maple Leaf Club. Stark publishes it. Maple Leaf Rag goes on to sell in numbers no piano piece had managed before, and it does so because of one thing: the right hand keeps landing in the wrong place.

Joplin's left hand is metronomic, a plain 2/4 bass note and chord, bass note and chord. His right hand accents notes that fall between those beats. The result pulls against itself, and the pull is what made people buy the sheet music. Joplin recorded the piece himself on a piano roll in 1916; a transfer is on Wikimedia Commons. Put it on, tap the left hand's steady beat with one foot, and listen to how often the melody refuses to agree with your foot.

This lesson follows that disagreement forward, from Joplin's parlour piano to a snare drum on beats two and four to a sampled drum break, and it picks up the notation you need along the way: the dot, the tie, and the word syncopation.

The dot adds half again

A dot placed immediately after a notehead makes the note longer by half its own value. One rule, no exceptions.

A second dot adds half of the first dot's value again, so a double-dotted half note is 2 + 1 + 0.5, that is three and a half beats. Double dots turn up constantly in Baroque and Classical music and almost never in pop.

The dotted quarter followed by an eighth is the workhorse of the whole system. Count it as: clap on 1, hold through the and of 1 and through 2, clap on the and of 2. Written out, the two notes occupy beats 1 and 2 exactly, but the second clap lands off the beat, and that single displacement is responsible for an enormous amount of the music you like.

The tie adds durations together

A tie is a curved line joining two noteheads of the same pitch. You play once and hold for the sum. It exists because bar lines are inflexible: if a note needs to last from beat 4 of one bar into beat 1 of the next, there is no single symbol for that, so you write a quarter note tied to a quarter note across the bar line.

Ties also spell durations that no single symbol covers. Five eighth notes' worth of sound is written as a half note tied to an eighth. And ties are the standard way to notate syncopation, because tying a short note across a strong beat is exactly how you stop the strong beat from being struck.

Syncopation: hitting where the ear did not expect

In any metre some beats are strong and some are weak. In 4/4 the hierarchy runs: beat 1 strongest, beat 3 next, beats 2 and 4 weaker, and the "and" between beats weaker still. Syncopation is any deliberate contradiction of that hierarchy: an accent on a weak part, or a rest or tie where a strong beat should have been struck.

Read the red row carefully. Three claps across four beats: on beat 1, on the and of 2, and on beat 4. Beat 3, the second strongest beat in the bar, passes without an attack. The ear keeps counting to it anyway, and finds nothing there. That expectation, raised and then dodged, is the entire mechanism. Syncopation is not randomness; it works only because the listener is still keeping the straight beat in their head.

The core of it: a syncopated rhythm and the pulse it contradicts have to coexist. Take away the steady pulse and the syncopation disappears, because there is nothing left to be off. That is why Joplin's left hand never wavers.

The backbeat

Fifty years after Maple Leaf Rag, American rhythm and blues drummers settled on a new way to make the same point. Instead of accenting beats 1 and 3, the strong ones, the snare drum hits beats 2 and 4, every bar, without fail. That is the backbeat, and by the mid-1950s it was the default of popular music. When Bill Haley and His Comets released Rock Around the Clock in 1954, the backbeat was the engine of it, and it has been the engine of most of what followed.

A basic rock drum kit pattern in 4/4 stacks three layers:

Read the grid down rather than across and you can hear it: the hi-hat keeps the subdivision, the bass drum marks the strong beats, and the snare cracks on the weak ones. Clap this with a friend. One of you taps the bass drum on 1 and 3, the other claps the snare on 2 and 4. It will feel wrong for about fifteen seconds and then it will feel like every record you have ever heard.

Audiences at concerts in Europe are famous for clapping on 1 and 3 while the band plays on 2 and 4, which is a nice demonstration that the backbeat is learned, not natural.

One bar, five and a half seconds, and a thousand records

The thread runs into hip-hop through sampling. Two drum breaks in particular got reused more than any others. In 1969 a Washington band called The Winstons released a B-side called "Amen, Brother", in which drummer Gregory Coleman plays a four-bar unaccompanied break beginning about 1 minute 26 seconds in. That break, the Amen break, became the foundation of drum and bass and jungle, and it is one of the most reused recordings ever made.

In 1970 James Brown recorded Funky Drummer, in which Brown tells the band to drop out and lets Clyde Stubblefield play alone for a bar or two, around the five-and-a-quarter-minute mark. What Stubblefield plays is the backbeat with sixteenth-note ghost notes filling the gaps, and hundreds of hip-hop records are built on those seconds. Neither of these drummers was paid for the sampling, which is a genuine and unresolved injustice in the history of the music, and worth knowing about when you hear the word sample.

Swing: when eighth notes are not equal

One more thing the page cannot show you honestly. In jazz, blues and a lot of early rock, a pair of eighth notes is not played as two equal halves. The first is held longer and the second is clipped, roughly in a two-to-one relationship, as if the beat were divided into three with the first two thirds tied together. That is swing, and the ratio is not fixed: it is looser at slow tempos and flattens out towards even at very fast ones. Scores usually just say "swing" at the top and trust the player, which is a rare admission by notation that it has limits.

Common misconceptions

• Syncopation is not playing out of time. It requires the pulse to be rock steady underneath, otherwise there is nothing to push against.
• A dot does not add one beat. It adds half of whatever the note is worth, so a dotted half adds one beat and a dotted eighth adds a quarter of a beat.
• The backbeat is not the same as the beat. The pulse is still 1 2 3 4; the backbeat is an accent placed on the weak members of it.
• A tie is not a slur. Same pitch means tie and one attack; different pitches mean slur and a smooth connection between two attacks.
• Swing is not sloppiness. It is a consistent, learned uneven division, and a player who swings inconsistently sounds wrong to everyone in the room.

Clap these, then check

All in 4/4 at a slow 60 beats a minute, counting aloud.

1. dotted quarter, eighth, half. Answer: clap on 1, clap on the and of 2, clap on 3 and hold through 4. Three claps.

2. quarter, then an eighth tied to a quarter, then an eighth, then a quarter. Answer: clap on 1. Clap on 2 and hold that sound for a beat and a half, so it is still ringing when beat 3 goes by. Clap again on the and of 3, and once more on 4. Four claps at beats 1, 2, the and of 3, and 4. Beat 3 is never struck, which makes this the most syncopated bar in the set.

3. eighth rest, eighth, quarter, eighth rest, eighth, quarter. Answer: silence on 1, clap on the and of 1, clap on 2, silence on 3, clap on the and of 3, clap on 4. Four claps, and not one of them on beat 1 or beat 3.

4. dotted eighth, sixteenth, quarter, half. Answer: count 1 e and a. Clap on 1, clap on the a of 1, clap on 2, clap on 3 and hold through 4. That long-short opening is the dotted rhythm of a march.

5. Backbeat check: tap your foot on 1 2 3 4 and clap only on 2 and 4 for eight bars without drifting. Answer: if your claps start creeping towards 1 and 3, slow the metronome to 50 and try again. This is harder than it sounds and it is worth five minutes a day.

Where this leaves us

A dot lengthens a note by half again. A tie sums two durations of the same pitch and is the standard way to carry sound across a bar line. Syncopation puts weight where the metre did not ask for it, and it only exists in relation to a pulse the listener is still counting. The backbeat is a particular, hugely successful syncopation: the snare on 2 and 4, everywhere in popular music since the mid-1950s.

Bottom line: rhythm is a conversation between what the metre promises and what the player actually does. Joplin's right hand, a rock drummer's snare and a sampled break are three versions of one idea a century apart. You now have every rhythmic symbol you need for the rest of this course; from here on, the questions are about pitch, and the first of them is which seven notes a piece has chosen to use.

Sources

1. Hamm, C. (n.d.). Other rhythmic essentials. In Open Music Theory (2nd ed.). VIVA Open Publishing. viva.pressbooks.pub
2. Peterson, J., et al. (n.d.). Drumbeats. In Open Music Theory (2nd ed.). VIVA Open Publishing. viva.pressbooks.pub
3. musictheory.net. (n.d.). Dots and ties. musictheory.net
4. Hutchinson, R. (n.d.). Afterbeats and offbeats. In Music Theory for the 21st-Century Classroom. University of Puget Sound. musictheory.pugetsound.edu

Start on C, then start on G

Sit at a keyboard, or open a picture of one. Play the white keys from C up to the next C, eight notes, and stop. What you just played is the major scale, the sound behind most of the melodies you have known since you were small. The carol Joy to the World, in the tune Lowell Mason published in 1848, opens with that scale played straight downward from top to bottom; sing the first line and you are singing all eight notes in order.

Now do the same thing starting on G. Play the white keys G A B C D E F G. Something goes wrong at the seventh note. Instead of leaning into the final G the way the C scale leaned into its C, the F sits there flat-footed and the ending sounds unfinished, almost medieval. Nothing is broken; you have simply produced a different pattern of distances. This lesson is about the pattern, why it must be preserved, and what has to be added to preserve it.

The pattern, measured in steps

Go back to the C scale and measure the gap between each note and the next, using the half steps and whole steps from Lesson 2. Remember that E to F and B to C have no black key between them, so those two gaps are half steps.

Written out: whole, whole, half, whole, whole, whole, half. That seven-gap pattern is the major scale. C major is not special; it is simply the one place on the keyboard where the pattern happens to use only white keys, which is an accident of how keyboards are built, not a fact about music.

Now redo G with the pattern in hand. G to A whole, A to B whole, B to C half, C to D whole, D to E whole, E to F is only a half step and the pattern demands a whole one. So raise it: F sharp. Then F sharp to G is a half step, exactly as required. G major is G A B C D E F sharp G, and the leaning, finished sound returns.

Try F the same way. F to G whole, G to A whole, A to B is a whole step but the pattern wants a half, so lower it: B flat. Carry on and F major comes out as F G A B flat C D E F.

So what?: you never have to memorise which notes are in a key. You need one pattern and the ability to count half steps on a keyboard. Every one of the fifteen major key signatures falls out of that.

Key signatures: doing it once instead of every bar

Writing a sharp in front of every F in a piece in G major would be absurd, so the sharps are collected at the start of every staff, immediately after the clef. That collection is the key signature, and it applies to every octave, for the whole piece, until cancelled.

Sharps always appear in the same order, and so do flats:

• Order of sharps: F C G D A E B. Remember it with Father Charles Goes Down And Ends Battle.
• Order of flats: B E A D G C F. That is the sharps list backwards, and the first four spell the word BEAD.

The order is not arbitrary. Each new sharp is a fifth above the last; each new flat is a fifth below. A key signature with three sharps therefore always has F sharp, C sharp and G sharp, in that order, in those positions on the staff. There is no such thing as a key signature with only C sharp.

Two shortcuts let you name a key in a second:

• Sharps: look at the last sharp and go up one half step. Last sharp F sharp means G major. Last sharp C sharp means D major. Last sharp G sharp means A major.
• Flats: look at the second-to-last flat and that is the key. Two flats, B flat and E flat: the second-to-last is B flat, so B flat major. The only one to memorise is a single flat, which is F major.

The circle of fifths

Arrange the keys so that each step clockwise moves up a perfect fifth and you get the circle of fifths, the single most useful diagram in music.

Read it clockwise from C: C has nothing, G has one sharp, D has two, A three, E four, B five, F sharp six. Read it anticlockwise: F has one flat, B flat two, E flat three, A flat four, D flat five. At the bottom the two directions meet, which is why F sharp major with six sharps and G flat major with six flats are the same set of piano keys spelled two ways. Those are enharmonic keys, and which spelling a composer picks depends on what the players will find easier to read.

Adjacent keys on the circle differ by exactly one accidental, which is why modulating to the neighbouring key is the smoothest move in tonal music and why guitarists, who think in shapes, still tend to write in E, A, D and G.

The seven degrees have names, and the names describe jobs

Each note of the scale is a scale degree with a number and a traditional name. The names are worth learning now because the harmony lessons use them constantly.

The leading tone explains the failed G scale at the start of the lesson. In C major, B to C is a half step, and a half step below home feels like an unfinished sentence demanding its last word. In the white-key scale on G, the seventh note F sits a whole step below G, too far away to lean, so the scale does not resolve. Raising it to F sharp restores the half step and restores the pull.

Listening for a key

Put on the Prelude No. 1 in C major from Bach's Well-Tempered Clavier, Book 1, finished in 1722. The whole piece is broken chords, one per bar, and the first bar is nothing but C, E, G and C. You can hear the key established in about four seconds. The score is at IMSLP, and it is worth looking at even if you cannot yet read it fluently, because the shape of the notes on the page is so regular that you can see the harmony change.

Then try this on any song you like. Hum along until you find the note that feels like the end, the one you could hold forever and be satisfied. That note is the tonic. If the third note of the scale above it sounds bright, you are in a major key; if it sounds shadowed, you are in a minor key, which is where the next lesson goes.

Common misconceptions

• C major is not "the scale with no pattern". It has exactly the same pattern as every other major scale. It just happens to need no black keys.
• A key signature of one sharp does not mean "one sharp anywhere". It always means F sharp, because sharps are added in a fixed order.
• Sharps in the key signature are not accidentals. They apply for the whole piece and in every octave, not just for one bar.
• A piece in G major is not "C major with an F sharp". It has a different home note, so every degree has a different function even though six of the seven letters are shared.
• The circle of fifths is not a memory trick. It is a picture of a real fact: keys a fifth apart share six of their seven notes.

Try it: build and name

1. Build D major using the pattern. Answer: D, E, F sharp, G, A, B, C sharp, D. Whole, whole, half, whole, whole, whole, half. Two sharps, which matches the circle.

2. A piece has three sharps in the key signature. Name them in order and name the major key. Answer: F sharp, C sharp, G sharp. Last sharp G sharp, up a half step gives A major.

3. A piece has four flats. Name them and name the key. Answer: B flat, E flat, A flat, D flat. Second-to-last is A flat, so A flat major.

4. Build E flat major. Answer: E flat, F, G, A flat, B flat, C, D, E flat. Three flats, which matches the circle.

5. Which degree of B flat major is F, and what is it called? Answer: the fifth, the dominant. Counting B flat, C, D, E flat, F gives five.

The short version

One pattern of gaps, whole whole half whole whole whole half, generates every major scale from any starting note. Preserving that pattern on a starting note other than C forces you to add sharps or flats, and those additions are collected into a key signature at the front of the staff, always in a fixed order. The circle of fifths lays out all fifteen signatures so that neighbours differ by one accidental.

The point: a key is not a list of notes to memorise. It is a home note plus a fixed set of distances from it, and the seven degrees each have a job that stays the same whichever key you are in. That portability is why a song can be transposed for a singer with a different range and still sound like itself, and it is the reason the Roman numerals in Module 4 work at all.

Sources

1. Hamm, C. (n.d.). Major scales, scale degrees, and key signatures. In Open Music Theory (2nd ed.). VIVA Open Publishing. viva.pressbooks.pub
2. musictheory.net. (n.d.). The major scale. musictheory.net
3. musictheory.net. (n.d.). Key signatures. musictheory.net
4. Hutchinson, R. (n.d.). The circle of fifths. In Music Theory for the 21st-Century Classroom. University of Puget Sound. musictheory.pugetsound.edu

Same seven notes, two different homes

Play the white keys from C up to C. Bright, settled, the sound of a hymn. Now play the exact same seven white keys, but start and finish on A: A B C D E F G A. Nothing has been added or removed, yet the second scale sounds shadowed and unresolved in a way the first does not.

That should be startling. If a key were just a list of notes, these two would be the same key. They are not, because a key is a list of notes plus a home, and moving the home moves every half step relative to it. In C major the half steps land between degrees 3 and 4 and between 7 and 8. In the A scale they land between degrees 2 and 3 and between 5 and 6, which produces a completely different set of tensions.

This lesson compares five scales that are all built by changing which notes get used and where the half steps fall: three minors, the pentatonic, and the blues scale. Keep the table at the end in view as you read; the whole lesson is that table.

Natural minor

The scale you just played from A is the natural minor, and its step pattern is whole, half, whole, whole, half, whole, whole. Compared with major, three degrees are lowered by a half step: the third, the sixth and the seventh. Musicians write that as 1, 2, flat 3, 4, 5, flat 6, flat 7.

The lowered third is the one that does the heavy lifting. It is the reason a minor chord sounds darker than a major one, and if you play a C major triad and then lower only the E to E flat, you can hear the entire mood of the chord change on one finger.

Relative minor: the same key signature, a different home

Because A minor uses the same seven notes as C major, the two share a key signature of no sharps and no flats. A pair like that is called relative: A minor is the relative minor of C major, and C major is the relative major of A minor.

Finding it is arithmetic. The relative minor starts on the sixth degree of the major scale, which is the same as three half steps below the major tonic. So:

This means a key signature is ambiguous on its own. Two sharps could be D major or B minor, and you decide which by looking at the music: which note does the bass keep returning to, and which chord ends the phrases?

Parallel minor: the same home, a different signature

The other relationship is parallel: same tonic, different quality. C major and C minor are parallel keys. C minor has three flats, so the two do not share a signature at all, but they do share a home note, which is why a songwriter can slip from one to the other mid-song and the music still feels anchored.

Key idea: relative keys share a key signature and differ in tonic; parallel keys share a tonic and differ in key signature. Confusing the two is the single most common error in this part of the course, and it happens because both relationships are described with the word minor.

The leading tone problem

Natural minor has a weakness. Its seventh degree sits a whole step below the tonic: in A minor, G to A. As you saw last lesson, a whole step below home does not lean. Composers writing tonal music wanted the half-step pull, so they raised the seventh by hand.

Raise G to G sharp and you get the harmonic minor: A B C D E F G sharp A. The name is a clue. The alteration exists to serve the harmony, because it turns the chord built on the fifth degree into a major chord with a proper leading tone, which is what makes a minor-key cadence sound conclusive.

The fix creates a new problem. Between F and G sharp there is now a step of three half steps, an augmented second, which is a strange interval to sing. That gap is the exotic, slightly Eastern sound you hear in klezmer, in flamenco, and in the last movement of Mozart's Piano Sonata K. 331, the movement usually called the Rondo alla turca, whose score is on IMSLP.

Melodic minor, and why it changes direction

To keep the leading tone and get rid of the awkward gap, raise the sixth degree as well. That is the melodic minor, and in classical practice it does something no other scale does: it is different going up and coming down.

• Ascending: A B C D E F sharp G sharp A. Raised 6 and raised 7, smooth all the way up.
• Descending: A G F E D C B A. Back to plain natural minor.

The logic is about where the line is going. On the way up, the melody is heading for the tonic and wants the pull. On the way down it is leaving, and the raised notes would pull the wrong way, so they are dropped. Jazz players use a different convention, keeping the raised sixth and seventh in both directions, and call it the jazz melodic minor.

The three minors, side by side

In real music these are not three separate scales so much as one minor key with movable sixth and seventh degrees, chosen bar by bar. Open any page of minor-key music and you will find both G and G sharp within a few bars of each other.

For a minor key at full strength, listen to the second movement of Beethoven's Symphony No. 7, premiered in 1813. It is in A minor, it begins with one repeated chord, and the theme that follows is little more than a rhythm walking through the notes of the scale. Within thirty seconds you can hear how much weight a lowered third carries.

Five notes instead of seven

Now take notes away. A pentatonic scale has five notes per octave instead of seven, and it appears independently in folk traditions on every continent, which suggests it is doing something fundamental rather than being a local taste.

• Major pentatonic: degrees 1, 2, 3, 5, 6. In C: C D E G A. It is the major scale with the fourth and seventh removed, and those are exactly the two notes that create the strongest dissonances, which is why nothing you play in a pentatonic scale sounds wrong.
• Minor pentatonic: degrees 1, flat 3, 4, 5, flat 7. In A: A C D E G. Note that this contains the same five pitches as C major pentatonic, just with a different home. Relative keys again.

Two examples you already know. The hymn tune Amazing Grace, in the melody called New Britain published in 1835, uses only five notes from beginning to end. So does Auld Lang Syne. Sing either one and count the different pitches; you will not get past five. And if there is a piano nearby, play only black keys, in any order, at any speed. You cannot produce a wrong note, because the five black keys are a pentatonic scale.

The blues scale and the notes between the keys

Take the minor pentatonic and add one note, the lowered fifth, and you have the blues scale. On A: A C D E flat E G. That added E flat is the most famous passing note in popular music, and guitarists learn the shape before they learn anything else.

But the scale is a simplification of something a keyboard cannot do. The blue notes of African American vocal and instrumental traditions are not fixed pitches; they are the third, fifth and seventh degrees sung or bent somewhere between the major and minor versions. A singer slides through the space a piano has to skip over. A guitarist bends a string a quarter of the way to the next fret. Writing the blues scale on a staff captures the outline and loses the thing itself, which is worth remembering whenever notation is described as a complete record of music.

Common misconceptions

• Minor does not mean sad. It is a set of intervals, not an emotion. Plenty of dance music is in minor keys, and plenty of genuinely bleak music is in major.
• Relative and parallel are not the same relationship. C major and A minor are relative, sharing a signature; C major and C minor are parallel, sharing a tonic.
• Harmonic minor is not "the main one". It is an adjustment made for cadences. Most minor-key melodies mix all three forms.
• Pentatonic is not a beginner's scale. It is the backbone of Scottish, Chinese, West African and Appalachian traditions and of most rock guitar solos ever recorded.
• The blues scale is not the blues. The bent, in-between pitches that define the style cannot be written with the twelve keys of a keyboard, and the scale is only an approximation of them.

Try it: build and identify

1. Write E natural minor. Answer: E F sharp G A B C D E. It shares one sharp with G major, its relative major.

2. Write D harmonic minor and name the awkward interval. Answer: D E F G A B flat C sharp D. The gap from B flat to C sharp is an augmented second, three half steps.

3. A piece has three flats and keeps ending on C. Major or minor, and which key? Answer: C minor. Three flats is E flat major or its relative, C minor, and the ending decides it.

4. Name the five notes of G major pentatonic, and say which minor pentatonic uses the same five. Answer: G A B D E. The same five notes make E minor pentatonic.

5. Build the C blues scale. Answer: C E flat F G flat G B flat C. Minor pentatonic on C plus the lowered fifth.

Looking back

Minor is not one scale but a key with a lowered third and two flexible degrees at the top. Natural minor is what the key signature gives you. Harmonic minor raises the seventh to manufacture a leading tone for cadences and pays for it with an augmented second. Melodic minor raises the sixth as well on the way up and reverts on the way down. Pentatonic scales remove the two most collision-prone degrees and turn up everywhere on earth. The blues scale adds a lowered fifth to minor pentatonic and gestures at pitches that live between the keys.

Why this matters: every one of these scales is the same idea applied differently, which is choosing where the half steps go and which degrees you are willing to leave out. Once you hear a scale as a pattern of distances rather than a list of letters, you can build any of them on any note, and you can recognise which one a song is using by listening for the third and the seventh. Next lesson measures those distances one at a time and gives each one a name.

Sources

1. Hamm, C. (n.d.). Minor scales, scale degrees, and key signatures. In Open Music Theory (2nd ed.). VIVA Open Publishing. viva.pressbooks.pub
2. Duker, P., et al. (n.d.). Blues melodies and the blues scale. In Open Music Theory (2nd ed.). VIVA Open Publishing. viva.pressbooks.pub
3. musictheory.net. (n.d.). The minor scales. musictheory.net
4. Hutchinson, R. (n.d.). Minor scales. In Music Theory for the 21st-Century Classroom. University of Puget Sound. musictheory.pugetsound.edu

Two students, the same count, two different sounds

Ask a student how far it is from C up to E. They count C, D, E and say three. Ask another how far it is from C up to E flat. They count C, D, E flat and also say three. Both counts are correct. Play the two on a keyboard one after the other and they are obviously not the same distance: the first is the bright opening leap of When the Saints Go Marching In, the second is the sound the same melody would make in a minor key.

So counting letter names cannot be the whole story, and yet it is clearly part of it. This is the problem interval naming solves, and it solves it by giving every interval two pieces of information rather than one: a number, which comes from the letter names, and a quality, which comes from the half steps.

Step one: the number

Count the letter names from the lower note to the upper note, including both ends. C to E includes C, D, E, so it is a third. C to G includes C, D, E, F, G, so it is a fifth. C to C is a first, called a unison, and C up to the next C is an eighth, called an octave.

On the staff this is even quicker, because you are counting lines and spaces rather than letters. Two notes both on lines with one line between them make a fifth. A note on a line and the next note in the space directly above make a second. Accidentals never change the number: C to E flat and C to E sharp are both thirds, because the letters C, D, E are the same either way.

The short line under each pair marks the ledger line for middle C. Count the positions with your eye: three positions for the third, five for the fifth, eight for the octave.

Step two: the quality

Quality answers the question the number cannot: how many half steps is it actually? Intervals come in two families, and which family an interval belongs to depends only on its number.

• Perfect intervals: unison, fourth, fifth, octave. These are the ones with simple harmonic ratios, and they get the name perfect because they sound stable and hollow rather than sweet.
• Major and minor intervals: seconds, thirds, sixths, sevenths. A minor interval is exactly one half step smaller than the major one of the same number.

There is no such thing as a major fifth or a perfect third. If you catch yourself writing one, you have mixed the families.

The table worth memorising

Count the half steps from the lower note and read off the name. This is the single most useful table in the module.

A useful cross-check: every interval formed between the tonic and another note of a major scale is either perfect or major. So if you can build the major scale on the lower note, you can name any interval without counting half steps at all. Is D up to B a major or minor sixth? Build D major: D E F sharp G A B C sharp. B is in it, so D to B is a major sixth. Is D up to B flat? One half step smaller, so a minor sixth.

The upshot: the major scale is an interval ruler. Anything found in the scale above the tonic is major or perfect; anything a half step smaller is minor or diminished.

Augmented and diminished

Two more qualities extend the system at the edges.

• Augmented is one half step wider than perfect or major. C to G sharp is an augmented fifth; C to D sharp is an augmented second, the interval you met in harmonic minor.
• Diminished is one half step narrower than perfect or minor. C to G flat is a diminished fifth; C to B double flat is a diminished seventh.

The spelling matters. C to D sharp and C to E flat are the same two keys on a piano, yet one is an augmented second and the other a minor third, and they behave differently: a D sharp is on its way up to E, while an E flat is likely to fall to D. Notation records intention as well as sound.

The tritone

Six half steps splits the octave exactly in half, and the interval has two names depending on spelling: an augmented fourth (C to F sharp) or a diminished fifth (C to G flat). Either way, musicians call it the tritone, because it spans three whole tones.

It is the most unstable interval in the system and it is everywhere. It sits inside every dominant seventh chord, which is why that chord pushes so hard towards resolution. It opens the theme of The Simpsons, written by Danny Elfman in 1989, whose first two notes are a tritone apart. Leonard Bernstein built the song Maria in West Side Story of 1957 on a rising tritone that then resolves upward by a half step, which is why the phrase feels like it is straining and then arriving.

Inversion halves the work

Turn an interval upside down by moving the lower note up an octave. C up to E, a major third, becomes E up to C, which is a minor sixth. That is not a coincidence, and the rule has two halves:

• The two numbers always add up to nine. Third and sixth, second and seventh, fourth and fifth, unison and octave.
• Quality flips: major becomes minor, minor becomes major, augmented becomes diminished, diminished becomes augmented. Perfect stays perfect.

Remember: learn the small intervals thoroughly and you get the large ones free. If you know that C to E is a major third, you know without further counting that E to C is a minor sixth, and that is exactly half the table you no longer have to memorise.

Intervals wider than an octave are compound. An octave plus a second is a ninth, octave plus a third a tenth, and so on. Subtract seven to get the simple interval underneath: a thirteenth is a sixth plus an octave. Jazz chord symbols use those larger numbers constantly.

Hearing them: one song per interval

The fastest way to identify intervals by ear is to attach each one to the opening leap of a melody you already know, then sing the first two notes of that melody whenever you hear the interval. Sing these out loud now, and check each against a keyboard.

Two warnings about this method. It works only for ascending intervals unless you build a second list for descending ones, and it is a crutch you should eventually drop: experienced musicians hear an interval as a size, not as a song. Use the list for a term, then start testing yourself without it, which is what the free drill at musictheory.net is for.

Common misconceptions

• Counting notes is not counting half steps. The number comes from letter names inclusive; the quality comes from half steps. You need both.
• There is no major fourth. Unisons, fourths, fifths and octaves are perfect; seconds, thirds, sixths and sevenths are major or minor.
• An augmented second and a minor third are not the same interval. They sound alike on a piano and are spelled differently because they come from different places and go to different places.
• The tritone was not banned by the medieval church. The old teaching phrase about the devil in music was a rule of thumb about awkward melodic writing, not a legal prohibition, and the story that singers were punished for it is a modern invention.
• Inversion does not mean playing backwards. It means moving the lower note up an octave, or the upper note down one.

Try it: name and invert

1. Name the interval from F up to C. Answer: F, G, A, B, C is five letters, so a fifth; F major contains C, so it is perfect. A perfect fifth, seven half steps.

2. Name the interval from E flat up to C. Answer: six letters, a sixth. E flat major contains C, so it is major. A major sixth, nine half steps.

3. Name the interval from B up to F. Answer: five letters, a fifth. B major contains F sharp, and F is a half step lower, so it is a diminished fifth: six half steps, the tritone.

4. Invert a minor seventh. What do you get? Answer: a major second. Seven and two add to nine, and minor flips to major.

5. Name the interval from D up to F sharp, then say what it becomes when inverted. Answer: a major third; inverted it becomes a minor sixth.

Pulling it together

Every interval gets two labels. The number is the count of letter names, inclusive, and accidentals never alter it. The quality is the count of half steps, and it belongs to one of two families: perfect for unisons, fourths, fifths and octaves, major or minor for the rest, with augmented and diminished at the edges. The major scale on the lower note is the fastest ruler there is. Inversion gives you the second half of the table free, because the numbers sum to nine and the quality flips.

Intervals are the last thing you need before harmony makes sense, because a chord is nothing but a stack of intervals chosen on purpose. Stack a major third and then a minor third and you get a major chord; swap their order and you get a minor one. That is the whole of the next lesson, and you have just built the tools for it.

Sources

1. Hamm, C., and Gotham, M. (n.d.). Intervals. In Open Music Theory (2nd ed.). VIVA Open Publishing. viva.pressbooks.pub
2. musictheory.net. (n.d.). Generic intervals. musictheory.net
3. musictheory.net. (n.d.). Specific intervals. musictheory.net
4. Hutchinson, R. (n.d.). How to identify intervals. In Music Theory for the 21st-Century Classroom. University of Puget Sound. musictheory.pugetsound.edu

One finger changes everything

Put your right hand on a keyboard and play C, E and G together. That is a C major chord, and it sounds open and settled. Now move only the middle finger, the E, down one key to E flat, and play the three notes again. The bottom and top notes have not moved. One finger has travelled one half step, and the chord has gone from bright to shadowed.

That is the whole of chord quality in one gesture. A chord is a set of pitches sounded together, and the distance between them decides how it feels. This lesson builds chords systematically: first three notes, then four, then the same notes rearranged, and finally a labelling system that describes a chord's job rather than its letter name.

How a triad is built: stack two thirds

A triad is three notes stacked in thirds. Start on any note, skip the next letter, take the one after, skip again, take the next. From C: C, skip D, take E, skip F, take G. The three notes are named from the bottom up:

• the root, which gives the chord its letter name;
• the third, which decides major or minor;
• the fifth, which mostly just confirms the root.

On a staff, a root-position triad is unmistakable: three noteheads all on lines, or all in spaces, like a small snowman.

The four triad qualities

Measure the two stacked thirds in half steps and four possibilities appear. That is all there are.

Major and minor differ only in the order of the two thirds, which is why one finger flips them. Diminished contains the tritone from the last lesson, which is why it will not sit still. Augmented divides the octave into three equal parts and therefore has no clear root at all; Franz Liszt opened his Faust Symphony of 1857 with a theme spun entirely from augmented triads, precisely because the listener cannot tell where home is.

Chord symbols: what a lead sheet actually says

Above the staff of a song you will find letters rather than Roman numerals. This is the lead sheet system used by guitarists, pianists and every band that has ever busked.

• C means C major. A bare letter always means major.
• Cm or Cmin means C minor.
• Cdim means diminished; Caug or C+ means augmented.
• C/E is a slash chord: play a C chord but put E in the bass.

Seventh chords: add one more third

Keep stacking. Add a fourth note a third above the fifth and you have a seventh chord, so called because that top note is a seventh above the root. Five types cover almost everything you will meet.

The dominant seventh deserves special attention because it drives tonal music. Inside C7 sit E and B flat, which are a tritone apart. That tritone is unstable, and it resolves most naturally by both notes moving a half step inward, E up to F and B flat down to A. Those two notes belong to an F chord, which is why C7 pulls so hard towards F.

The fully diminished seventh is the one that sounds like a silent film. Beethoven uses one within the first few bars of the Pathetique Sonata, Op. 13, of 1798, and the score is on IMSLP if you want to see it written down. Because it is built from four equal minor thirds, it can resolve to several different keys, which makes it the most useful hinge in nineteenth-century harmony.

Inversions: the same chord, a different bottom note

A chord's identity comes from which notes are in it, not from which one is lowest. Rearranging them gives an inversion.

A seventh chord has one more option, third inversion, with the seventh in the bass. The little numbers, called figured bass, started life in the seventeenth century as shorthand telling a keyboard player what to improvise above a written bass line, and they survived into modern analysis. The numbers are intervals above the bass: in E G C, the C is a sixth above E, hence the figure 6.

Inversions matter because the bass line is a melody too. A progression whose bass walks smoothly by step sounds completely different from one whose bass jumps by fifths, even if the chords above are identical. What matters here: choosing an inversion is choosing a bass note, and the bass note is what the ear tracks most closely after the tune itself.

Roman numerals: naming a chord by its job

Roman numeral analysis labels a chord by which scale degree it is built on, so the label stays the same when the music is transposed. The conventions:

• Upper case for a major triad: I, IV, V.
• Lower case for a minor triad: ii, iii, vi.
• Lower case with a small circle after it for diminished, usually written vii in analysis and read as "seven diminished".
• Upper case with a plus sign for augmented.
• A 7 after the numeral for a seventh chord: V7.
• Figures for inversions: V6 is a dominant chord in first inversion.

The seven chords of a major key

Build a triad on each degree of a major scale, using only notes of that scale, and the qualities come out in a fixed order that is the same in every major key.

Memorise the pattern rather than the letters: major, minor, minor, major, major, minor, diminished. It never varies. Notice that C major and G major share four of the same chords, which is the circle of fifths showing up again.

In a minor key the qualities shift, because the scale has different degrees. In natural minor: i, ii diminished, III, iv, v, VI, VII. But composers almost always raise the seventh degree to get a leading tone, which turns the v into a major V and gives minor-key cadences their bite. So in practice you will see a major V in a minor key far more often than a minor one, and the raised note is written in as an accidental because the key signature does not supply it.

Common misconceptions

• A chord is not defined by its lowest note. E G C is still a C chord, in first inversion, because C is the root of the stack of thirds.
• Upper and lower case Roman numerals are not a typing accident. Case carries the quality, so writing V and v in the same analysis means two different chords.
• C7 is not "C major seventh". C7 is the dominant seventh with B flat; Cmaj7 has B natural. The two are a half step apart and sound nothing alike.
• Diminished is not just "very minor". Its fifth is lowered as well as its third, and the resulting tritone makes it unstable rather than merely dark.
• Roman numerals are not a key-specific code. The point of them is that V means the same thing in every key, which is exactly what letter names cannot do.

Try it: build, name, invert

1. Spell a D major triad and a D minor triad. Answer: D F sharp A, and D F A. Only the third changes.

2. Spell G7 and name the tritone inside it. Answer: G B D F. The tritone is B to F, and it resolves inward to C and E, which is why G7 leads to C.

3. Name the chord spelled A C E flat. Answer: A diminished. Two stacked minor thirds, A to C and C to E flat.

4. A bass plays E while the band plays C, E and G. What is the chord and its inversion? Answer: C major in first inversion, written C/E, figured 6.

5. In the key of F major, what chord is vi, and what quality is it? Answer: D minor. The sixth degree of F major is D, and the sixth chord is always minor.

6. In the key of A minor, which chord is usually altered and why? Answer: the chord on the fifth degree. E minor becomes E major by raising G to G sharp, supplying the leading tone that makes the cadence pull home.

What you now know

Triads are two stacked thirds, and the order of those thirds gives four qualities: major, minor, diminished, augmented. A fifth note-name away sits the seventh, giving five common four-note chords, of which the dominant seventh is the engine of tonal music because of the tritone locked inside it. Inversions rearrange the same notes and change the bass line without changing the chord. Roman numerals name each chord by the scale degree it grows from, which is what makes a progression portable between keys.

The core of it: you now have the vocabulary but not yet the grammar. Knowing that C major contains I, ii, iii, IV, V, vi and a diminished seventh chord tells you nothing about which order they go in or why some orders sound finished and others do not. That is the next lesson, and it is where theory starts to explain songs you already know.

Sources

1. Peterson, J., et al. (n.d.). Triads. In Open Music Theory (2nd ed.). VIVA Open Publishing. viva.pressbooks.pub
2. Peterson, J., et al. (n.d.). Seventh chords. In Open Music Theory (2nd ed.). VIVA Open Publishing. viva.pressbooks.pub
3. musictheory.net. (n.d.). Introduction to chords. musictheory.net
4. Hutchinson, R. (n.d.). Roman numeral chord symbols. In Music Theory for the 21st-Century Classroom. University of Puget Sound. musictheory.pugetsound.edu

A railway platform in Mississippi, about 1903

A bandleader named W. C. Handy is asleep on a bench at Tutwiler station, waiting for a train that is nine hours late. He wakes to a man beside him playing a guitar with the back of a knife blade pressed against the strings, sliding between the notes, singing one line about a railway junction and then singing it again. Handy later wrote that it was the weirdest music he had ever heard.

Within a decade Handy had published The Memphis Blues in 1912 and St. Louis Blues in 1914, and the twelve-bar form had a printed shape that any band in the country could read. That form uses three chords. Not three chords out of laziness; three chords because those three do the three things harmony can do. This lesson is about those jobs, about how a phrase ends, and about the handful of chord loops that turn out to be behind an enormous amount of the music you know.

Three jobs a chord can hold

Every chord in a key belongs to one of three functional families. This idea is doing more work than any other in tonal music, so it is worth stating plainly.

Music of this kind moves left to right across that table and then jumps back: tonic, predominant, dominant, tonic. Going backwards, from dominant to predominant, sounds odd in classical style precisely because it undoes the setup, although rock and blues do it constantly and it is one of the ways those styles announce that they are not classical.

I, IV and V, and why three chords are enough

Take C major. I is C, IV is F, V is G. Between them these three contain every note of the scale: C E G, F A C, G B D. That is the practical reason a guitarist with three chords can accompany most folk songs, most hymns and most early rock and roll. Any melody note in the key will belong to at least one of them.

Add the seventh to the dominant, making G7, and the pull sharpens. As you saw last lesson, G7 contains B and F, a tritone, which resolves inward to C and E. The blues then does something almost perverse: it puts a seventh on every chord, so C7, F7 and G7 all appear. In classical terms that should be unbearable tension with no release. In blues it is simply the colour of the style, and it is one of the clearest cases of a tradition taking a rule and using it as a texture instead.

The twelve-bar blues

Here is the form Handy printed, in C. Each cell is one bar of four beats.

Read it as three four-bar lines, because that is what the words do: a line, the same line again, and a third line that answers them. The harmony matches that shape. Line one stays home. Line two moves to IV and comes back, so the repeated words arrive over a new chord. Line three brings in V, the strongest chord, for the punchline, and then the last bar goes back to V to push the whole thing round again. That last bar is called the turnaround.

Variants are everywhere. The "quick change" puts IV in bar 2. Jazz replaces bar 9 with ii and bar 10 with V. Chuck Berry built Johnny B. Goode on this grid in 1958 and changed almost nothing about it. In short: if you learn one chord progression in your life, learn this one, because it will let you sit in with strangers in any country on earth.

The four cadences

A cadence is how a phrase ends, and it works exactly like punctuation: some endings are full stops, some are commas, one is a question mark and one is a joke.

The half cadence is the one that changes how you hear whole pieces once you notice it. Melodies are usually built in pairs of phrases: the first stops on the dominant and sounds like a question, the second returns to the tonic and sounds like the answer. Sing the first eight bars of the Ode to Joy tune from Beethoven's Ninth Symphony, finished in 1824, and stop halfway. The stopping point feels wrong, and it feels wrong because the harmony underneath has landed on V and is waiting.

The deceptive cadence is a composer's way of saying "not yet". The listener hears the dominant, braces for the tonic, and gets the relative minor instead, which shares two of the tonic chord's three notes and so is close enough to feel like a near miss rather than a mistake.

ii-V-I, the sentence jazz is written in

Take the functional table and pick the strongest member of each family: ii for predominant, V for dominant, I for tonic. That gives ii-V-I, and in jazz it is played with sevenths: in C, that is Dm7, G7, Cmaj7.

Look at what the bass does: D, G, C. Each root falls a perfect fifth, which is the strongest root movement there is. Then look at the inner voices: the note F is in Dm7 and in G7, then slides a half step to E in Cmaj7; the note C is in Dm7, becomes B in G7, and returns. Very little moves, and what moves, moves by a half step. That economy is why the progression sounds inevitable rather than arbitrary. The standard Autumn Leaves, written in 1945, opens with two of them back to back and is the tune every young jazz musician learns first for exactly that reason.

The loops behind an enormous number of songs

Pop and rock mostly do not cadence in the classical sense. They loop. A four-chord pattern repeats under everything, and the sense of arrival comes from the melody and the arrangement rather than from the harmony stopping.

The I-V-vi-IV loop is the famous one, and a comedy group called The Axis of Awesome made a well-known routine in 2009 out of singing dozens of hits over it without changing chords. The interesting question is not why so many songs share it, but why it works: it contains all three functions, it ends on a predominant which leads straight back to the start, and it never fully closes, so the loop can run forever.

Common misconceptions

• A cadence is not the last chord. It is the last two, because what matters is the motion into the ending, not the ending alone.
• The twelve-bar blues is not always twelve bars of the same thing. Its shape is three four-bar lines with a specific harmonic plan, and the variants are part of the form, not departures from it.
• A plagal cadence is not a weak authentic cadence. It is a different motion, IV to I, without the leading tone, which is why it sounds settled rather than driven.
• Songs sharing a progression are not copies of each other. Chord sequences are common property; melody, lyric, rhythm and arrangement are what make a song a song.
• Seventh chords on every degree do not mean the blues is unresolved. The style redefines those chords as stable, which is a real historical change rather than a mistake.

Try it: label and predict

1. In G major, name the chords I, IV and V. Answer: G major, C major and D major.

2. A phrase ends on the chords D major then G major, in the key of G. What cadence is it? Answer: an authentic cadence, V to I; if both are in root position with G on top, perfect authentic.

3. A phrase in C major ends on a G major chord and feels unfinished. Name the cadence. Answer: a half cadence, ending on V.

4. Write the twelve-bar blues in G. Answer: G7 G7 G7 G7, C7 C7 G7 G7, D7 C7 G7 D7.

5. A song in F major plays C7 and then lands on D minor. What happened, and why does it not sound like an error? Answer: a deceptive cadence, V to vi. D minor shares the notes F and A with the F major chord, so it is a near miss rather than a wrong turn.

6. Name the ii-V-I in the key of B flat, with sevenths. Answer: Cm7, F7, B flat major seventh.

The takeaway

Chords have jobs. Tonic is home, predominant leaves it, dominant demands a return, and nearly all tonal music is that cycle run at different speeds. Cadences are the punctuation: authentic is a full stop, half is a question mark, plagal is a quiet close and deceptive is a delayed arrival. The twelve-bar blues organises three chords into three four-bar lines and has outlived every genre built on it. The pop loops recycle the same functions without ever quite stopping.

Bottom line: once you can hear a chord as tonic, predominant or dominant, you can predict what is coming next in an unfamiliar song, and that prediction is most of what people mean when they say someone has a good ear. Harmony is now in place. The next lesson asks what to put on top of it.

Sources

1. Peterson, J. (n.d.). Introduction to harmony, cadences, and phrase endings. In Open Music Theory (2nd ed.). VIVA Open Publishing. viva.pressbooks.pub
2. Duker, P., et al. (n.d.). Blues harmony. In Open Music Theory (2nd ed.). VIVA Open Publishing. viva.pressbooks.pub
3. Hutchinson, R. (n.d.). Cadences. In Music Theory for the 21st-Century Classroom. University of Puget Sound. musictheory.pugetsound.edu
4. Handy, W. C. (1941). Father of the Blues: An Autobiography. New York: Macmillan. (Handy's own account of the guitarist at Tutwiler station.)

A melody with nothing wrong with it

Here is eight bars a student wrote for a songwriting assignment. It is in C major, 4/4, every note is a quarter note, and every single note belongs to the chord underneath it. Read the letters aloud in rhythm.

Nothing here breaks a rule. The harmony is correct, the rhythm is in time, no note clashes. And nobody can sing it back after one hearing, including the person who wrote it. That gap, between correct and memorable, is what this lesson is about, and the fastest way to understand a good melody is to find out exactly what is missing from a bad one.

Fault one: nothing ever comes back

Read the table again and look for anything that repeats. There is nothing. Every bar presents new material, so the listener has nothing to hold on to and nothing to recognise when it returns, because it never returns.

A motive is the smallest idea a listener can recognise: a shape of two to five notes with a rhythm attached. Beethoven opened his Fifth Symphony in 1808 with four notes, three repeated and one a third lower, and then built an entire movement out of that one cell; a public-domain recording is on Wikimedia Commons, and you can hear the figure return, transformed, dozens of times in seven minutes.

Repetition is not laziness. It is the only mechanism by which a listener hearing something once can remember it. A sequence, the same motive repeated a step or two higher or lower, is repetition that also moves the music forward, which is why it appears in almost every melody that has survived.

Fault two: one rhythm all the way down

Thirty-two quarter notes in a row. The metre never gets contradicted, nothing is held, nothing is short. Rhythm is the most memorable thing about most melodies, more memorable than pitch: tap out the rhythm of a famous tune without any pitches at all and people will name it.

The fix is not complexity. It is contrast. One long note among short ones, or one syncopation in a bar that has been square until then, does more than a page of sixteenth notes.

Fault three: no shape, and no single high point

Plot the pitches in the table and the line wanders up and down without going anywhere. The highest note occurs in bar 1 and again in bars 5 and 8, so the melody has no destination.

Good melodies have a contour you could draw with one stroke: usually a rise to a high point and a descent from it. The high note, the climax, is most effective when it appears once, somewhere around three quarters of the way through, and is approached by step rather than jumped at. Once you know this you will start noticing it everywhere.

Fault four: no phrases, so no punctuation

The student's eight bars are one undifferentiated stream. Melodies breathe. A phrase is a musical sentence, most often four bars long, and two phrases usually work as a pair called a period: an antecedent that ends on a half cadence and sounds like a question, and a consequent that begins the same way and ends on an authentic cadence, answering it.

That structure, question and answer, is old, universal, and the single most reliable way to make eight bars feel finished. Why this matters: a listener who can predict where a phrase will end can relax into the music; a listener who cannot is working, and working listeners stop listening.

The rebuild

Same key, same chords, same eight bars. The only changes are the four faults, corrected.

Trace the blue line with a finger. It rises, falls, rises again a little further, pauses at the half cadence in bar 4, restarts from the same place, climbs to a single peak in bar 7 and comes down to rest. That drawing is what a listener remembers, far more than the individual letters.

Chord tones and the notes between them

The student's melody used only chord tones, which is safe and dull. The notes that are not in the chord underneath are called non-chord tones, and they supply nearly all the expressiveness in a tune. The four you need now:

The suspension is the great one. It creates a dissonance on a strong beat, holds it just long enough to be uncomfortable, and then resolves. That small ache, repeated, is most of what people mean when they call a piece of music moving.

What a hook does

In popular music the equivalent of a motive is the hook: the short phrase that gets stuck in your head. The mechanics are the same. A hook is short, it repeats, it has a distinctive rhythm, and it usually sits at the top of the song's range so it arrives as a release.

Look at the opening of the 1939 song Over the Rainbow, by Harold Arlen and E. Y. Harburg. The first two notes leap a full octave, the largest interval in common use, and then the line walks downward by step. That is textbook melodic practice: a big leap is paid for by stepwise motion in the opposite direction, which is why an enormous interval can still sound singable rather than awkward.

Common misconceptions

• Repetition is not a sign of a poor imagination. It is the only way a listener can remember anything on a first hearing, and almost every enduring melody is built on it.
• Using only chord tones is not the safe choice. It is the bland choice. Passing tones, neighbours and suspensions are where the expression lives.
• A wide range does not make a melody impressive. Most singable tunes stay within an octave or a tenth, and a melody that exceeds a singer's range is simply unusable.
• More notes is not more melody. The Fifth Symphony motive has four notes and one rhythm, and it is the most recognised phrase in Western music.
• A climax is not the loudest moment. It is the highest note, and it works best when it happens once, late, and is approached by step.

Try it: diagnose and repair

Here are four bars in C major over the chords C, F, G, C. Every note is a quarter note: bar 1, C E G E; bar 2, F A C A; bar 3, G B D B; bar 4, C E G C.

1. Name the two biggest faults. Answer: nothing repeats as a recognisable motive, and the rhythm never varies. The contour is also flat, since every bar has the same up-and-down shape.

2. Rewrite bar 1 so that it contains a motive of two repeated notes followed by a step up, ending with a note twice as long. Answer: one good solution is E, E, G held for two beats. Any two repeated quarters plus a longer third note works.

3. Add a passing tone in bar 2 between A and C. Answer: A, B, C. B is not in the F chord, so it is a passing tone, and it must keep moving in the same direction.

4. Where should the highest note of a four-bar phrase usually fall? Answer: late, typically in bar 3 or early bar 4, and once only.

5. The phrase ends on C over a C chord. What cadence is that, and what would you change to make it a question instead? Answer: an authentic cadence. End on B or D over the G chord instead, making a half cadence.

Recap

A memorable melody is not a lucky accident. It has a motive short enough to recognise, repetition so that the motive can be recognised, rhythmic contrast so the ear has something to grip, a contour with one clear high point late in the line, and phrases that pose a question and then answer it. Non-chord tones supply the expression, and the suspension in particular supplies the ache.

Remember: when a tune of yours is not working, do not add notes. Find which of the five things is missing. Nine times out of ten it is repetition, because writers who are worried about sounding boring keep introducing new material and end up with music that has nothing to hold on to. You will use every one of these tools directly in the final lesson, when you write sixteen bars of your own.

Sources

1. Peterson, J., et al. (n.d.). Melody and phrasing. In Open Music Theory (2nd ed.). VIVA Open Publishing. viva.pressbooks.pub
2. Peterson, J., et al. (n.d.). Embellishing tones. In Open Music Theory (2nd ed.). VIVA Open Publishing. viva.pressbooks.pub
3. Hutchinson, R. (n.d.). Rules of melody. In Music Theory for the 21st-Century Classroom. University of Puget Sound. musictheory.pugetsound.edu
4. Hutchinson, R. (n.d.). Period form. In Music Theory for the 21st-Century Classroom. University of Puget Sound. musictheory.pugetsound.edu

Two dots and a double bar

Sixteen bars into the Minuet in G major, BWV Anh. 114, the printed page shows a thin line, a thick line, and two dots. That is a repeat sign, and it is architecture rather than decoration. It says: everything up to here is one unit, and you are going to hear it twice.

The minuet has two of those units. The first sixteen bars start in G major and end in D major, which is a stopping place but not home. The second unit travels further, brings the opening tune back near its end, and finishes in G. Two halves, each played twice. That is the whole design, and it is the design of hundreds of dance movements written between about 1680 and 1780. You can hear all of it in a fifty-second public-domain recording on Wikimedia Commons. Listen for the moment the music stops without sounding finished; that is the end of the first half.

Now think about the last song you streamed. It almost certainly had a section that came back with the same words each time, and another that came back with different words each time, and a third section that happened once and never again. That is also a design, and this lesson puts the two side by side, because the eighteenth-century minuet and the three-minute pop song are solving the same problem with different equipment.

The problem every form solves

Music happens in time, and the listener cannot look back at page one. Everything you know about a piece at minute three, you know because you remembered it. Form is the arrangement of repetition and contrast that makes remembering possible: enough return that the listener feels oriented, enough new material that the listener does not get bored.

That is the trade. Every form in this lesson is a different answer to the same two questions: what comes back, and how far away do we go before it does?

How the letters work

Analysts label sections with capital letters. The rule is short: the first section is A; a section made of new material gets the next unused letter; a section made of material you have already heard gets the letter it had before. If a section returns changed but recognisable, it gets a prime mark, written A1 here because a raised prime is hard to read on screen.

So ABA means: something, then something different, then the first thing back. AABA means the opening idea is stated twice before the contrast arrives. AAB, ABAC and AABBACCDD are all real forms you will meet.

Two warnings, because both trip people. First, the letters describe musical material, not words. A verse and a second verse of a folk song have the same letter even though the story has moved on, because the music is the same. Second, the letters say nothing about length. An A section can be four bars or four minutes.

Binary: two halves that need each other

Binary form is two sections, usually both repeated, written as ||: A :||: B :||. What makes the two halves halves rather than two separate pieces is the key plan. In a major-key binary movement the first half normally starts at home and ends on the dominant, a fifth above. It is the musical equivalent of a sentence ending with a comma. The second half begins away from home and works its way back, ending on the tonic. Neither half can stand on its own: the first has no ending, the second has no beginning.

Simple binary keeps the two halves melodically distinct. Rounded binary, far commoner, brings the opening tune back inside the second half, so the shape is really A, then B leading to A again, all inside a repeat structure: ||: A :||: B A1 :||. The Minuet in G is rounded binary. So is most of the dance music of the period.

The minuet, by the way, is not by Bach. It comes from a harpsichord suite that Christian Petzold wrote around 1720, and it reached us because someone copied it into the 1725 Notebook for Anna Magdalena Bach, a household book of pieces the Bach family liked to play. Generations of piano students were told it was Bach. It is a useful reminder that the music in a notebook is not always by the person whose notebook it is.

Ternary: go away, come back, and mean it

Ternary form is ABA, where A is a complete, self-contained piece of music that ends properly in its own key, B is a genuinely different section often in a different key, and A returns whole.

The classic case is the minuet and trio of a symphony or string quartet. The minuet is played complete. Then a contrasting section called the trio is played complete, usually lighter in texture and in a related key. Then the score says da capo, from the head, and the players go back and perform the minuet again, this time without its internal repeats. Minuet, trio, minuet: ABA on the large scale, even though the minuet and the trio are each rounded binary on the small scale. Forms nest.

The distinction everyone gets wrong

Rounded binary also ends with the A material returning. So how is it not ternary? The test is what happens at the end of the first A.

What matters here: ternary is three closed things in a row. Rounded binary is two open things, the second of which happens to contain a memory of the first. If the opening section could be performed alone and sound like a complete piece, you are in ternary.

Strophic: one tune, many verses

Strophic form is the oldest and simplest arrangement in this lesson: the same music repeated for every stanza of text, AAAA and onward. Hymns work this way. So do most folk ballads, including Greensleeves, whose tune was already circulating when a ballad of that name was registered with the London Stationers' Company in September 1580.

Many strophic songs add a refrain: a short section at the end of each stanza whose words stay the same. Greensleeves does this, and the refrain is where everyone in the room joins in. Hold on to that, because the refrain is the ancestor of the chorus, and the difference between them is worth a paragraph of its own later.

Multi-strain form: the rag and the march

Between the parlour song and the symphony sits a family of pieces built from a chain of sixteen-bar strains, each one repeated, with a return or two along the way. Scott Joplin published the Maple Leaf Rag in 1899, and its plan is AA BB A CC DD: four different strains, the first one coming back once in the middle, and a change of key for the third strain. A 1916 piano roll played by Joplin himself is on Wikimedia Commons, and the score is free on IMSLP. Follow the page while it plays and you will see the strains go by like railway carriages.

Marches are laid out the same way, which is not a coincidence: both grew out of the same nineteenth-century band and parlour-piano publishing trade.

AABA: thirty-two bars that ran popular music for forty years

From roughly the 1920s to the 1950s, the standard American popular song was thirty-two-bar AABA form: four eight-bar sections. A is the tune. A comes again, usually with a new ending. B, called the bridge, the release or the middle eight, goes somewhere else, often to a different key and always to a different melodic shape. Then A returns and the song is over.

Blue Moon, written by Richard Rodgers and Lorenz Hart in 1934, is the textbook case: eight, eight, eight, eight, with the bridge lifting away from the endlessly circling chords of the A sections. Over the Rainbow by Harold Arlen and E. Y. Harburg, from 1939, is the same shape, and its bridge is where the octave leap of the opening stops being the point and the line starts moving in steps.

The form did not die with the big bands. The Beatles built Yesterday on it in 1965, with one deliberate irregularity: the A sections are seven bars long rather than eight, which is why the song feels like it is slightly ahead of you. Paul McCartney has said the odd bar count was not planned. That is worth knowing, because it shows a form is a habit rather than a law.

Verse and chorus: the shape that replaced it

From the mid-1950s onward, verse and chorus form took over, and it is still the default. Its sections are defined by function rather than by bar count.

• Verse. Same music each time, new words each time. It carries the story and usually sits low in the singer's range.
• Chorus. Same music and same words each time. It carries the title, sits higher, is louder and thicker, and is the point of the song.
• Prechorus. An optional link that builds tension and makes the chorus arrive as a release. Often it withholds the tonic chord.
• Bridge. Happens once, roughly two thirds of the way in, contrasting in key, texture or both. Its job is to make the last chorus feel earned rather than repeated.
• Post-chorus or drop. A hook after the chorus, frequently instrumental. In dance and electronic styles this is where the strongest material lives.

A very common layout is: intro, verse, prechorus, chorus, verse, prechorus, chorus, bridge, chorus, chorus, outro. Nirvana built Smells Like Teen Spirit in 1991 on almost exactly that plan, with a guitar figure as the intro hook. Adele's Rolling in the Deep, from 2010, is another, with a post-chorus that repeats the title phrase over a stomping backbeat.

Chorus or refrain?

A refrain is a line or two at the end of a verse, using the verse's own music. A chorus is a separate section with its own music, its own chords and usually its own register. If the memorable words arrive without the music changing, it is a refrain. If the music opens out and lifts at the same moment, it is a chorus.

Reading the four across

Read the table by column rather than by row and the family resemblance appears. Every form has something that returns and something that does not, and the differences are about size and about whether the returning thing is the tune, the words, or both.

Common misconceptions

• A chorus is not simply the loudest part. It is the section whose words and music both stay the same. Plenty of quiet songs have choruses, and plenty of loud instrumental passages are not choruses.
• ABA is not the same as rounded binary. The test is whether the first A ends closed, at home, sounding finished. If it ends on the dominant, you have rounded binary.
• A bridge is not any instrumental section. A guitar solo over the verse chords is not a bridge; it is a solo over the verse. A bridge introduces material you have not heard.
• Form letters do not track lyrics. Verse one and verse two are both A, however different the words are, because the music is what the letter names.
• Repeat signs are not an instruction to the listener to be patient. In binary form the repeat is structural: the halves are short precisely because they will be heard twice.

Try it: label three pieces

1. A piano piece has sixteen bars ending on the dominant, marked to be repeated, then twenty bars that begin in a new key, bring back the opening melody at bar 13 of the twenty, and end at home, also marked to be repeated. Name the form. Answer: rounded binary. Two repeated halves, the first ending open on the dominant, the opening tune returning inside the second half.

2. A song has an eight-bar tune, the same eight-bar tune with a different final two bars, eight bars in a new key with a new melody, then the original eight bars. Name the form and the section in the new key. Answer: thirty-two-bar AABA. The new-key section is the bridge, also called the release or the middle eight.

3. A track runs: four bars of drums, sixteen bars of singing over four chords with the story moving forward, eight bars that hold off the home chord and get louder, sixteen bars with the title sung high and the same words every time, then the sixteen-bar story section again. Label the sections. Answer: intro, verse, prechorus, chorus, verse. The prechorus is identifiable because it withholds the tonic and builds.

4. A movement is marked Menuetto, then Trio, then Menuetto da capo. On the large scale, what form is that, and what form is the Menuetto likely to be on its own? Answer: ternary on the large scale, and the Menuetto by itself is almost certainly rounded binary. Forms nest inside one another.

5. Two songs use the same four chords for every section. Can they still be in different forms? Answer: yes. Form is about which sections return and when, not about harmony. Sections can be distinguished by melody, register, texture, words and length while the chords stay put, which is exactly what a lot of modern pop does.

The short version

Form is the listener's map. Binary is two open halves joined by a key plan; rounded binary slips the opening tune back into the second half; ternary is three closed sections with a real departure in the middle; strophic repeats everything but the words; AABA states a tune twice, leaves for eight bars, and returns; verse and chorus alternate story and payoff, with one bridge to keep the last chorus from feeling automatic.

The upshot: when you cannot name a form, stop trying to match it to a template and ask the two questions instead. What comes back? How far did we go before it did? Those two answers will get you to the right label nearly every time, and they will also tell you what to do when you write your own sixteen bars in the last lesson of this course.

Sources

1. Hughes, B., and Hamm, C. (n.d.). Binary form. In Open Music Theory (2nd ed.). VIVA Open Publishing. viva.pressbooks.pub
2. Hughes, B., and Hamm, C. (n.d.). Ternary form. In Open Music Theory (2nd ed.). VIVA Open Publishing. viva.pressbooks.pub
3. Hutchinson, R. (n.d.). AABA form. In Music Theory for the 21st-Century Classroom. University of Puget Sound. musictheory.pugetsound.edu
4. Hutchinson, R. (n.d.). Verse-chorus form. In Music Theory for the 21st-Century Classroom. University of Puget Sound. musictheory.pugetsound.edu
5. Joplin, S. (1899). Maple Leaf Rag [score]. John Stark and Son. Reproduced by the International Music Score Library Project. imslp.org

A joke at the Hanover Square Rooms, 23 March 1792

A crowd has paid for the fifth concert of Johann Peter Salomon's London series. Joseph Haydn, sixty years old and the most famous composer in Europe, is directing from a fortepiano. The second movement of his new symphony begins with a tune so plain that a beginner could play it: eight bars, then eight more, each half played twice. On the repeat of the first eight bars the strings drop to pianissimo, the lower strings pluck instead of bowing, and the music almost disappears. Then the whole orchestra, timpani included, plays one fortissimo chord.

Haydn later told his biographer Georg August Griesinger that the point was not to wake anyone up. He wanted something new and startling, partly because his former pupil Ignaz Pleyel had opened a rival concert series in London a week earlier and Haydn did not intend to be outdone. The audience shouted for an encore. The symphony has been called the Surprise ever since.

That one chord is the way into this lesson, because the joke only works if you know what is supposed to happen next. Haydn's audience knew, because they knew the forms. This lesson walks through that symphony movement by movement and lets the three large forms of instrumental music arrive as they are needed: theme and variations, rondo, and sonata form. Roughly twenty-four minutes of music, four movements, three forms, and one chord that has been startling people for more than two centuries.

Movement two: theme and variations

Start with the movement the joke lives in, because it is the easiest form to hear. The Andante is in C major, the subdominant of the symphony's G major, in 2/4 time. A public-domain recording of the whole movement is on Wikimedia Commons, and the full score is free on IMSLP.

The design of theme and variations is: state a tune plainly, then play it again and again, changing something each time while keeping enough of the original that the listener can still hear it underneath. It is the most honest form in music, because it puts the raw material on the table first and then shows you what a composer can do with it.

Here is what Haydn changes, variation by variation.

Read the right-hand column downward and you have the entire toolkit of variation writing: decorate the melody, switch the mode, rescore it, change the rhythm, reharmonise it. Nothing else is needed. The core of it: a variation keeps a skeleton and replaces the flesh, and the skeleton is usually the harmony and the phrase lengths rather than the tune itself.

The oldest version of the idea keeps the bass rather than the tune. A ground bass is a short bass line repeated without pause while everything above it changes, which is what a chaconne does. Bach built the Goldberg Variations, published in 1741, on the bass of a single aria: thirty variations, and in almost none of them does the aria's melody appear at all. If you have ever heard a producer loop four bars of bass and build an entire track on top, you have heard a ground bass.

Movement four: rondo, and how a refrain becomes a form

Haydn's finale is fast, loud and built for an ending. Its form is a rondo, or more precisely a sonata rondo, and it is worth hearing next because the principle is one you already know from songs.

A rondo has a refrain, labelled A, that keeps coming back in the home key, separated by contrasting sections called couplets or episodes. The simplest plan is A B A C A. Longer ones run A B A C A B A, and in that last shape the B that returns near the end comes back at home rather than in its original key, which is the detail that turns a rondo into a sonata rondo.

Two things make rondos work. First, the refrain is always in the tonic, so every return is a homecoming and the listener is never lost. Second, each episode is free to go somewhere the refrain cannot, which is why rondos were used for finales: the composer can be playful, distant and surprising, knowing the tune will restore order. The finale of Mozart's serenade Eine kleine Nachtmusik, K. 525, written in 1787, is a clean example, and there is a public-domain recording of it on Wikimedia Commons. Count the number of times the opening tune comes back. You will not need a score.

Movement one: sonata form, and why it is not a template

The first movement opens with a slow introduction in 3/4, marked Adagio cantabile, and then changes gear into a fast 6/8 marked Vivace assai. That fast section is in sonata form, the design that carried the opening movement of nearly every symphony, quartet, concerto and sonata written between about 1760 and 1900.

Sonata form is often taught as a diagram with boxes, which makes it sound like a filing system. It is better understood as a journey with a reason. The reason is the key plan. Here is the plan, in words, before any of the technical names arrive.

1. State some music at home, in the tonic key.
2. Travel to a second key, usually the dominant a fifth up, and state different music there. You are now away from home, and the listener can feel it.
3. Spend a while unsettled, taking the material apart and moving through several keys quickly, so that home becomes something you want.
4. Come back, and this time play everything at home, including the music that was in the second key. The tension of step two is resolved by geography, not by new ideas.

Now the names. Step one and two together are the exposition. Step three is the development. Step four is the recapitulation. A slow introduction can precede the whole thing, and a coda can follow it.

Look at the diagram and notice the one fact that matters more than any other: the second theme appears twice, in two different keys. First in the dominant, then at home. Every other feature of sonata form is negotiable. Composers add themes, drop the introduction, write developments that develop nothing, and recapitulate in the wrong order. The key plan is what makes the movement a single argument rather than a list.

What actually happens in a development

Students often expect the development to introduce the best new tune. It usually introduces nothing. Its techniques are four:

• Fragmentation. Take a two-bar idea, use only its last three notes, and repeat those.
• Sequence. Move that fragment up or down by step, again and again, so the music climbs without settling.
• Modulation. Change key often and without ceremony, so no key sounds like home.
• Texture and register shifts. Put the fragment in the bass, then in the violins two octaves up, then in canon between them.

The purpose is pressure. A good development makes the return of the first theme in the tonic feel like a door opening, and that moment, the start of the recapitulation, is the single most important second in a sonata-form movement.

A short worked map

Mozart's Eine kleine Nachtmusik begins with a compact sonata-form movement in G major, and there is a public-domain recording on Wikimedia Commons. Listen with this map in hand.

The row that teaches the form is the last one. The same tune you heard in D now arrives in G, and it is not a repeat but a resolution.

Movement three, and how the four fit together

The third movement of the Surprise is a minuet and trio, marked Allegro molto: ternary form, exactly as the previous lesson described. Haydn's tempo marking is worth a second glance, because a minuet at that speed is no longer danceable. Within a few years the movement would be renamed a scherzo, meaning joke, and by his last quartets Haydn was marking minuets presto.

The standard four-movement plan of a Classical symphony now reads as a sequence of forms:

Four movements, twenty-four minutes, and the forms are arranged so that no two adjacent movements ask the same thing of you. That is deliberate design, and it is the same instinct that keeps a producer from putting two ballads next to each other on an album.

Common misconceptions

• Sonata form is not a kind of piece. A sonata is a multi-movement work. Sonata form is the design of one movement, and it turns up in symphonies, quartets, concertos and overtures far more often than the name suggests.
• The development does not have to introduce a new theme. It usually takes existing material apart. Judging a development by whether it has a good tune is judging it by the wrong thing.
• The recapitulation is not a repeat. The second theme is transposed, which changes the meaning of the whole movement. A literal repeat would resolve nothing.
• A rondo is not just any piece with a repeated tune. The refrain must return in the home key, and it is the returns at home that carry the form.
• Variations do not have to keep the melody. Many keep only the bass and the harmonic plan. In the Goldberg Variations the aria's tune is almost never heard again.

Try it: name the form from a description

1. A movement presents a tune in the tonic, then the same tune with the right hand playing four notes to every one of the original, then the same tune in the parallel minor, then the same tune with the melody in the left hand. Name the form and the element changed in each stage. Answer: theme and variations; the changes are decoration, mode, and texture or register.

2. A finale presents a tune in C major, a contrasting section in G major, the tune again in C, a contrasting section in A minor, and the tune again in C. Name the form and write its letters. Answer: rondo, A B A C A. The refrain is in C every time, which is the identifying feature.

3. In a sonata-form movement in D major, where should the second theme be on its first appearance and on its second? Answer: in A major, the dominant, the first time; in D major, the tonic, in the recapitulation.

4. In a sonata-form movement in D minor, the second theme is in F major. Is that an error? Answer: no. Minor-key expositions normally go to the relative major, and F major is the relative major of D minor.

5. A movement runs A B A C A B A, and the second B is in the home key although the first was not. What is it, and why does the name matter? Answer: a sonata rondo. The transposed return of B is the sonata principle working inside a rondo, which is why Haydn's finale gets the longer name.

6. Why is the fortissimo chord in the Andante a joke that only works once? Answer: because the surprise depends on an expectation of quiet continuation. Haydn never repeats it, and the variations that follow proceed as if nothing had happened, which is the second half of the joke.

Looking back

Theme and variations puts its material on the table and changes one thing at a time: decoration, mode, scoring, rhythm, harmony. Rondo keeps bringing a refrain home between excursions. Sonata form leaves home, states new music in a second key, spends a development making home desirable, and then resolves the movement by bringing everything back into the tonic. Those three, plus the ternary minuet, account for almost every movement in a Classical symphony.

Bottom line: you do not need a score to follow any of them. Ask what returns and whether it returns in the same key as before. A refrain always at home is a rondo. A tune that comes back in a new key the second time and at home the third is sonata form. A tune that comes back changed but in the same place every time is a variation set. One chord in London in 1792 is still funny because Haydn knew his listeners were asking exactly that question.

Sources

1. Hughes, B., and Hamm, C. (n.d.). Sonata form. In Open Music Theory (2nd ed.). VIVA Open Publishing. viva.pressbooks.pub
2. Hughes, B., and Hamm, C. (n.d.). Rondo. In Open Music Theory (2nd ed.). VIVA Open Publishing. viva.pressbooks.pub
3. Hutchinson, R. (n.d.). Sonata form: four structural functions. In Music Theory for the 21st-Century Classroom. University of Puget Sound. musictheory.pugetsound.edu
4. Haydn, J. (1791). Symphony No. 94 in G major, Hob. I:94 [score]. Reproduced by the International Music Score Library Project. imslp.org
5. Rosen, C. (1988). Sonata Forms (rev. ed.). W. W. Norton. (Unlinked: the standard study of how far real movements depart from the textbook plan.)

Page one, top to bottom

Open the conductor's score of Haydn's Symphony No. 94 and page one has about eleven staves stacked down the page, all sounding at once. Two flutes share a stave. Below them two oboes, then two bassoons, then two horns, then two trumpets, then the timpani, then four staves of strings. Every stave starts at the same instant, and the conductor has to take the whole column in at a glance.

A modern full score of a large twentieth-century work can run to thirty staves on a page the size of a newspaper. The order, though, is the same order it has been since the 1800s, and knowing it lets you find any instrument in under a second. This lesson is a procedure: we will read one page of score correctly from top to bottom, then change one thing about the page and watch the right answer change with it.

The order of the staves, and why it is that order

Instruments are grouped by family, and within each family they run from highest to lowest.

One oddity is worth flagging because it looks like a mistake. Within the brass, horns sit above trumpets even though horns sound lower. The reason is historical: horns were written with the woodwind for much of the eighteenth century, because they blended with them, and when brass acquired its own block the horns kept their place at the top of it. Score order is a record of how orchestras used to sit, not a pitch chart.

Worked example one: a page with nothing transposing

Here are four bars of an imagined page, written to be read rather than played, using only instruments that sound exactly what is printed. Every instrument is printed with the note C, the C above middle C, except where noted.

Seven of the eight rows are identical on both sides. The eighth is the first trap. The double bass sounds an octave lower than it is written, purely so that its part does not need a forest of ledger lines below the bass staff. Cello and double bass often share a stave, and when they do, they are playing in octaves rather than in unison. That is why an orchestral bass line sounds so much deeper than it looks.

The piccolo does the same thing in the opposite direction: it sounds an octave higher than printed, for the same reason.

Worked example two: change the instruments, and the chord changes

Now take the same page and replace three staves. Everything is still printed as C5 or C4. Watch the right-hand column come apart.

The printed page shows a unison on C. What comes out of the orchestra is C, F, B flat, F, B flat, C: three different pitch classes stacked in fourths. Nobody made an error. This is what a transposing instrument is.

The point: for a transposing instrument, the name of the key tells you what sounds when the player reads C. A clarinet in B flat reading C produces B flat. A horn in F reading C produces F. That is the entire rule, and once you have it, every transposition in the orchestra is a subtraction you can do in your head.

Why does anyone put up with this? Because a clarinettist owns instruments in B flat and in A, and an orchestral horn player is heir to a family of instruments in half a dozen keys. Transposing notation means one set of fingerings works on all of them: written C is always the same fingering, whatever tube is in your hands. The reading burden moves from the player to the conductor and the composer, which is where it has stayed.

Here is the reference list.

What each family is actually doing

Strings are four instruments built to the same plan at four sizes. A bowed string is not plucked and released; the bow's rosin grips the string, drags it sideways, lets it snap back, and grips again, hundreds of times a second. That grip-and-release is why a string can hold a note forever, and why the section can swell and fade as one. The violin and viola are tuned in fifths, the double bass in fourths. The viola reads alto clef, a C clef whose centre sits on middle C, which keeps its part on the staff instead of hanging between two.

Woodwind instruments make sound three different ways, despite the family name. The flute has no reed at all: the player splits a stream of air across an edge, and the air column does the rest. The oboe and bassoon use a double reed, two blades of cane beating against each other, which is why they sound nasal and cut through a full orchestra. The clarinet uses a single reed beating against a mouthpiece, and its cylindrical tube gives it a range of well over three octaves with a noticeably different colour in each part of it. The Philharmonia's own figures put the clarinet's tube at about 60 cm with a frequency range from roughly 146 Hz to 2.1 kHz.

Brass instruments are the odd family out, because the reed is the player. Lips buzz against a cup mouthpiece; the tube amplifies and selects. The harmonic series from the first lesson is not background here, it is the mechanism: a bugle with no valves can play only the notes of one harmonic series, and valves or a slide exist to let the player switch to a different fundamental and so reach the notes in between. A trombone slide has seven positions, each lowering the tube by one semitone.

Percussion splits into definite pitch and indefinite pitch. Timpani, glockenspiel, xylophone, marimba, tubular bells and celesta play named notes; the modern timpani has a pedal that retunes the drum during a performance. Snare drum, bass drum, cymbals, triangle and tam-tam do not play named notes, and their parts are written on a single line or on a staff used purely for position.

The harp deserves its own sentence. It has one string per letter name, so the seven pedals each have three positions, flat, natural and sharp, and the player changes key with their feet. Rapid chromatic writing for harp is a request the instrument cannot fill.

The conductor: what the hands are for

A conductor makes no sound. The job has three parts: decide what the piece should sound like, get the orchestra to agree in rehearsal, and in performance keep eighty people in the same instant of time.

The right hand, with or without a baton, beats time in a pattern the players can read from the far side of the stage. Beat one is always straight down, so it can be found from anywhere, and the last beat of the bar always goes up, so the next downbeat has somewhere to fall from.

The left hand does everything the pattern cannot: dynamics, shaping a phrase, warning an entry a bar ahead, holding a fermata, and cutting off. The single most useful gesture in conducting is the upbeat that precedes the first sound, because it has to communicate tempo, dynamic and character before anyone has played a note. If the upbeat is wrong the entry will be ragged no matter how good the players are.

Most of the real work happens in rehearsal, and it is not about time-beating at all. It is balance, who is too loud; intonation, which chord is sour and which player has to move; articulation, whether a passage is separated or joined; and agreement on what the piece means. By the concert, a well-rehearsed orchestra could play most of it without a conductor. The conductor is there for the moments when they could not.

The voice, the instrument everyone has

Singing works by the same three-part scheme as a clarinet: a power source, a vibrator and a resonator. The lungs and diaphragm supply pressure; the vocal folds in the larynx open and close hundreds of times a second, chopping the airstream into a buzz; the throat, mouth and nose shape that buzz into a vowel. Pitch comes from the length and tension of the folds, which is why a trained singer's control is muscular and mostly invisible.

The four standard choral voice types, with approximate comfortable ranges, are:

Those ranges are typical rather than legal limits, and individual singers vary a great deal. What matters more than the extremes is tessitura, the part of the range where a line spends most of its time. A melody that touches a high note once is easy; a melody that sits near the top for two minutes is exhausting, whatever its highest note.

Note the tenor row: written in treble clef but sounding an octave lower. That is the same transposing trick you met in the brass, applied to a voice, and it is why a tenor line printed above the bass in a hymn book looks higher than it sounds.

Common misconceptions

• The conductor is not keeping the players in time the way a metronome would. Professional players listen to each other and can hold an ensemble unaided. The conductor sets tempo, balance, phrasing and character, and catches the places where listening alone fails.
• A transposing instrument is not out of tune or badly made. The notation is transposed, not the instrument. A B flat clarinet plays perfectly in tune with everyone else; only its printed part is shifted.
• The flute is not made of wood, and that does not remove it from the woodwind. Family membership is about how the sound is made, not what the tube is made of, which is also why the brass section is defined by buzzing lips rather than by metal.
• Violin I and violin II are not first-class and second-class players. They are two sections with different parts, frequently in harmony or in dialogue, and the second violins often have the harder rhythmic job.
• Range is not the same as tessitura. Asking a singer for one high note is a different request from asking them to live up there.

Try it: sound the page

1. A clarinet in B flat is printed the note D5. What sounds? Answer: C5. The instrument sounds a major second lower than written.

2. You want a horn in F to sound the concert pitch A4. What do you print? Answer: E5. Going the other way, you write a perfect fifth higher than you want to hear.

3. Cello and double bass share one stave and the printed note is G2. What do you hear? Answer: G2 from the cello and G1 from the bass, an octave apart, which is the standard orchestral bass sound.

4. On a page of full score, which stave is directly above the violins? Answer: harp, keyboard or voices if any are present, and otherwise percussion, since the strings sit at the bottom of the page.

5. A trumpet in B flat and a clarinet in B flat are both printed E4. Do they sound the same pitch? Answer: yes, D4 for both, because they share a transposition. This is exactly why B flat instruments dominate wind bands: the parts are interchangeable on the page.

6. A composer writes a fast chromatic scale for harp lasting one bar at a brisk tempo. What is the problem? Answer: the harp changes accidentals with seven pedals, so a chromatic run needs pedal changes the player cannot make in time. The instrument is built around diatonic strings.

Putting it together

A full score is read top to bottom in fixed families: woodwind, brass, percussion, harp and voices, strings. Within a family, high to low, with horns sitting above trumpets for historical reasons. Some staves lie about pitch on purpose: the double bass and contrabassoon sound an octave lower, the piccolo an octave higher, and the transposing instruments sound the interval named in their title below what is printed. Strings are bowed and can sustain indefinitely; woodwind splits into edge-tone, single reed and double reed; brass is powered by the player's lips selecting a harmonic; percussion divides into definite and indefinite pitch. The conductor beats time with the right hand, shapes with the left, and does the real work in rehearsal. The voice is a power source, a vibrator and a resonator, and its four choral types are sorted by range, with the tenor part printed an octave above where it sounds.

Worth holding on to: when you look at an orchestral score and cannot work out what you are hearing, do not start with the notes. Start with the stave name. The name tells you the family, the family tells you the position on the page, and the key in the name tells you how far to move the printed pitch to get the sound.

Sources

1. Philharmonia Orchestra. (n.d.). Instruments of the orchestra. philharmonia.co.uk
2. Philharmonia Orchestra. (n.d.). Clarinet. philharmonia.co.uk
3. Gotham, M. (n.d.). Core principles of orchestration. In Open Music Theory (2nd ed.). VIVA Open Publishing. viva.pressbooks.pub
4. Adler, S. (2016). The Study of Orchestration (4th ed.). W. W. Norton. (Unlinked: the standard reference for ranges, transpositions and score layout.)

One line, no bar lines, no harmony

Play the Kyrie XI recording on Wikimedia Commons. A group of men sing one melody together. There is no accompaniment, no beat you could tap a foot to, and no second part. Everything you have learned in this course about chords, keys and metre is absent, and the music is not poorer for it.

This is Gregorian chant, the liturgical song of the Western church, and for several centuries it was essentially all the written music there was. Its texture is monophony: one melodic line, whether one person or a hundred are singing it. Its rhythm follows the Latin words rather than a metre. It uses modes rather than major and minor keys, which is why it sounds neither happy nor sad to modern ears but simply other.

From that starting point, this lesson follows one question through roughly eight hundred years: what happens when you add a second voice? The answer takes us from a monastery to Notre Dame de Paris, to a Mass written by a poet, to a Roman legend that is not true, to the first opera, and finally to a man in Leipzig writing fugues.

Writing it down: Guido, around 1026

The first problem was memory. Chant was learned by ear, which meant a singer had to hold hundreds of melodies in their head, and a monastery two hundred miles away would sing the same chant differently. Early notation used neumes, marks above the text showing whether the voice rose or fell, but not by how much. They were reminders, not instructions.

Guido of Arezzo, a Benedictine monk working in Italy, fixed this around 1026 by ruling lines across the page and pinning the neumes to them. Suddenly the distance between two marks meant something exact. He also gave singers the syllables ut, re, mi, fa, sol, la, taken from the successive opening pitches of a hymn to John the Baptist, which is the direct ancestor of do re mi. Guido claimed a singer could now learn in a few months what had taken ten years. The staff you learned in lesson 2 is his.

The second voice, around 900 to 1200

A treatise called Musica enchiriadis, from around 900, describes something new: sing the chant, and have a second voice sing the same melody a fourth or a fifth below it, in parallel, all the way through. That is organum, and in its first form it is barely two-part music at all. The second voice has no independence. It is a shadow.

Two hundred years later the shadow is gone. At the new cathedral of Notre Dame in Paris, composers known to us as Léonin and Pérotin were writing music in which the chant is stretched into enormously long held notes in the lowest voice while one, two or three upper voices move above it in rapid, measured patterns. Pérotin's four-voice setting of Viderunt omnes, from about 1200, is the famous case: a single syllable of the original chant can last half a minute underneath while the upper parts trade rhythmic figures over it.

Two enormous things had to be invented for that music to exist. First, a way of notating rhythm, because three voices moving independently cannot coordinate by feel. Second, the idea that a composer might be a named individual with a style, rather than an anonymous transmitter of a repertoire.

Machaut, and music as a made object

Guillaume de Machaut, who died in 1377, was a poet and a canon of Reims Cathedral, and he is the first composer whose complete works survive largely because he supervised the copying of them himself. His Messe de Nostre Dame, from the 1360s, is the earliest complete setting of the Mass Ordinary by one identifiable composer, in four voices.

Listen for what is difficult about it. The four parts are rhythmically independent to a degree that can sound almost mechanical, and the harmonies arrive at bare fifths and octaves at the ends of phrases, without the thirds that make a triad sound full. Fourteenth-century ears heard a third as mildly unstable. Ours hear it as home. That difference is not a matter of one era being right.

Imitation: everybody sings the same idea, one after another

By the time of Josquin des Prez, who died in 1521, the standard technique had changed completely. Instead of one borrowed melody with parts built over it, a composer would take a short phrase, give it to the sopranos, then have the altos enter with the same phrase a few beats later, then the tenors, then the basses. That is a point of imitation, and stacking dozens of them is how a Renaissance motet or mass is built.

Imitation solved a real problem. Four independent lines risk sounding like four people ignoring each other. If all four are working the same material, the texture holds together no matter how freely the parts move. This is counterpoint in its mature form, and it dominated European music for a century and a half.

A Roman legend worth checking

Giovanni Pierluigi da Palestrina published the Missa Papae Marcelli in 1567. The story usually attached to it says that the Council of Trent was about to ban polyphony from church because the words could not be understood, and that this mass, in which every word is audible, changed the cardinals' minds and saved polyphonic music.

It is a good story and there is no contemporary evidence for it. The Council's actual decree on church music, from 1562, asks that the sacred texts be intelligible and that lascivious or impure elements be kept out; it does not threaten to abolish polyphony. The legend grew in the decades after Palestrina's death and was fixed in place by a nineteenth-century opera about him. Listen to the Kyrie on Wikimedia Commons and you will hear the real achievement: six voices moving with such smooth, stepwise, unhurried motion that nothing ever sounds crowded.

1607: somebody decides the words matter more

Around 1600 a group of Florentine musicians and intellectuals argued that Renaissance counterpoint had it backwards. If four voices all sing different words at different times, nobody understands anything, and music that is supposed to move you cannot. Their proposal: one singer, delivering the text at the speed of speech, over the plainest possible accompaniment.

That proposal produced recitative, and recitative produced opera. Claudio Monteverdi's L'Orfeo, staged in Mantua in 1607, is the earliest opera still regularly performed. Monteverdi defended writing dissonances that the older rules forbade by saying that there were now two practices: the old one, where the counterpoint ruled, and a new one, where the words ruled.

Basso continuo: the invention that defines the Baroque

The accompaniment those singers needed became a system. In basso continuo, the composer writes out only the bass line, with small numbers under it, and a keyboard or lute player reads those numbers and improvises the chords above. The numbers are figured bass, and they say what intervals to build over the bass note: a 6 means a chord in first inversion, a 6 and a 4 together mean second inversion, and no number at all means a plain root-position triad.

Two players are needed: one to play the bass line itself, usually a cello or bassoon, and one to fill in the chords. That pair sits underneath almost every piece of music written between about 1600 and 1750, which is why the era sounds the way it does.

Vivaldi, and a form built out of returns

The Four Seasons was published in Amsterdam in 1725 as the first four concertos of Antonio Vivaldi's Opus 8. Each concerto comes with a sonnet printed above the music, and the score is annotated to say which line the music is illustrating: birds, a storm, a barking dog, ice underfoot. It is programme music a century before the term existed.

Structurally, every fast movement uses ritornello form. The full ensemble plays a memorable block of music, the ritornello, meaning the little thing that returns. Then the soloist plays an episode. Then the ritornello comes back, often shortened and in a different key. Then another episode. The movement ends with the ritornello complete and at home. If that plan sounds like a rondo, it nearly is, with one difference: the returns are usually partial and are often in other keys until the last one.

Play the first movement of Spring, in a public-domain recording on Wikimedia Commons, and count the returns of the opening tune. You will find it easy, which is the point of the form.

Bach, and the last word on counterpoint

Johann Sebastian Bach was not famous in his lifetime as a composer of great works; he was known as an organist and was employed to supply music weekly. He sent the six Brandenburg Concertos to the Margrave of Brandenburg in 1721, apparently in search of a job, and there is no record that they were ever played there. The first movement of the third concerto is on Wikimedia Commons and the score is on IMSLP: nine solo strings plus continuo, treated as three groups of three that trade the same material.

The form Bach perfected is the fugue, and it is Josquin's point of imitation grown into an entire piece. One voice states the subject alone. A second enters with the same subject transposed to the dominant, while the first continues with a counter-melody. A third enters, then a fourth. After the exposition, episodes made from fragments of the subject alternate with further entries in other keys, and near the end the entries may pile up on top of each other before the original key returns.

Bach wrote The Well-Tempered Clavier, a prelude and fugue in every one of the twenty-four keys, in 1722, and a second such book about twenty years later. The title is a claim about tuning, and it connects directly to lesson 1 of this course: a keyboard tuned so that every key is usable. It is not, however, a claim about equal temperament. Well-tempered tunings of the period still left the keys sounding subtly different from one another, which was considered a feature.

Common misconceptions

• Palestrina did not save polyphony from the Council of Trent. The council's 1562 decree asked for intelligible words and no impurity; it did not propose banning polyphony, and the rescue story appears only long afterwards.
• Gregorian chant is not slow and solemn by nature. It has no fixed metre at all, so its pace follows the Latin text. The heavy, even, drawn-out delivery many people expect is a nineteenth-century performing style.
• Well-tempered does not mean equally tempered. Bach's title means every key is playable, not that every key sounds identical, and the difference was part of the appeal.
• Early polyphony was not primitive harmony. A fourteenth-century cadence on a bare fifth is not a triad with a missing note; thirds were genuinely heard as unstable, so the ending is doing what its listeners expected.
• Basso continuo is not a written-out accompaniment. The player reads a bass line and numbers and invents the chords in real time, so two performances of the same piece differ in the middle of the texture.

Try it: place five sounds in order

1. You hear voices singing one melody, no accompaniment, no steady beat. What is the texture and roughly what period? Answer: monophony, and it could be chant from any century, since the repertoire was sung continuously for well over a thousand years.

2. You hear a very long held note underneath rapid, patterned upper voices. What are you hearing and where does the held note come from? Answer: Notre Dame organum. The held note is a syllable of the original chant, stretched out.

3. You hear four voices entering one after another with the same tune, then continuing independently. Name the device and a composer associated with it. Answer: a point of imitation, associated with Josquin des Prez and the Renaissance generally, and later grown into the fugue by Bach.

4. You hear a single singer, a cello and a harpsichord, with the harpsichord playing chords that are not in the printed score. What is the harpsichordist reading? Answer: a figured bass, that is a bass line with numbers indicating the intervals to be filled in above it.

5. An orchestral block returns five times in a movement, shortened and in different keys, with violin solos between the returns. Name the form and the difference from a rondo. Answer: ritornello form. Unlike a rondo refrain, the returns are usually partial and often away from the home key until the final one.

6. A friend says a bare fifth at the end of a Machaut phrase is a mistake by an early composer who did not yet understand chords. What do you say? Answer: that the third was heard as unstable in the fourteenth century, so a fifth was the stable, finished sound. The ending is not an incomplete triad; it is a complete cadence by the standards in use.

What to carry forward

Eight hundred years in one sentence each. Chant is one line, free in rhythm, modal. Organum adds a second voice, first as a parallel shadow and then, at Notre Dame around 1200, as independent parts over a stretched chant. Machaut composes a whole Mass as a single made object. Josquin builds music out of points of imitation. Palestrina perfects that style and acquires a legend he did not need. Around 1600 the words take command, recitative is invented, opera follows, and basso continuo becomes the engine room of European music for a hundred and fifty years. Vivaldi builds concerto movements out of returns. Bach turns imitation into the fugue and writes in every key.

In short: the whole story is about how many independent things can happen at once, and who is in charge when they do. Chant has one. Organum has two, then four. The Renaissance has four equals. The Baroque has one melody in charge with a bass and improvised chords underneath, and then Bach, almost out of time, makes four equals do it again.

Sources

1. Hamm, C., and Hughes, B. (n.d.). Texture. In Open Music Theory (2nd ed.). VIVA Open Publishing. viva.pressbooks.pub
2. Hughes, B., and Hamm, C. (n.d.). Figured bass. In Open Music Theory (2nd ed.). VIVA Open Publishing. viva.pressbooks.pub
3. Palestrina, G. P. da. (1567). Missa Papae Marcelli [score]. Reproduced by the International Music Score Library Project. imslp.org
4. Bach, J. S. (1721). Brandenburg Concerto No. 3 in G major, BWV 1048 [score]. Reproduced by the International Music Score Library Project. imslp.org
5. Taruskin, R. (2010). The Oxford History of Western Music, Volume 1: Music from the Earliest Notations to the Sixteenth Century. Oxford University Press. (Unlinked: the source for the reception history of the Palestrina legend.)

An album entry, Bonn, autumn 1792

A twenty-one-year-old viola player from Bonn is about to leave for Vienna. Friends sign his album, and one of them, Count Ferdinand von Waldstein, writes that he hopes the young man will receive the spirit of Mozart from Haydn's hands. Mozart had died ten months earlier. Haydn was sixty and the most celebrated composer in Europe. The viola player was Ludwig van Beethoven, and the lessons with Haydn did not go especially well.

Those three names get bundled together as the Classical period, which suggests a single sound written by three interchangeable men. They were not interchangeable. They were paid differently, wrote for different rooms, and left the forms of music in a different state from the one in which they found them. This lesson sets the three beside each other and reads the differences.

What the style actually sounds like

Before the people, the sound. Put the Bach of the last lesson next to any of these three and four differences jump out.

The typical accompaniment figure is worth naming because you will hear it in hundreds of pieces. An Alberti bass takes a triad and plays it low, high, middle, high, over and over. In C major that is C, G, E, G. It keeps the harmony sounding and the rhythm moving without ever competing with the tune. Try it on any keyboard and the period arrives instantly.

Haydn: thirty years on a payroll

From 1761 Haydn was employed by the Esterházy princes, first as deputy and then as director of music, at a palace in what is now Hungary. He wore a uniform. He was contractually the prince's servant. He also had a permanent orchestra, a theatre, singers, and an employer who wanted new music constantly.

Haydn later said that being cut off from the rest of the world forced him to become original, and the output supports him: more than a hundred symphonies and about seventy string quartets, most of them written to be tried out within days. When he published the six quartets of Opus 33 in 1781 he advertised them as written in a new and special manner, and the claim holds up: instead of a first violin tune with three accompanists, the four instruments pass fragments of the same idea between them.

When Prince Nikolaus died in 1790 his successor dismissed the orchestra, and Haydn, suddenly free at fifty-eight, went to London and wrote the twelve symphonies that made him rich. His last large works, including The Creation of 1798, were written for a public that bought tickets rather than for a prince.

Mozart: the freelance experiment

Mozart spent his childhood being exhibited across Europe by his father and his early twenties in a job he hated in Salzburg. In 1781 he quarrelled with his employer, was dismissed, and stayed in Vienna as a freelance: concerts he promoted himself, pupils, publications and commissions.

The piano concerto is the form that career produced. Mozart wrote most of his twenty-seven concertos for concerts he organised and played in himself, which is why they are showpieces with a dramatic structure: the orchestra states the material, the soloist enters and argues with it, and near the end everything stops for a cadenza the soloist improvises. The minor-key Piano Concerto No. 20 in D minor, first played in 1785, is the one to hear first.

His operas are the other half. Le nozze di Figaro of 1786, Don Giovanni of 1787 and Die Zauberflöte of 1791 do something new: the music carries the plot forward while it is happening, with several characters singing different things at once and meaning different things by them. Mozart died in December 1791, aged thirty-five, leaving his Requiem unfinished; his pupil Franz Xaver Süssmayr completed it, and arguments about which bars are whose have never stopped.

Beethoven: the freelance experiment, working

Beethoven arrived in Vienna in 1792 and never held a court post. He was supported instead by a group of aristocrats who, from 1809, paid him an annual sum simply to stay in Vienna and compose what he liked. That arrangement, patronage without employment, is the hinge between the servant-composer and the modern artist.

The other decisive fact is his hearing. From about 1798 it began to fail. In October 1802, staying in the village of Heiligenstadt, he wrote a letter to his brothers, never sent, describing his despair and his decision to go on living for the sake of his art. The Heiligenstadt Testament was found among his papers after his death. Within a year he was writing the Third Symphony.

The Eroica, composed in 1803 and first performed publicly in 1805, is nearly twice the length of a typical Haydn symphony and changes what a symphony is for. His pupil Ferdinand Ries reported that the title page originally carried Napoleon's name and that Beethoven scratched it out in a rage when Napoleon declared himself Emperor in 1804. The story comes from Ries rather than from Beethoven, and the surviving title page is indeed damaged. Listen to the first movement in a public-domain recording on Wikimedia Commons and follow it with the score on IMSLP: two chords, then a theme built from a plain E flat triad, and then a development section longer than some entire earlier symphonies.

By the Ninth Symphony, premiered at the Kärntnertortheater in Vienna on 7 May 1824, he was profoundly deaf and had put four vocal soloists and a chorus into the finale of a symphony, which no one had done. He had to be turned round to see the applause.

The three side by side

Read the bottom row across. That progression, invent, perfect, stretch, is the actual content of the phrase Classical period, and it happened inside about sixty years in one city.

One test case: the minuet becomes a scherzo

You already know the minuet slot: third movement, ternary, a dance in three. Haydn kept the name and raised the tempo until dancing was impossible. Beethoven kept the metre and the ternary shape, renamed it scherzo, meaning joke, and used it for music that is often not funny at all: driving, loud, rhythmically disruptive.

The Fifth Symphony of 1808 goes further. Its scherzo does not finish. It sinks to near silence over a held note and a soft drum pulse, and then grows straight into the finale without a break, so that the triumphant C major arrives as a release from the C minor that came before. Two movements have been welded into one dramatic event. Haydn would have recognised every technique and would not have written that paragraph.

Common misconceptions

• Classical is not a synonym for old or serious music. Used precisely it names the style of roughly 1750 to 1820. A Vivaldi concerto is Baroque and a Brahms symphony is Romantic, and calling either Classical loses the distinction.
• Mozart did not compose everything effortlessly in finished form. Surviving sketches and abandoned drafts show him working, and the myth of flawless dictation comes largely from a letter that scholars have long regarded as a forgery.
• Beethoven did not go deaf suddenly at the end of his life. The loss began around 1798, when he was in his late twenties, and it was gradual, so most of his famous music was written by someone who was losing his hearing rather than by someone who had already lost it.
• Haydn was not called the father of the symphony because he invented it. Symphonies existed before him. The title records how thoroughly he standardised and developed the form over a hundred attempts.
• Beethoven did not simply dedicate the Eroica to Napoleon and then undedicate it. The one detailed account is his pupil Ries's, written decades later; the damaged title page is consistent with it but does not prove the scene.

Try it: attribute by evidence

1. A symphony's third movement is marked Menuetto but is played so fast that no one could dance it, and the composer worked for a prince. Who is most likely, and what is the movement turning into? Answer: Haydn, and the movement is on its way to becoming a scherzo.

2. A first movement is built almost entirely from a three-note rhythmic cell that appears in every section and in the accompaniment. Which composer, and why does that matter? Answer: Beethoven. Building a long movement from a tiny motive is how he generates scale without adding new tunes.

3. Four characters sing at once, each pursuing a different intention, and the plot advances while they do. Which composer and which genre? Answer: Mozart, in opera. The ensemble that carries the action forward is one of his central achievements.

4. A piece has a left hand playing C, G, E, G repeatedly under a right-hand tune. Name the device and roughly date the style. Answer: an Alberti bass, typical of the Classical period, roughly 1750 to 1820.

5. Why does Beethoven's financial arrangement after 1809 matter to the history of music, not just to his bank account? Answer: because he was paid to compose whatever he wished rather than to supply music on demand, which shifts the composer from employee to independent artist and changes what a piece is expected to be.

6. A friend says the Classical period sounds all the same. Give two concrete counter-examples from this lesson. Answer: any two of: Haydn's Opus 33 quartets sharing material between four equal players, Mozart's D minor concerto with a soloist arguing against the orchestra, and the Fifth Symphony's scherzo running without a break into its finale.

Pulling it together

The Classical style trades Baroque continuity for balance and contrast: four-bar phrases, a tune with a written-out accompaniment, slower harmonic rhythm, and opposition built into a single movement. Haydn worked it out over thirty years on a salary with an orchestra at hand, and turned the symphony and the string quartet into forms other people could use. Mozart took the same materials into the theatre and the concert hall and made them dramatic, with several people meaning different things at once. Beethoven, paid to please nobody, stretched the same forms until a symphony could last fifty minutes, the third movement could stop being a dance, and the finale could contain a choir.

Why this matters: forms are shaped by the conditions people work in. Haydn wrote a hundred symphonies because a prince wanted new music every week. Mozart wrote concertos because he needed something to play at his own concerts. Beethoven wrote works that take an hour because nobody could tell him not to. When you meet a form you do not understand, ask who was paying, and for what.

Sources

1. Beethoven, L. van. (1806). Symphony No. 3 in E flat major, Op. 55 [score]. Reproduced by the International Music Score Library Project. imslp.org
2. Musopen Symphony Orchestra. (n.d.). Beethoven: Symphony No. 3, first movement [recording]. Wikimedia Commons. commons.wikimedia.org
3. Rosen, C. (1997). The Classical Style: Haydn, Mozart, Beethoven (expanded ed.). W. W. Norton. (Unlinked: the standard account of what the three composers share and where they part.)
4. Solomon, M. (1998). Beethoven (2nd rev. ed.). Schirmer Books. (Unlinked: the source used here for the Heiligenstadt Testament and the patronage contract of 1809.)

Two chords that do not go home

The prelude to Richard Wagner's Tristan und Isolde, composed between 1857 and 1859, begins with cellos alone rising a minor sixth and falling by step. Then the woodwind answer with a chord: F, B, D sharp, G sharp. It is dissonant, and by the rules you learned in Module 4 it should resolve. It does resolve, but only to another unstable chord, a dominant seventh, which then fails to resolve either. The phrase stops and the whole gesture starts again a step higher.

That chord has its own Wikipedia article and a century of analytical argument attached to it, and the reason is simple: the opera runs for about four hours and the harmony does not settle onto a stable tonic until the final minutes. Wagner had found a way to make unresolved tension the normal state of the music rather than an event inside it.

Fifty years later, in Vienna, Arnold Schoenberg stopped writing in keys at all. Whether that step was the inevitable consequence of what Wagner started, or a choice that could have gone otherwise, is a real disagreement among people who know the music well. This lesson lays out the century that produced the question, then puts the two answers side by side.

The piano becomes a character: Schubert, 1815

Franz Schubert set Goethe's ballad Erlkönig in 1815, when he was eighteen. The poem has a father riding through the night with a sick child who believes a supernatural king is calling him. One singer performs all four roles, narrator, father, child and king, distinguished by register and by harmony: the child's cries rise higher each time and land on dissonances, the king is smooth and in a major key, the father is low and steady.

The piano plays relentless repeated octaves in triplets for nearly four minutes, and they are the horse. When the last line announces that the child is dead, the piano stops. A recording made in 1913 by Ernestine Schumann-Heink is on Wikimedia Commons and is in the public domain. It is old and hissy, and it is still frightening.

The Lied, a German song for one voice and piano, is the small form at the centre of Romanticism. Schubert wrote over six hundred, and in Winterreise, twenty-four songs completed in 1827, the piano carries most of the meaning that the words leave out.

The orchestra becomes a novel: Berlioz, 1830

Hector Berlioz was twenty-six when his Symphonie fantastique was first performed in Paris in 1830, three years after Beethoven died. He supplied a printed programme: a young artist poisons himself with opium, dreams of the woman he loves, imagines murdering her, is executed, and attends his own witches' sabbath.

The musical device that holds it together is the idée fixe: one melody representing the beloved, which returns in every movement, transformed to fit the scene. In the ball it becomes a waltz. In the finale it becomes shrill and vulgar on a high clarinet. The tune is the same and its meaning has been inverted. The score is free on IMSLP, and the orchestra it asks for is enormous by 1830 standards, with four bassoons, two harps, cornets, and bells.

Two camps, 1850 to 1880

By mid-century the argument about where music should go had become public and bad-tempered. On one side, the New German School around Franz Liszt and Wagner held that instrumental forms had been used up by Beethoven and that music must now be attached to poetry, drama or a programme. On the other, the circle around Johannes Brahms and the critic Eduard Hanslick held that music means what its own structures do, and that a symphony needs no story.

Both sides wrote first-rate music, which is the most useful thing to notice about the quarrel.

Wagner's own solution to the problem of long-form drama was the leitmotif: short musical labels for people, objects and ideas, recombined and transformed so that the orchestra can tell you what a character is thinking while they say something else. Fifteen hours of the Ring cycle are held together that way. Every film score you have ever heard is descended from it.

Chromaticism, and why the tonic started disappearing

Under all this, one technical thing is happening. Chromaticism, the use of notes outside the key, keeps increasing. There is a clear line of development:

Claude Debussy supplies the 1894 row. His Prélude à l'après-midi d'un faune, first performed in December 1894, opens with an unaccompanied flute sliding down and back up through a tritone, the one interval that belongs to no key in particular. Debussy used the whole-tone scale, which has six equal steps and therefore no leading tone and no natural home. He is not abandoning tonality. He is refusing to let it push.

1913, and a disturbance in Paris

Igor Stravinsky's ballet The Rite of Spring was first performed at the Théâtre des Champs-Élysées in Paris on 29 May 1913. The audience made enough noise that the dancers could not hear the orchestra, and Vaslav Nijinsky had to shout counts from the wings.

What was new was mostly rhythm and sound, not the absence of keys. One famous chord in the second scene is an E flat seventh stacked on an F flat major triad, hammered in irregular groupings that displace the accent constantly. That chord is built out of ordinary tonal materials used in a way that cancels their function. Stravinsky spent the rest of his long career writing music with clear pitch centres.

The riot has been retold until it has become larger than the evidence. Contemporary reports describe uproar, whistling, shouting and some scuffles, and the work was performed several more times in the same season without a disturbance. Treat the famous version as a story that has been polished.

The dispute: was atonality necessary?

Between 1908 and 1909 Schoenberg wrote pieces with no key signature, no tonic and no functional cadences, including the Three Piano Pieces of his Opus 11. Around 1923 he supplied those pieces' successors with a new organising principle, the twelve-tone method: order all twelve chromatic pitches into a row and derive the whole piece from that row and its transformations. Here are the two positions on whether this had to happen.

Position one: it was the next step and someone had to take it. Schoenberg argued that dissonance and consonance differ in degree rather than kind, that the ear had been absorbing steadily more dissonance for two centuries, and that by 1908 the remaining triadic conventions were a polite fiction. He called the change the emancipation of the dissonance. The supporting evidence is specific: the Tristan prelude, which withholds a stable tonic for minutes at a time; the late works of Liszt, some of which end without a tonic chord; Mahler's habit of ending a symphony in a different key from the one it started in. On this account, tonality was a resource being consumed, and it ran out.

Position two: tonality was not exhausted, and the break was a local decision. The evidence here is what other composers did with the same inheritance. Stravinsky, Béla Bartók and Jean Sibelius all wrote demonstrably new music in the twentieth century that keeps audible pitch centres. Bartók built harmony from Hungarian and Romanian folk modes he collected on wax cylinders from 1906 onwards, which is a different escape route from the same corner. Meanwhile the blues, jazz and everything descended from them expanded tonal harmony enormously, and the next two lessons are about that. On this account, a small group in Vienna, working within a strong belief in historical progress, mistook their own artistic problem for a law of history.

What would settle it? Not a list of great works, because both sides have one. Three kinds of evidence bear on it. First, whether listeners can actually perceive the structures that twelve-tone organisation provides: experimental work on this has generally found that untrained and even trained listeners do not reliably hear row relationships, which weakens the claim that the method replaced tonality's job. Second, whether exhaustion is a property of a musical system at all, or a description of one generation's sense of its own options. Third, the plain historical fact of what happened next: concert audiences did not follow, while tonal music went on being written continuously, and by the 1970s a good many composers who had been trained in serialism were writing with keys again.

The point: you do not have to decide. You do have to notice that the sentence tonality collapsed describes a historical narrative and not a physical event, and that whether you accept it changes which twentieth-century music looks central and which looks peripheral.

Common misconceptions

• Atonal does not mean random or unstructured. Schoenberg's twelve-tone pieces are among the most tightly organised music ever written; what they lack is a tonic, not a system.
• The Rite of Spring is not atonal. It is rhythmically radical and harmonically harsh, and it is built from stacked triads and sevenths with audible centres.
• Debussy did not abandon tonality. He kept the chords and removed their obligations, using harmony as colour rather than as a chain of forces pulling toward a tonic.
• The Paris premiere was a disturbance, not a full riot with arrests. The repeated telling has added detail that the contemporary reports do not support.
• Brahms and Wagner were not conservative versus progressive in any simple sense. Schoenberg himself wrote an essay arguing that Brahms was the true progressive, on the grounds of how densely he developed his material.

Try it: argue both sides in writing

1. In one sentence each, state the strongest version of both positions on whether atonality was necessary. Answer: that dissonance had been increasing for two centuries until the triadic conventions no longer did any work, so someone had to take the step; and that the same inheritance produced Bartók's modal harmony, Stravinsky's pitch centres and the whole of jazz, so the step was one option among several.

2. Which piece of evidence in this lesson most damages position one, and why? Answer: the listening research indicating that row relationships are not reliably perceived, because position one claims the twelve-tone method took over an organising job that the ear needs done.

3. Which piece of evidence most damages position two? Answer: the Tristan prelude and the late Liszt pieces, which show the dissolution well under way decades before Schoenberg and inside the central tradition rather than at its edges.

4. A friend says the Tristan chord is simply a half-diminished seventh, so there is nothing special about it. Respond. Answer: the chord's identity is not the point; what matters is that it resolves onto another unstable chord, so the expected release never comes, and that pattern is sustained for hours.

5. How is Berlioz's idée fixe different from a Wagnerian leitmotif? Answer: the idée fixe is one melody returning across a symphony in altered guises; leitmotifs are a whole vocabulary of short labels, woven and combined continuously so that the orchestra comments on the drama in real time.

6. Why does the phrase tonality collapsed need care? Answer: because it names a narrative about historical necessity, not an observed event. Tonal music continued to be written throughout the period in which tonality is said to have collapsed.

Where this leaves us

The Romantic century did two things at once. It made music personal and literary: the Lied, the programme symphony, the leitmotif, the recital built around a virtuoso. And it steadily loosened the grip of the key, from Schubert's borrowed chords to Wagner's suspended resolutions to Debussy's whole-tone colour. Around 1910 that loosening reached a point where two different futures were available. Schoenberg took one and organised it with the twelve-tone method. Stravinsky, Bartók and almost everyone outside the concert tradition took the other and kept audible centres while changing nearly everything else.

The core of it: the interesting question is not who was right. It is that a technical development, chromatic harmony, reached a point where reasonable people drew opposite conclusions about what had to happen next, and that both conclusions produced music still being played. Hold that, and the twentieth century stops looking like a wrong turn and starts looking like a fork.

Sources

1. Peterson, J., et al. (n.d.). Basics of twelve-tone theory. In Open Music Theory (2nd ed.). VIVA Open Publishing. viva.pressbooks.pub
2. Peterson, J., et al. (n.d.). History and context of serialism. In Open Music Theory (2nd ed.). VIVA Open Publishing. viva.pressbooks.pub
3. Berlioz, H. (1845). Symphonie fantastique, H 48 [score]. Reproduced by the International Music Score Library Project. imslp.org
4. Schumann-Heink, E. (1913). Erlkönig, by Franz Schubert [recording]. Victor Talking Machine Company. Wikimedia Commons. commons.wikimedia.org
5. Taruskin, R. (2010). The Oxford History of Western Music, Volume 4: Music in the Early Twentieth Century. Oxford University Press. (Unlinked: the source for the reception history of the 1913 premiere and for the critique of the exhaustion narrative.)

A guitar played with a knife, Tutwiler, Mississippi

In his 1941 autobiography, the bandleader and publisher W. C. Handy described waiting for a delayed train at Tutwiler, Mississippi, some time around 1903, and watching a man press a knife blade against the strings of a guitar while he sang, repeating one line three times. Handy, a trained musician who read and wrote music, said it was the strangest music he had ever heard.

He went on to publish Memphis Blues in 1912 and St. Louis Blues in 1914, putting on paper a music that had been passed hand to hand and unwritten. That act, writing it down and copyrighting it, is where the recorded history of the blues starts, and it is also the first appearance of a pattern that repeats through this lesson: Black American musicians invent a music, and the money is made somewhere else.

This lesson follows one line from that railway platform to a New York studio in 1959, and the features you will meet along the way, blue notes, call and response, swing, improvising over a fixed harmonic frame, are the foundation of most popular music made since.

What makes the blues the blues

You met the twelve-bar form in lesson 10. Here is the rest of the toolkit.

The blue third is the one to understand first. On a piano you approximate it by playing E flat against a C major chord, which is why the blues scale contains a flat third over a major chord, a combination that would have been an error in every style before it. In the voice or on a guitar the note is not fixed at all; it lives somewhere between E flat and E natural and moves while it sounds.

1920: the record industry discovers there is a market

On 14 August 1920 Mamie Smith recorded Crazy Blues for Okeh Records, the first blues record by a Black singer. It sold far beyond anything the label expected; the often-repeated figure of a million copies in the first year is hard to verify, but the commercial effect is not in doubt. Every label immediately began recording Black artists for a market they then labelled race records, a category that existed until 1949.

The 1920 recording is on Wikimedia Commons, in the public domain. Play it and listen past the surface noise for two things: the singer's phrasing behind the beat, and the clarinet answering her at the end of every line.

Bessie Smith, 1923

Bessie Smith made her first record, Downhearted Blues, for Columbia in 1923. She was twenty-nine, had been performing since her teens, and became the highest-paid Black entertainer in the United States. Listen to the public-domain transfer on Wikimedia Commons and notice how little she does: the tempo is slow, the notes are few, and almost every line is shaped by sliding into a pitch and then leaning on it.

Two years later she recorded St. Louis Blues with a young cornet player named Louis Armstrong. That 1925 recording is also public domain, and it is the clearest demonstration of call and response you will find: she sings a line, he answers it, and the answer is never the same twice.

New Orleans, and who got recorded first

Jazz came together in New Orleans in the first two decades of the century out of blues, ragtime, brass band music, church music and dance music. Its early ensemble style is collective improvisation: cornet carries the tune, clarinet weaves a decorated line above it, trombone slides underneath, and a rhythm section keeps time. All three front-line instruments improvise at once, which is why an early jazz record sounds busy in a way that a later solo does not.

The first jazz record commercially released was Livery Stable Blues, recorded in February 1917 by the Original Dixieland Jass Band, five white musicians from New Orleans. The recording is on Wikimedia Commons. It is worth hearing both as music and as evidence: the players who created the style were not the players the industry recorded first.

Armstrong is the musician who changed what jazz was for. In his Hot Five and Hot Seven recordings of 1925 to 1928 the collective texture gives way to the individual solo, and the soloist becomes the point of the record. West End Blues, recorded in 1928, opens with an unaccompanied trumpet cadenza of about twelve seconds that trumpet players have been learning by heart ever since.

Swing: the rhythm, and the era named after it

Written jazz looks like pairs of eighth notes. Played jazz turns them into something closer to a long note followed by a short one, roughly in the ratio of two to one, so that each pair leans forward.

That unevenness, plus a rhythm section that keeps the pulse steady while the soloist plays across it, is what musicians mean by swing. It cannot be notated exactly and is not meant to be: the exact ratio changes with tempo and with the player.

In the 1930s the big bands made swing the popular dance music of the United States, with fifteen or more players arranged in sections of saxophones, trumpets and trombones, reading written arrangements and leaving holes for solos. Duke Ellington, whose orchestra held a residency at the Cotton Club in Harlem from December 1927, is the composer who used that ensemble best: he wrote for the specific players he had, so that a passage was not scored for three saxophones but for those three saxophonists. Mood Indigo, from 1930, gets its strange sound from an unusual combination of muted trumpet, muted trombone and low clarinet. Billy Strayhorn, his writing partner from 1939, wrote the band's theme, Take the A Train, in 1941.

What a jazz performance actually is

Strip away the style and the structure is simple and consistent.

1. The head. The tune is played once through, usually in a thirty-two-bar AABA or a twelve-bar blues.
2. The changes. The chord sequence of that tune is now repeated as many times as needed. One pass is called a chorus, which in jazz means a full cycle of the form rather than the section of a song.
3. The solos. Each soloist improvises over the changes for one or more choruses, while the rhythm section keeps the form and supplies chords.
4. The head again. The tune returns and the performance ends.

This is why jazz musicians talk about knowing tunes. Knowing a tune means knowing its chord sequence in any key, well enough to invent a melody over it in real time, and to hear where you are in the form without counting.

1945: bebop makes the changes the point

By the mid-1940s a group of younger players, among them the alto saxophonist Charlie Parker and the trumpeter Dizzy Gillespie, were playing at tempos and with a harmonic density that made bebop unusable for dancing. Small groups replaced big bands. Melodies became fast, angular and full of notes borrowed from outside the chord.

One habit is worth naming because it explains a lot of jazz repertoire. A contrafact is a new melody written over the chord sequence of an existing song. Parker's Ko-Ko, recorded in 1945, is built on the changes of the 1938 standard Cherokee. Writing a new tune over borrowed changes was partly artistic and partly economic: chord sequences are not protected by copyright, melodies are.

1959: take the chords away

Bebop had pushed harmony so far that a soloist might face two chord changes per bar. Miles Davis, who had played in Parker's band as a teenager, went the other way. On Kind of Blue, recorded in two sessions in 1959 and released that August, the material is a handful of scales rather than a sequence of chords.

So What, the opening track, is a thirty-two-bar AABA form, but each A section is sixteen bars of one scale, D dorian, and the B section is eight bars of the same scale a semitone higher, on E flat. Two scales in five minutes. The soloist is no longer being carried from chord to chord; they have to make the interest themselves out of melody, rhythm and space. That is modal jazz, and Kind of Blue has remained one of the best-selling jazz albums ever made.

The band on that record is worth knowing by name: Davis on trumpet, John Coltrane on tenor saxophone, Julian Adderley on alto, Bill Evans and Wynton Kelly on piano, Paul Chambers on bass and Jimmy Cobb on drums. Much of it was recorded on first takes from sketches rather than from full arrangements.

Common misconceptions

• Improvising is not making it up with no rules. A soloist is tracking a fixed form and a known chord sequence, in time, and choosing notes that fit or deliberately do not. It is closer to speaking a language than to guessing.
• Blue notes are not simply flattened thirds and sevenths. In the voice and on a guitar the pitch is unfixed and often moves during the note, which is why a piano can only approximate the effect.
• The first jazz record was not made by the musicians who created the style. The 1917 Original Dixieland Jass Band session recorded a white group playing a Black New Orleans idiom, and the recording industry followed that pattern for years.
• A chorus in jazz is not the catchy section of a song. It means one complete pass through the form, so a player taking three choruses has played the whole sequence three times.
• Modal jazz is not easier than bebop. Fewer chords means less scaffolding, so the soloist has to generate the shape of the solo from melody and rhythm rather than from the harmony moving underneath.

Try it: read a performance

1. A recording runs: tune played once, piano solo, saxophone solo, tune again. Name the four parts in the standard vocabulary. Answer: head, solo choruses, more solo choruses, head out.

2. A soloist says they took four choruses on a twelve-bar blues. How many bars did they play? Answer: forty-eight, because a chorus is one full pass through the twelve-bar form.

3. A tune has a new melody but the same chord sequence as a 1930s standard. What is it called, and why were so many written? Answer: a contrafact. Melodies are protected by copyright and chord sequences are not.

4. In So What, what changes at the bridge? Answer: the scale moves up one semitone, from D dorian to E flat dorian, and after eight bars it moves back.

5. Why is the seventh on a blues I chord not an error, when the same chord in a Mozart symphony would demand resolution? Answer: because blues treats the seventh as a stable colour rather than as a tension, which is a genuine difference of grammar, not a mistake.

6. Listen to the 1925 Bessie Smith and Louis Armstrong recording and describe in one sentence what Armstrong is doing. Answer: he is answering each sung line with a different improvised phrase, which is call and response between a singer and an instrument.

What you now know

The blues supplied a text form, a set of pitch practices, a harmonic grammar in which sevenths are stable, and a habit of answering every phrase. Recording it from 1920 turned it into an industry. In New Orleans those materials combined with ragtime and brass band playing into jazz, where the collective texture of the 1910s gave way, through Armstrong, to the individual solo. Swing rhythm and the big band made it popular music; bebop made it a listener's art with dense harmony at speed; and in 1959 Kind of Blue took most of the chords away and left the soloist with two scales and a great deal of responsibility.

So what?: almost every feature of the popular music in the next lesson comes from this one. The backbeat, the bent note, the twelve-bar form, the rhythm section, the solo, the idea that a performance can differ from the written version and be better for it. Whatever you listen to, you are listening to the consequences of what happened between that Mississippi railway platform and a New York studio in 1959.

Sources

1. Smith, B. (1923). Downhearted Blues [recording]. Columbia. Wikimedia Commons. commons.wikimedia.org
2. Smith, B., and Armstrong, L. (1925). The St. Louis Blues [recording]. Columbia. Wikimedia Commons. commons.wikimedia.org
3. Shaffer, K., et al. (n.d.). Blues harmony. In Open Music Theory (2nd ed.). VIVA Open Publishing. viva.pressbooks.pub
4. Shaffer, K., et al. (n.d.). Swing rhythms. In Open Music Theory (2nd ed.). VIVA Open Publishing. viva.pressbooks.pub
5. Handy, W. C. (1941). Father of the Blues: An Autobiography. Macmillan. (Unlinked: the source of the Tutwiler account, told by Handy himself decades after the event.)

A record nobody ever played

Good Vibrations was released as a single on 10 October 1966. Brian Wilson had worked on it for about seven months across four Los Angeles studios, recording short sections separately and then splicing the tape together into a running order. Reported costs run into tens of thousands of dollars, which for a single in 1966 was unheard of. The figure is an estimate, but the method is not in dispute: the record was assembled, not performed.

So here is the problem this lesson works. If no performance of Good Vibrations ever took place, who performed it? And if the answer is nobody, what exactly is the musical work: the song, the tape, or the decisions?

The question is not a riddle. Answering it will tell you what a producer does, why hip-hop is composition rather than collage, and what changed between a band in a room in 1955 and a fifteen-year-old with a laptop today.

Step one: rock and roll, and the room

Start where the recording is still a document. In 1951 a band led by Ike Turner drove to Memphis and recorded Rocket 88, released under the name of its singer Jackie Brenston. The guitar amplifier had been damaged in transit and buzzed; the engineer stuffed it with paper and recorded it anyway. That distortion, an accident nobody could have notated, is part of why the record is remembered.

Rock and roll came out of rhythm and blues, with country, gospel and boogie-woogie piano feeding in. Sister Rosetta Tharpe had been playing electric guitar with gospel repertoire and a heavy backbeat since the late 1930s. Chuck Berry put a country storytelling style over twelve-bar blues and wrote lyrics about teenagers, cars and school; Johnny B. Goode, from 1958, opens with a guitar figure that thousands of players have learned as their first real lick.

The industry's habit here matters. Songs first recorded by Black artists were routinely re-recorded by white artists for a wider market, and the cover version often outsold the original while the writer got the smaller share. The pattern from the last lesson repeats.

Step two: the rhythm moves

Three changes in where the emphasis sits define three styles. This is the most useful table in the lesson, and it is worth clapping while you read it.

James Brown's change is the sharpest. From about 1965 his bands played music in which the harmony barely moves for minutes at a time while guitar, bass, drums and horns lock into separate repeating figures that only line up on the first beat of the bar. Melody and chord progression stop being the carriers of interest. Rhythm becomes the content. Everything from disco to hip-hop to most of what is in the charts this week is downstream of that decision.

Step three: soul, and two house bands

Soul is what happens when gospel singing meets rhythm and blues. Ray Charles is usually given the pivotal role for taking the vocal style and structure of church music into secular songs in the mid-1950s, which scandalised some listeners at the time. Aretha Franklin, a preacher's daughter who had been singing in church since childhood, is the voice the style is measured against.

Two companies shaped the sound, and comparing them teaches something about production.

Same era, same country, same basic materials. The difference is the process, which is the first piece of the answer to the opening question.

Step four: the tape machine becomes an instrument

Until the 1950s a record was one performance captured at once. Multitrack recording ended that. Tape is divided into parallel tracks that can be recorded at different times and mixed afterwards, so a musician can play a part, listen back, and add another against it. Les Paul was building records out of stacked guitar and vocal parts in the early 1950s; by 1966 four and eight track machines were normal in professional studios, and by the mid-1970s twenty-four tracks were.

Four consequences follow immediately, and all four are still true:

• Overdubbing. One person can be a whole band. The performance no longer has to exist in one place at one time.
• Editing. A record can be assembled from the best fragments, which is exactly what Good Vibrations was.
• Mixing. Balance becomes a decision made afterwards rather than a matter of where people stood.
• The studio as instrument. Reverb, echo, tape speed, backwards playback and distortion become compositional choices, not faults.

The job of record producer expands into this space. George Martin, a trained musician, scored strings, spliced tape and suggested structures for the Beatles. Phil Spector built the Wall of Sound by doubling and tripling every instrument in one room and drowning the result in echo. By 1966 the producer is not a supervisor. The producer is an author.

Step five: 1973, a recreation room in the Bronx

On 11 August 1973 Clive Campbell, who performed as DJ Kool Herc, played a party in the recreation room of 1520 Sedgwick Avenue in the Bronx. He noticed that dancers responded most to the break: the few bars in a funk record where the singing and most instruments drop out and the drums carry on alone. So he bought two copies of the same record, cued both to the break, and cut back and forth between the turntables to extend those few seconds indefinitely.

That technique makes a new piece of music out of a fragment of an old one. It requires no notation, no instrument in the usual sense, and an extremely precise sense of time. Grandmaster Flash refined it with the technique of marking the record and keeping the beat matched by hand.

The most reused fragment in this history is the Amen break: about seven seconds of drums played by Gregory Coleman on Amen, Brother, a 1969 B-side by the Winstons. It has been sampled on thousands of records and is the rhythmic basis of entire genres. Coleman died in poverty and the group received nothing for decades.

Step six: samplers, and the law

When digital samplers arrived in the 1980s the break could be captured, looped, pitched and triggered from pads. The Akai MPC, designed with Roger Linn and first released in 1988, put sampling and a drum sequencer in one box and became the standard instrument of hip-hop production. The Roland TR-808 drum machine, a commercial failure in 1980, became the sound of hip-hop and dance music because it was cheap secondhand and its kick drum could be tuned to a long, booming note.

Then the law arrived. In 1991 a federal court in Grand Upright Music v. Warner Bros. ruled against a producer who had used an uncleared sample, and opened the judgment by quoting the commandment against stealing. In 2005 the Sixth Circuit, in Bridgeport Music v. Dimension Films, held that even a two-second altered guitar sample required a licence. Clearing samples became expensive and slow, and the dense collage style of the late 1980s became commercially impossible for anyone without a major label's legal budget. Producers moved toward fewer, bigger samples, or toward playing the parts themselves.

Step seven: the laptop

A digital audio workstation puts multitrack recording, sampling, editing, synthesis and mixing in one program. Two of its features are musical decisions disguised as buttons.

Quantisation snaps recorded notes onto an exact grid. Set to one hundred per cent it removes every timing imperfection, including the ones that made the groove. Most producers therefore quantise partially, or nudge notes deliberately late to get a laid-back feel, which is a modern way of doing what a drummer does by ear.

Auto-Tune, released by Antares in 1997, corrects pitch. Set gently it hides small errors. Set to its fastest retune speed it produces the hard, stepped vocal sound first made famous on Cher's 1998 single Believe, and used since as an instrument in its own right by a great many artists. The tool was built to fix a fault and became a timbre.

So who performed Good Vibrations?

Here is the answer the lesson has been building. Musicians played every sound on it, and no one performed the record, because the record is not a performance. It is a designed object whose author is the person who chose the sections, the order, the balance and the effects.

That is not a modern betrayal of real music. It is the same shift that happened when Guido ruled lines on a page in 1026: a new technology changed what could be fixed, transmitted and worked on. Notation let a composer write music no one could improvise. Recording lets a producer build music no one could play. In both cases the work moves out of the moment of performance and into an object.

Why this matters: it settles the argument about whether a producer is a musician. If composing means deciding which sounds occur in which order with what weight, then arranging drums on a grid at two in the morning is composing, and the fact that no one played a violin is beside the point.

Common misconceptions

• Sampling is not simply copying. A producer chooses a fragment, pitches it, cuts it, filters it, places it against a new tempo and builds a structure around it. The legal question and the musical question are different questions.
• Rock and roll was not invented in 1955 by one person. It emerged from rhythm and blues, gospel, country and boogie-woogie over years, and the earliest records usually named as candidates are disputed among historians.
• Auto-Tune is not only used to fix bad singers. Used gently it is invisible on nearly every commercial vocal, and used extremely it is an audible instrument chosen on purpose.
• The backbeat did not begin with rock and roll. Snare emphasis on beats 2 and 4 was already present in gospel and rhythm and blues; rock and roll made it louder and put it on every record.
• Quantising everything does not make a track tighter. Perfect timing removes the small deviations that produce groove, which is why producers quantise partly or shift notes off the grid deliberately.

Try it: diagnose four records

1. A track has one chord for three minutes, a guitar playing a scratchy one-bar figure, a bass line that lands hard on beat 1, and horns punching offbeats. Which style, and what is carrying the interest? Answer: funk, and rhythm is carrying it, not harmony or melody.

2. A 1965 single has strings, tambourine, layered backing vocals and an unusually bright mix. The players are not credited. Which label is likely? Answer: Motown, whose house band went uncredited for years and whose records were mixed to sound good on a car radio.

3. A hip-hop track from 1988 contains more than a dozen recognisable fragments of other records. Why would it be hard to release now? Answer: because after the 1991 and 2005 rulings each fragment needs a licence, so the cost and the legal work make dense collage impractical.

4. A producer records a drummer, then moves every hit exactly onto the grid, and the track sounds worse. What happened, and what should they try? Answer: the small timing deviations that created the groove have been removed. They should undo it and quantise partially, or move only the worst hits.

5. Somebody says a song made entirely from samples is not really composed. Give the strongest argument against them. Answer: composing is choosing which sounds occur when, in what order, at what pitch and with what weight. Every one of those choices is made when a track is built from samples, and none of them is made by the original records.

The takeaway

Rhythm and blues fed rock and roll, which put a hard backbeat on beats 2 and 4. Soul added gospel singing, and two house bands in Detroit and Memphis showed how much of a record's identity comes from its process rather than its notes. James Brown moved the weight to beat 1 and made rhythm the content. Multitrack tape turned a record from a captured performance into a built object, and the producer from a supervisor into an author. In 1973 a DJ in the Bronx made new music out of the drum break of an old record, samplers industrialised the technique, and two court rulings changed what was affordable. Today a laptop contains all of it, and its two most ordinary tools, quantisation and pitch correction, are musical decisions you have to make on purpose.

Bottom line: every technology in this lesson did the same thing. It moved a choice that used to be made in the moment of playing into a choice that can be made, unmade and remade afterwards. That is more power and more responsibility, and it is why the last lesson of this course asks you to record something as well as write it.

Sources

1. Shaffer, K., et al. (n.d.). Drumbeats. In Open Music Theory (2nd ed.). VIVA Open Publishing. viva.pressbooks.pub
2. Shaffer, K., et al. (n.d.). Rhythm and meter in pop music. In Open Music Theory (2nd ed.). VIVA Open Publishing. viva.pressbooks.pub
3. United States Court of Appeals for the Sixth Circuit. (2005). Bridgeport Music, Inc. v. Dimension Films, 410 F.3d 792. (Unlinked: the opinion itself, which sets out the two-second sample holding.)
4. Chang, J. (2005). Can't Stop Won't Stop: A History of the Hip-Hop Generation. St. Martin's Press. (Unlinked: the standard account of the Bronx parties of 1973 and what followed.)

Two gamelans that cannot play together

A Javanese gamelan is a set of bronze gongs, metallophones and drums that is tuned as a single object. The tuner adjusts every instrument to match the others, and the result is a scale that belongs to that set alone. Take a metallophone from one gamelan and put it in another and it will be out of tune, even if both are tuned to the same named system.

Listen to a freely licensed recording in slendro and then to one in pelog, both on Wikimedia Commons. Try to write down what you hear on a staff. You cannot, and not because the music is difficult. The staff has no way to say a pitch that is a third of the way between two of its lines, and no way to say that the exact pitch is a property of one ensemble.

That is the subject of this lesson. Staff notation is an extraordinary invention, and it carries four assumptions that most of the world's music does not share. We will name them, then look at three traditions that do things differently, and finish with what each one keeps that the staff cannot record.

The four assumptions

1. Twelve fixed pitches per octave. Everything on the page is one of twelve names, and modern instruments are built to produce those twelve at standard frequencies.
2. Time as regular groups of two or three. Bar lines imply a repeating accent and a division you can conduct.
3. Harmony as the organising force. The page stacks simultaneous pitches vertically because chords are what hold Western music together.
4. The score is the work. A composer writes, a performer realises, and the written object is what is transmitted, taught and copyrighted.

Every one of those is a choice, and each one is contradicted somewhere in what follows.

India: a melody with rules, and a cycle instead of a bar

In Hindustani and Carnatic classical music, the melodic material is a raga. A raga is more than a scale. It specifies which notes are used going up and which coming down, which notes are stressed, which are approached from above or below, characteristic short phrases, and often a time of day or a mood. Two ragas can contain identical pitches and be different ragas because the rules of movement differ.

Underneath everything a tanpura plays a continuous drone, usually the tonic and the fifth. That drone is the reference point: there is no key change, so every note is heard in a fixed relation to one home pitch. This is why Indian classical music can afford microtonal inflection. The ear always has the tonic present for comparison. Theory describes twenty-two shrutis, intervals smaller than a semitone, and performers bend and shade pitches within the named notes constantly.

Time is organised as a tala, a repeating cycle of beats divided into sections. Teentaal has sixteen beats in four groups of four. Beat 1 is called sam and is the point of arrival: soloist and drummer can wander for a long time, and the pleasure for the audience is hearing them land together on sam. Beat 9 is khali, the empty one, marked by a wave of the hand rather than a clap, which tells a listener where they are in the cycle.

A performance is not written down and then played. A solo alap explores the raga slowly with no pulse at all, then a pulse enters, then composed material and improvisation alternate over the tala. Transmission is oral, from teacher to student over years. Listen to a short freely licensed sitar recording in raga Yaman and try to hear the drone under the melody rather than the melody over the drone.

Java and Bali: tuned as a set, structured by gongs

Gamelan uses two tuning systems. Slendro divides the octave into five roughly equal steps. Pelog has seven unequal steps, from which five are usually selected for a given piece. Neither maps onto Western semitones, and as the opening of this lesson said, neither has fixed frequencies.

The structure of a piece is colotomic, which means that the form is marked out by which gong sounds when. The largest gong marks the end of the longest cycle, smaller gongs and other instruments subdivide it, and everything is aimed at the stroke of the big gong. Notice the difference from Western metre: the emphasis falls at the end of a cycle, not the beginning. Western music counts one two three four and arrives on the next one. Gamelan aims at the gong.

Balinese playing adds kotekan: two parts, each with gaps, played by two players so that the combined result is a single stream of notes faster than either could play alone. The music that exists is the one neither player is playing.

Notation does exist, in the form of cipher numbers used in Javanese court manuscripts, but it functions as a memory aid and a record. It is not the object from which a performance is generated.

West Africa: several metres at once

In drumming traditions across West Africa, an iron bell plays a short repeating pattern that everyone else locates themselves against. One widespread figure occupies twelve pulses and places seven strokes among them. A public-domain rendering of that pattern is on Wikimedia Commons.

The twelve pulses can be felt as four groups of three or as three groups of four, and the ensemble deliberately uses both at once. That is cross-rhythm: not one metre with syncopation against it, but two metres both true at the same time. A Western analyst writing this in 6/8 or 4/4 has already chosen one and thrown the other away.

Read the diagram by following the blue marks with one hand and the green with the other. They coincide only at pulse 1. A drummer holds both, and a dancer's feet may take one while their arms take the other.

The Arab world: notes between the notes

The maqam system organises melody in a way that resembles raga: a set of notes plus rules about how a melody moves through them, with characteristic phrases and typical resting points. The pitch material, though, includes intervals that fall between the Western semitones. Maqam rast starting on C uses a third that lies roughly halfway between E flat and E natural.

Modern Arabic notation handles this by inventing new accidentals, a half-flat and a half-sharp, which is a straightforward extension of the staff. What the extension still cannot capture is that the exact size of that interval varies between regions and between performers, and that the variation is part of the style rather than an imprecision.

Rhythm is organised by iqa, cycles defined by a pattern of low and high drum strokes rather than by a count of accented beats.

The four traditions across

What matters here: the row that changes most is the last one. In three of these four columns the music is carried by people rather than by paper, which means a performance is not a version of something written but the thing itself.

What the staff is still very good at

None of this makes staff notation bad. It does a specific job extremely well: it stores exact pitch and exact duration for many simultaneous parts, so that a hundred players can realise a piece none of them has heard, and so that a work can survive its composer by centuries. No oral tradition can reconstruct a Mahler symphony from memory.

What it stores badly is everything that made the previous nineteen lessons hard to write down: exact timbre, microtonal shading, the swing ratio, the small timing deviations that create groove, and how loud is loud. Every one of those is left to the performer, which is why two recordings of the same score are different pieces of experience.

Common misconceptions

• Music without harmony is not simpler. Indian classical music has no chords and enormous melodic and rhythmic complexity, including improvisation inside rules that take years to learn.
• A raga is not a scale. Two ragas can use exactly the same pitches and remain different, because a raga specifies movement, emphasis and characteristic phrases as well as notes.
• Gamelan is not out of tune. Each set is tuned deliberately to itself, and the small differences between instruments produce the shimmer that is part of the intended sound.
• Cross-rhythm is not syncopation. Syncopation displaces accents within one metre, whereas cross-rhythm keeps two metres running at once and both are real.
• Oral transmission is not a failure to invent writing. Traditions that could have adopted notation often did not, because what they transmit includes things notation cannot hold.

Try it: identify the system from the clue

1. A performance begins with several minutes of unmeasured melody over a continuous drone, with no drum. Which tradition, and what is that opening called? Answer: Indian classical music, and the opening is the alap.

2. An ensemble's cycle ends on the stroke of the largest gong, and everything before it is subdivision. Which tradition, and what is the principle called? Answer: gamelan, and the principle is colotomic structure.

3. Two players each play a part full of gaps, and the audience hears a fast unbroken line neither is playing. Name the technique. Answer: kotekan, the Balinese interlocking style.

4. A bell repeats a seven-stroke figure over twelve pulses while dancers move in three and drummers play in four. Is this syncopation? Answer: no. Both metres are genuinely present, which makes it cross-rhythm.

5. A melody uses a note halfway between E flat and E natural, and the exact size varies from player to player. Which tradition, and how is it notated? Answer: Arabic maqam music, notated with an invented half-flat sign, which records the note but not the variation.

6. A friend says these traditions never developed notation because they were less advanced. What is wrong with that? Answer: several of them did develop notation and use it as a record or memory aid. What they transmit, including timbre, ornament and the relationship between teacher and student, is not what notation stores, so writing was never the point.

Summing up

Staff notation assumes twelve fixed pitches, metre in twos and threes, harmony as the organising force, and the score as the work. Indian classical music replaces harmony with a drone, allows continuous microtonal shading, and organises time as a cycle that everyone aims to land on together. Gamelan tunes each ensemble to itself in five or seven unequal steps and marks form with gongs at the ends of cycles rather than accents at the beginnings. West African ensemble drumming runs two metres at once against a bell pattern. Arabic maqam music uses intervals between the semitones whose exact size is part of the style. In three of the four, the music lives in people rather than on paper.

Worth holding on to: when you meet music that sounds wrong, the first question is not what rule it is breaking. It is which system it belongs to, and what that system is organised by. You have spent this course learning one very powerful set of tools. Knowing where its edges are is part of using it well.

Sources

1. Karawitan Marta Yogiswara. (2026). Ketawang Sekar Teja, slendro manyura [recording]. Wikimedia Commons. commons.wikimedia.org
2. Karawitan Marta Yogiswara. (2026). Ketawang Mijil Wigaringtyas, pelog nem [recording]. Wikimedia Commons. commons.wikimedia.org
3. Wikipedia contributors. (n.d.). Raga. Wikipedia. en.wikipedia.org
4. Sorrell, N. (1990). A Guide to the Gamelan. Faber and Faber. (Unlinked: the source used here for gamelan tuning practice and colotomic structure.)
5. Agawu, K. (2003). Representing African Music: Postcolonial Notes, Queries, Positions. Routledge. (Unlinked: the argument that transcribing a bell pattern into one Western metre discards information.)

Eight notes on a phone

Here is the exercise this whole lesson is built around. Someone plays a C major chord, then plays this melody twice at a moderate speed: C, D, E, G, E, D, C, C, with the last note twice as long as the others. Your job is to write it down.

Most people who have not trained hear that and freeze, because they try to measure each jump. What is the distance from D to E, and from E to G? Then they lose the melody while calculating and have to start again.

There is a better way, it is the way most working musicians actually hear, and it takes about fifteen minutes a day to build. The rest of this lesson is that method, worked end to end on this melody, then tested on a second one where a single change makes the naive approach fall over.

Two ways to hear a note

The interval method treats a melody as a chain of distances: up a step, up a step, up a minor third, down a minor third. It works, and it is how most apps teach, but it has two weaknesses. Errors accumulate, because one wrong interval throws off everything after it. And it discards the most useful information available, which is where each note sits in the key.

The scale-degree method treats every note as a number relative to the tonic. In C major, C is 1, D is 2, E is 3, G is 5. You hear each note against the key rather than against the note before it. An error does not propagate, because the next note is measured from the tonic, not from your mistake.

The reason the second method works is that your ear is already doing it. You met this in lesson 6: the leading tone pulls upward, the fourth degree leans down onto the third, the fifth feels open and stable. Those sensations are scale-degree recognition. Training is mostly a matter of learning to notice and name what you already feel.

Solfege puts a syllable on each degree: do, re, mi, fa, sol, la, ti. Use it in its moveable form, where do is always the tonic whatever the key. Numbers work equally well. What matters is that the label names the function, not the letter.

Where the reference-song trick stops helping

You have probably been told to learn intervals by attaching each to the opening of a familiar tune: a perfect fifth to the first two notes of the Star Wars main title, a minor third to the opening of Brahms's Lullaby, an octave to the first two notes of Over the Rainbow.

These work for a few weeks. Three problems then appear. Retrieving a song takes about a second, which is too slow for a melody at speed. Reference songs identify ascending intervals but rarely descending ones, so half the job is untrained. And an interval sounds different depending on where it sits in the key: the fifth from degree 1 up to degree 5 does not feel like the fifth from degree 2 up to degree 6, even though both are seven semitones.

Key idea: use reference songs as scaffolding in week one, and then move to scale degrees, because that is what the ear is actually organised around.

The procedure, worked

Do these steps in this order every time. The order is the method.

1. Establish the key. Before anything else, play or sing the tonic chord and then the scale up and down. Hum the tonic until you can find it without the instrument.
2. Get the rhythm first. Listen once without trying to hear pitch at all. Tap and count. Write the rhythm on a line with no noteheads.
3. Find the first and last notes. Sing the tonic, then sing the melody's first note, and work out its number. Do the same for the last note. These two anchor everything.
4. Fill in by contour. On the second hearing, mark only whether each note goes up, down or stays. You now have a shape.
5. Name the degrees. On the third hearing, sing each note and compare it with the tonic you are holding in your head. Write numbers, not letters.
6. Translate and check. Convert the numbers to letters for the key, then sing your answer and play the original. Any mismatch is information about which degree you are weak on.

Applied to the opening melody: the key is C major, established by the chord. The rhythm is seven short notes and one long one, in 4/4, which works out as six quarter notes, a quarter, and a half. The first note is the tonic, so 1. The last note is also 1. The contour is up, up, up, down, down, down, same. The degrees come out as 1, 2, 3, 5, 3, 2, 1, 1. Translated into C major, that is C, D, E, G, E, D, C, C.

Change one input: the same shape in minor

Now the test. Someone plays an A minor chord and then this melody: A, B, C, E, C, B, A, A, same rhythm. If you were counting intervals you would get an identical chain of distances for the first four notes as before, a step, a step, a minor third. The interval method cannot tell the two melodies apart until it reaches the end and notices the tonic changed.

The scale-degree method gets it immediately, because the first note is heard as 1 in a minor key, and degree 3 in minor is a different colour from degree 3 in major. That difference, the minor third above the tonic, is one of the most recognisable sounds in music, and it is available on note three rather than note eight.

The upshot: train the key first and the notes second. A melody heard inside a key is eight decisions; a melody heard as a chain of intervals is seven measurements with no error correction.

Rhythm first, always

Pitch errors are annoying. Rhythm errors make a transcription unusable, and rhythm is easier, so do it first and get it certain. The procedure is short: find the beat by tapping, decide whether the beat divides into two or three, count out loud in bars while the melody plays, and write only stems and beams. Only then go back for pitch.

Use the counting syllables from lesson 3: one and two and for simple metre, one and a two and a for compound. If you cannot say them in time with the recording, slow the recording down; almost every player and app can do that now, and slowing down is not cheating.

Chords: quality first, then position

Identifying a chord by ear is a two-question procedure, and doing the questions in order is most of the skill.

A useful shortcut: play the chord and try to sing each note from the bottom up. Whichever note you cannot find is the one carrying the information.

Progressions: three you should know cold

Chord progressions are easier to identify than single chords, because the bass line tells you nearly everything. Train these three first, all from lesson 10:

• I, IV, V, I. The bass rises a fourth, rises a step, falls a fifth. The V feels like a question and the last I answers it.
• I, V, vi, IV. The third chord is the surprise: the music turns minor without leaving the key. Once you can hear that turn you will hear it constantly.
• ii, V, I. Two falling fifths in the bass. Listen for the smoothness of the upper voices, which mostly move by half step.

To practise without a teacher, play a progression on a keyboard or guitar with your eyes shut, wait ten seconds, and then say what it was before checking. The ten-second gap matters: retrieving after a delay is what builds durable memory, and immediate checking mostly trains recognition of what is still ringing in your ears.

The fifteen-minute routine

Fifteen minutes on six days beats ninety minutes on one, and that is not a motivational slogan: practice distributed across days produces better retention than the same total time massed into one session, a finding that has held up across a large body of research.

Common misconceptions

• You do not need absolute pitch. Naming a note with no reference is rare and is not what musicians use. Everything in this lesson is relative pitch, and relative pitch is trainable at any age.
• Being tone deaf is not the usual explanation. Congenital amusia is a real condition, and prevalence estimates put it at a small percentage of people. Almost everyone who says they are tone deaf is untrained.
• Apps alone are not enough. Multiple choice trains recognition. Singing and writing train production, which is what you need when there are no four options on the screen.
• Intervals in isolation are not the foundation. Interval drills are useful, but a melody is heard inside a key, so scale degrees transfer to real music and bare intervals often do not.
• Getting it wrong is not wasted time. An attempt followed by the correct answer produces more learning than simply listening to the correct answer, which is why every step in the routine has a check after the attempt rather than a hint before it.

Try it: five dictations you can mark yourself

Establish C major first by playing C, E, G and then the scale. Then work each one out, writing numbers first.

1. C, E, G, E. Answer: 1, 3, 5, 3. The shape is the tonic chord going up and coming back one step of the chord.

2. C, B, C, D, C. Answer: 1, 7, 1, 2, 1. Notice the pull of 7 back to 1; that leading-tone tug is the easiest degree to identify.

3. G, F, E, D, C. Answer: 5, 4, 3, 2, 1. A plain descent from the fifth, which is the single most common melodic shape in Western music.

4. C, F, E, D, C. Answer: 1, 4, 3, 2, 1. The leap up to 4 is the difficult moment; 4 leans down onto 3, which is how you confirm it.

5. Now in A minor: A, C, B, A, G sharp, A. Answer: 1, 3, 2, 1, 7, 1. The raised seventh is the harmonic minor's leading tone, and it should sound urgent in a way the natural minor's flat seventh does not.

6. Play a chord and answer the two questions in order: a chord containing D, F, A. Answer: the third is minor, three semitones, and the fifth is perfect, so it is D minor.

What to remember

Establish the key before you listen to anything. Take rhythm first and finish it. Anchor a melody with its first and last notes, sketch the contour, then name each note by its scale degree rather than by its distance from the note before. Check by singing your answer against the original and noting which degree failed. For chords ask about the third, then the fifth, then the seventh, in that order. For progressions follow the bass. Fifteen minutes a day, six days a week, with a delay before every check.

The core of it: ear training is not a talent test. It is a habit of listening for function, practised in short sessions with feedback, and every professional you admire built it the same way. The next two lessons ask you to use it: once on a stage, and once on a page of your own.

Sources

1. Hamm, C., and Hughes, B. (n.d.). The basics of sight-singing and dictation. In Open Music Theory (2nd ed.). VIVA Open Publishing. viva.pressbooks.pub
2. Ricci Adams. (n.d.). Ear training exercises. musictheory.net. musictheory.net
3. Cepeda, N. J., Pashler, H., Vul, E., Wixted, J. T., and Rohrer, D. (2006). Distributed practice in verbal recall tasks: A review and quantitative synthesis. Psychological Bulletin, 132(3), 354-380. (Unlinked: the evidence that spacing practice across days beats massing it.)
4. Peretz, I., and Vuvan, D. T. (2017). Prevalence of congenital amusia. European Journal of Human Genetics, 25(5), 625-630. (Unlinked: the prevalence estimate behind the tone-deafness misconception.)

The passage you have played fifty times and still cannot play

Here is a situation you may recognise. There are four bars in a piece that go wrong. You have played them again and again, from the top of the page each time, always at full speed, and you get them right maybe seven times out of ten. In the lesson or the concert, you get them right two times out of ten.

Nothing about that is mysterious, and it is not a lack of talent. Almost everything wrong with it is visible in the description, and this lesson works through it: first the practising, then reading music you have never seen, then playing with other people, then what happens to your hands when people are watching.

Fault one: you are practising the mistake

Playing a passage at full speed with a seventy per cent success rate means that three times in ten you are rehearsing the wrong version. Repetition strengthens whatever you repeat, and it has no opinion about whether the thing is right.

The fix has a number attached. Slow the passage until you can play it correctly five times in a row. If that means half speed, use half speed. If it means playing two notes at a time, play two notes. Then raise the tempo by a small amount, five beats per minute at a time on a metronome, and require five correct repetitions again before the next increase. A failure sends you back one step, not to the beginning.

This sounds slow and it is faster, because the thing you are building is a reliable version rather than a lucky one.

Fault two: you always start from the top

Starting each attempt at bar 1 means the difficult four bars get practised once per run, while the easy opening gets practised every time. Worse, you only ever arrive at the hard part in one state: already playing, already warm, already in the flow of the piece.

Two corrections. Isolate: practise the four bars on their own, many times, and separately from the piece. Then connect: practise the two bars before and the two bars after, so that the join is rehearsed as well as the passage. Most failures in performance happen at joins, because a join is the one place nobody practises.

Fault three: everything in one block

Practising one passage forty times in a row produces good results inside the session and poor results the next day. Mixing several passages or several pieces in one session, and returning to each one after a gap, feels worse while you are doing it and produces more durable skill. This is the same spacing and retrieval effect you met in the ear-training lesson, and it is one of the best-supported findings in the study of learning.

What matters here: how well a practice session goes is a poor guide to how much you learned in it. The methods that feel hardest, slow repetition with a standard, isolating joins, mixing material, and putting the music away and trying to recall it, are the ones that hold.

What deliberate practice is, and what the evidence says

The term deliberate practice comes from a 1993 study of violinists at a Berlin music academy by Anders Ericsson and colleagues. It means practice that is effortful, aimed at a specific weakness, immediately corrected, and repeated, as distinct from playing through things you can already do.

That definition is useful. The popular version of the finding, that ten thousand hours produces expertise, is not something the paper claimed, and later work has qualified it. A 2014 meta-analysis by Brooke Macnamara and colleagues gathered the available studies and found that accumulated deliberate practice accounted for roughly a fifth of the variation in musical performance between people. That leaves a great deal unexplained, including starting age, teaching quality, sleep, and whatever else turns out to matter.

Two honest conclusions follow. Practice quality matters enormously and is the part you control. And the number of hours is not a guarantee, so a practice diary that records only time is measuring the wrong thing. Record what you worked on, at what tempo, and what your success rate was.

Sight-reading: a different skill, with its own procedure

Sight-reading is playing music you have never seen, once, in time. It is not a test of how well you know the notes. It is a test of whether you can keep going.

The one rule that beats every other piece of advice: never stop, and never go back. A wrong note is a small error. Stopping to correct it is a large one, because it destroys the pulse, and if you are playing with anyone else it destroys theirs too.

Before you play, spend thirty seconds on five things, in this order.

Then choose a tempo you can hold through the hardest bar, count yourself in for a full bar, and go. If a chord is too thick, play the bass note and the top note and leave the middle. If a run is too fast, play its first and last notes in time. Keeping the pulse and the harmony is worth more than every note.

Sight-reading improves only by sight-reading a lot of new material, which by definition you can only read once. Free graded examples are available in Open Music Theory's sight-counting and sight-singing examples and a harder second level, and IMSLP contains more free music than you could read in a lifetime.

Playing with other people

Everything changes when there is a second person. The skill is no longer producing notes; it is agreeing about time.

• Count in properly. Give a full bar out loud, at the tempo you actually want, not a vague one two three four that speeds up. Everyone should hear the beat before anyone plays.
• Breathe together. Even on instruments that do not need breath, a shared intake before the first note is how ensembles start together. Watch a string quartet: the first violinist lifts and breathes.
• Watch the person with the pulse. In a rock band that is usually the drummer's hi-hat or kick. In a small classical group it is whoever has the moving notes. In an orchestra it is the conductor and the leader.
• Balance is your job, not the sound engineer's. If you cannot hear the singer, you are too loud. That is the whole rule.
• Get lost gracefully. If you lose your place, stop playing, listen for a landmark, count yourself back in at the top of a phrase. Do not hunt for your place while making noise.
• Tune before you start, and again after twenty minutes. Strings and wind drift as the room and the instrument warm up.

Nerves: what is happening, and what to do about it

Before a performance the body does a set of specific things: heart rate rises, breathing goes shallow and high in the chest, hands sweat and go cold, the mouth dries, and fine motor control degrades slightly. That is the stress response, and it is the same in a musician, an athlete and a person about to give a speech.

Performance anxiety is common among musicians at every level, including professionals, and studies have reported substantial rates of it in orchestral players. It is not a sign that you are unsuited to performing.

Four things are worth doing, and all four are ordinary rather than dramatic.

1. Over-prepare the start. Anxiety peaks in the seconds before and after the first note. Know the first eight bars so well that you could begin them while thinking about something else.
2. Simulate the conditions. Play the piece straight through, once, with no restarts, for one other person, or to a phone recording with the red light on. Do this repeatedly in the weeks beforehand. Practising alone prepares you for playing alone.
3. Lengthen the out-breath. Slow breathing with a longer exhalation than inhalation reduces the physical arousal enough to steady the hands. Four counts in, six or eight out, for a minute.
4. Relabel the feeling. A 2014 set of experiments by Alison Wood Brooks found that people told to say aloud that they were excited, rather than to calm down, performed better on public singing, speech and maths tasks. The arousal is the same; treating it as readiness rather than as danger is easier than making it go away.

Two cautions. Beta blockers are sometimes used by professional musicians for performance anxiety; they are prescription medicines with real effects and real contraindications, and that is a decision for a doctor, not for a course. And if anxiety about performing is affecting your life outside music, that is worth telling an adult you trust, because it is treatable and common.

Common misconceptions

• More hours is not the same as better practice. The evidence gives accumulated practice a large but partial role, so a diary that records only minutes is measuring the wrong variable.
• Stopping to fix a wrong note is not conscientious. In performance and in sight-reading it converts a small error into a breakdown, and it trains you to stop under pressure.
• Nerves are not a sign of poor preparation. Experienced professionals report them too. What preparation changes is how much the nerves can damage.
• A practice session that felt good is not evidence of learning. Blocked repetition raises performance within the session and lowers retention the next day, which is why the harder methods win.
• Playing loudly is not playing confidently. In an ensemble, volume you cannot hear past is the main cause of bad balance, and the fix is always the person who cannot hear the others.

Try it: fix the four bars

1. You can play a passage correctly seven times in ten at full speed. What tempo should you practise it at? Answer: whatever tempo lets you play it correctly five times in a row, however slow that is, and then raise it in small steps with the same standard.

2. Where in a piece do most performance failures happen, and why? Answer: at joins between sections, because people practise sections and rarely practise the transition between them.

3. You are sight-reading and misread a note in bar 3. What do you do? Answer: keep going in time. Stopping costs more than the wrong note, and in an ensemble it costs everyone.

4. Which bar should set your sight-reading tempo? Answer: the hardest one. A tempo you cannot sustain through bar 12 is the wrong tempo in bar 1.

5. Your band cannot start together. Name two specific fixes. Answer: a full bar counted out loud at the real tempo, and a shared visible breath before the first note.

6. A friend says the ten thousand hour rule proves anyone can become an expert with enough practice. What is the accurate version? Answer: that accumulated deliberate practice accounts for roughly a fifth of the variation in musical performance in the available studies, so it matters a great deal and does not determine the outcome alone.

Recap

Practise for reliability, not for luck: slow enough to be correct, five in a row before speeding up, isolate the hard bars, then rehearse the joins, and mix material rather than blocking it. Judge a session by what you can do tomorrow, not by how it felt. Sight-reading is its own skill with its own rule, which is never stop, preceded by thirty seconds spent on key, metre, the hardest bar, the road map and any repeats. Playing with others is an agreement about time, made with a proper count-in, a shared breath, an eye on whoever carries the pulse, and a willingness to be quieter. Nerves are a physiological event you can prepare for by over-learning the opening, simulating the performance, slowing the out-breath and relabelling the feeling.

Remember: everything in this lesson is a method rather than a trait. The player who never falls apart is not calmer than you; they have run the piece from memory in front of someone eleven times, and they have practised bar 24 into bar 25 more often than they have practised bar 1.

Sources

1. Hamm, C., and Hughes, B. (n.d.). Examples for sight-counting and sight-singing. In Open Music Theory (2nd ed.). VIVA Open Publishing. viva.pressbooks.pub
2. Wikipedia contributors. (n.d.). Sight-reading. Wikipedia. en.wikipedia.org
3. Ericsson, K. A., Krampe, R. T., and Tesch-Romer, C. (1993). The role of deliberate practice in the acquisition of expert performance. Psychological Review, 100(3), 363-406. (Unlinked: the Berlin violinist study that defined deliberate practice.)
4. Macnamara, B. N., Hambrick, D. Z., and Oswald, F. L. (2014). Deliberate practice and performance in music, games, sports, education, and professions: A meta-analysis. Psychological Science, 25(8), 1608-1618. (Unlinked: the source for the proportion of variance figure used here.)
5. Brooks, A. W. (2014). Get excited: Reappraising pre-performance anxiety as excitement. Journal of Experimental Psychology: General, 143(3), 1144-1158. (Unlinked: the reappraisal experiments described in the nerves section.)

Sixteen bars, about forty seconds, finished

At 88 beats per minute, sixteen bars of 4/4 last forty-four seconds. That is the piece you are going to write. It is short enough to finish this week and long enough to need every idea in this course: a key, a progression, a motive, phrases that ask and answer, one climax, and an ending that sounds like an ending.

This lesson builds one from nothing, step by step, and prints the result. Then it changes a single input, the chord under one bar, and shows what that does to the melody above it. Then it tells you how to get it onto a recording without a studio. Nothing here needs an instrument you do not have; a free keyboard app and a phone are enough.

Step 1: fix the frame before writing a note

Four decisions, and they take two minutes.

If you write in a minor key, or in 6/8, or at 140, everything below still applies. Fix the frame first so that every later choice has something to be measured against.

Step 2: the chords

Take a progression you can play. Ours uses only chords from lesson 9 and cadences from lesson 10.

Two things to notice. The bridge, bars 9 to 12, starts on vi rather than I, which is the cheapest way to make a section feel different without leaving the key. And bars 8 and 16 each hold two chords, two beats each, because a cadence needs the V and the I inside one bar to land properly.

Step 3: write the rhythm before any pitches

This is the step people skip, and skipping it is why melodies come out as streams of identical notes. Decide the rhythm of all sixteen bars first, using only two patterns plus one contrasting pattern for the bridge.

• Pattern a: quarter, quarter, half. Two short then one long. This is the rhythm of the motive.
• Pattern b: four quarters. Even, running, an answer to pattern a.
• Pattern c, bridge only: two eighths then three quarters. Busier, which is what makes the bridge feel like a different place.

Lay them out: a b a b, a b a b, c c a a, a b a b, roughly. Read that aloud as rhythm, clapping, before any pitch exists. If the rhythm alone is boring, no choice of notes will rescue it.

Step 4: the motive

Our motive is three notes: two quarters rising a third, then a held note repeating the second. In bar 1 over a C chord that is E, G, G, with the last G lasting two beats.

It is short, it has a distinctive rhythm, and it can be moved. Over an F chord it becomes F, A, A. Over a D minor chord it becomes D, F, A. In every case the shape is the same: up a third, then stay. That is what a listener recognises.

Step 5: the sixteen bars

Here is the finished melody. Read the letters in rhythm, out loud, before you play it.

The climax in bar 15 is worth a sentence on its own. The high E is the major seventh of the F chord underneath it, which is why it sounds bright and faintly aching rather than settled, and it resolves downward by step through D to C. That is the suspension effect from lesson 11, used at the one place in the piece where it will be noticed most.

The first four bars on a staff

Read that with the table beside you. The two open noteheads are the held notes of the motive in bars 1 and 3, and the last note of bar 4 is the D that leaves the question hanging.

Audit it against the five checks

From lesson 11, in order.

1. Motive. Bars 1, 3, 5, 7 and 13 all contain the rising third plus held note. Passed.
2. Rhythmic contrast. Three patterns, with the bridge clearly different. Passed.
3. Contour. The line rises and falls inside each phrase, and rises across the whole piece to bar 15. Passed.
4. One climax. The highest note, E above the staff, occurs once, in bar 15, and is approached and left by step. Passed.
5. Phrases. Bar 4 ends on a half cadence, bar 8 on an authentic cadence, bar 12 open again, bar 16 closed. Passed.

Range check: the lowest note is the D below the staff in bar 7 and the highest is the E above it in bar 15, a ninth apart. Anybody can sing that.

Change one input: what happens if bar 15 becomes D minor

Leave the melody exactly as written and change the chord in bar 15 from F to D minor. The notes of D minor are D, F and A. Our melody in that bar is C, D, then a held E.

Now C is the seventh of the chord, D is the root, and the climax E is the ninth. The bar has gone from bright to tense and unresolved, and the descent into bar 16 now sounds like a release rather than a flourish. Nothing in the melody changed. The point: a melody note has no fixed meaning. Its colour is decided by the chord underneath it, which is why changing one chord is the cheapest way to rescue a bar that is not working.

Try two more substitutions on your own piece when you get there. Replace a I with a vi and hear the phrase turn wistful. Replace a V with a V7 by adding the flat seventh and hear the pull to the tonic get stronger.

Writing it so somebody else can play it

A lead sheet is the standard minimum: melody, chord symbols above the staff, and the words if there are any. Everything else, the voicings, the bass line, the drum part, is left to the players.

You have three ways to produce one, in ascending order of effort.

• A table, like the one above. Bar number, chord symbol, notes with rhythms. Any musician can read this, and it costs nothing.
• Staff paper by hand. Draw four bars per line, write chord symbols above the staff, and keep the spacing proportional to the note lengths so it is readable.
• Notation software. MuseScore is free and will play your melody back to you, which is the fastest way to hear a mistake.

Use standard chord symbols: a plain letter for major, a letter plus m for minor, a 7 for a dominant seventh, maj7 for a major seventh. Write them above the bar where the chord starts, and do not repeat a symbol that has not changed.

Recording it on a phone

You do not need an interface, a microphone or a room. You need a click, one take, and honest listening.

1. Set a click. Use a free metronome app at 88, or a drum loop at the same tempo. Playing to a click feels awkward for a week and then becomes easier than playing without one.
2. Check the level before you commit. Play the loudest bar and watch the meter. If the recording clips, the distortion is permanent, so move the phone further away rather than playing more quietly.
3. Place the phone about a metre away and off to one side, not directly in front of a sound hole, a mouth or a speaker. Point it at the instrument, not at the ceiling.
4. Kill the room. Close the window, turn off the fan, and put something soft on a hard floor. A phone microphone records everything equally, so the only volume control you have is what you remove.
5. Count yourself in for a full bar and play all sixteen bars without stopping. If you make a mistake, keep going to the end; you can decide later whether it matters.
6. Do three takes and stop. After three, tiredness costs more than it gains. Name the files so you can tell them apart.

Then leave it for a day. Listening back immediately tells you mostly how you felt while playing. Listening back tomorrow tells you what is actually on the recording.

The second take is where the composing happens

After the day's gap, listen once with a pen and write down exactly one thing to change. Not five. One. Typical useful changes:

• The tempo is wrong. Move it by six beats per minute, not by one.
• Bar 12 is dull. Change the chord rather than the melody.
• The climax is not reaching. Take out a high note somewhere earlier so the top of bar 15 is genuinely the highest.
• The bridge is not contrasting enough. Change its rhythm again, or drop the accompaniment out for two bars.
• The ending stops rather than finishes. Hold the last note twice as long, or add a bar of the tonic chord.

Record a second take with that one change and keep both files. Comparing two versions that differ in one respect is the fastest way to learn what a decision does, and it is the method this whole course has used, from clapping 6/8 against 3/4 in lesson 4 to putting the same melody over a different chord ten minutes ago.

Common misconceptions

• You do not need to play an instrument well to compose. You need to be able to hear a note and find it, slowly, on something. Sixteen bars can be written entirely with a free keyboard app and a voice.
• A first draft is not supposed to be good. The audit and the second take are where a piece becomes worth hearing, and skipping them is the actual mistake.
• Using a common progression is not cheating. Chord sequences are shared material, as lesson 10 showed; what makes a piece yours is the melody, the rhythm and the arrangement.
• A recording is not a document of a performance any more. As lesson 19 showed, it is an object you build, so a take with one flaw and real energy can be better than a clean, dead one.
• More notes will not fix a weak bar. Nine times out of ten the answer is a different chord underneath or one note held longer.

Try it: your own sixteen bars

Do these in order. Each has a check.

1. Frame. Write down your key, metre, tempo and form. Check: can you clap four bars at your tempo without speeding up? If not, slow it down.

2. Chords. Write sixteen bars of chords using at most five different ones, with a half cadence at bar 4 and an authentic cadence at bars 8 and 16. Check: play the whole sequence twice. Does bar 4 sound like a comma and bar 8 like a full stop?

3. Rhythm. Write the rhythm of all sixteen bars with no pitches, using two patterns plus one for the bridge. Check: clap it. If you cannot tell the bridge from the rest with your eyes shut, change it.

4. Motive. Write three to five notes over your first chord. Check: sing it once, put the paper away, and sing it again an hour later. If you cannot, it is too complicated.

5. Melody. Fill in all sixteen bars, moving your motive to fit the chords in bars 3, 5 and 13. Check: run the five-point audit above and write pass or fail beside each item.

6. Lead sheet. Produce a table or a staff page with chord symbols. Check: hand it to somebody else and ask them to describe the shape of the tune without hearing it.

7. Record. Three takes to a click, one day's gap, one change, one more take. Check: write three sentences saying what the change did, whether it worked, and what you would do next.

What to carry forward

You now have a method that does not depend on inspiration. Fix the frame. Write the chords, with the cadences placed where the phrases need them. Write the rhythm before any pitch. Invent a motive short enough to remember. Build four phrases that ask, answer, leave and return, with one climax late and approached by step. Audit against five checks. Write it down so somebody else could play it. Record it against a click, leave it a day, change exactly one thing, and record it again.

Worth holding on to: everything in this course was pointed here. The harmonic series explained why your key has a tonic at all; notation let you fix the piece on a page; metre gave the rhythm its grid; scales and intervals supplied the notes; triads and cadences made the phrases mean something; form told you where the contrast goes; the listening history showed you a thousand years of people solving the same problem; the ear training let you hear what you wrote before you played it. Sixteen bars is a small thing. Writing a small thing properly, and finishing it, is how every larger thing gets written.

Sources

1. Peterson, J., et al. (n.d.). Melody and phrasing. In Open Music Theory (2nd ed.). VIVA Open Publishing. viva.pressbooks.pub
2. Shaffer, K., et al. (n.d.). Chord symbols. In Open Music Theory (2nd ed.). VIVA Open Publishing. viva.pressbooks.pub
3. Shaffer, K., et al. (n.d.). Four-chord schemas. In Open Music Theory (2nd ed.). VIVA Open Publishing. viva.pressbooks.pub
4. MuseScore BVBA. (n.d.). MuseScore [notation software]. musescore.org