Music Theory I

What the staff is

Western music is written on a staff (plural: staves): a set of five horizontal lines with four spaces between them. Every note symbol sits either on a line (the line runs through the middle of the notehead) or in a space (the notehead fills the gap between two lines). The staff is the grid on which pitch and time are drawn.

The core idea is simple: higher on the staff means higher in pitch; lower on the staff means lower in pitch. As you move a note upward from line to space to the next line, the pitch rises step by step. Musicians describe this vertical dimension as pitch - how high or low a sound is - which corresponds physically to the frequency of vibration.

Counting lines and spaces

Both lines and spaces are numbered from the bottom up. The lowest line is the first line; the line just above it is the second line, and so on to the fifth line at the top. Likewise the lowest space is the first space and the top space is the fourth space. When a musician says "third line," they always mean counting upward from the bottom.

Ledger lines

Music often needs pitches that are higher or lower than the five lines can show. To notate those, we add short ledger lines: tiny line segments drawn above or below the staff, one per pitch, extending the grid only as far as needed. A note sitting one ledger line below the staff is a step lower than the bottom line; a note on a ledger line above is a step higher than the top line. Ledger lines let a single staff reach a wide range without becoming an impossibly tall grid.

Why the staff matters

Notation is a coordinate system. The vertical axis (line/space position) encodes pitch, which we study in this module. The horizontal axis, reading left to right, encodes time and rhythm, which we take up in Module 2. Master the vertical axis first: if you can instantly tell whether a note is on a line or in a space, and count which line or space it is, you have the foundation for reading any melody. The staff by itself does not tell you the exact letter names of the notes - for that we need a clef, which is the very next lesson. But the geometry never changes: up is higher, down is lower, and lines and spaces alternate.

Why we need a clef

The staff shows relative height, but not which exact pitches the lines and spaces stand for. A clef, placed at the far left of every staff, assigns letter names to the lines and spaces. Music uses only seven letter names, A B C D E F G, which then repeat: after G we start again at A, one octave higher.

The treble clef (G clef)

The treble clef is used for higher instruments and voices and for the right hand on piano. Its curl wraps around the second line from the bottom, marking that line as the note G above middle C, which is why it is also called the G clef. From that anchor, the lines from bottom to top spell E G B D F (remember: Every Good Boy Does Fine) and the spaces from bottom to top spell F A C E (they literally spell the word "face").

The bass clef (F clef)

The bass clef is used for lower instruments and voices and for the left hand on piano. Its two dots sit above and below the fourth line from the bottom, marking that line as the F below middle C, which is why it is the F clef. On the bass staff the lines from bottom to top spell G B D F A (Good Boys Do Fine Always) and the spaces spell A C E G (All Cows Eat Grass).

Middle C, the meeting point

Middle C is the note near the center of the piano. It sits one ledger line below the treble staff and one ledger line above the bass staff. This shared reference is why piano music is usually written on two staves joined into a grand staff: treble on top, bass on the bottom, with middle C floating between them. Any note you can name on one clef, you can locate relative to middle C on the other.

Practice reading a few notes on each clef every day. Fluency comes from repetition, not cleverness. Once the letter names are automatic, everything that follows, scales, intervals, and chords, is just patterns of these seven letters.

Rhythm is the time axis

If pitch is the vertical dimension of notation, rhythm is the horizontal one: how long each sound lasts and when it happens. Durations are relative. The whole note is the reference; every shorter value is a fraction of it.

The doubling ladder

Each common note value lasts half as long as the one above it. This makes the system easy to remember as a ladder of halves:

So two half notes fill the same time as one whole note; two quarters fill one half; two eighths fill one quarter, and so on. When eighth or sixteenth notes come in groups, their flags are joined into a beam to make the grouping easy to read.

Rests: measured silence

Every note value has a matching rest of the same duration, but representing silence instead of sound. There is a whole rest, half rest, quarter rest, eighth rest, and sixteenth rest. Silence is part of rhythm: a well-placed rest shapes a phrase as much as the notes do.

Dots and ties extend duration

Two tools lengthen a note beyond its basic value:

• A dot placed right after a notehead adds half of that note's value to it. A dotted half note equals a half plus a quarter, that is 2 + 1 = 3 beats in 4/4. A dotted quarter equals 1 + 1/2 = 1.5 beats.
• A tie is a curved line joining two notes of the same pitch; you play the first and hold through the second without re-striking, adding their durations. A quarter tied to a quarter sounds for two beats. Ties are how you sustain a sound across a barline.

Worked example

How many beats is a dotted half note tied to a quarter note, in 4/4? The dotted half is 3 beats; the quarter adds 1; total = 4 beats, a full measure. Notice this is a different notation from a single whole note, but the same total duration.

Counting out loud while clapping is the fastest way to internalize these values. Say "1 - 2 - 3 - 4" steadily and place notes on and between the numbers until the ladder of halves feels automatic.

Organizing the beat

Beats do not just tick by; they group into repeating patterns. That grouping is meter, and it is declared by a time signature, the pair of stacked numbers at the start of a piece. A vertical bar line divides the music into measures (also called bars), each holding one full group of beats.

Reading the two numbers

The time signature is not a fraction, even though it looks like one. Read it as two separate facts:

• The top number tells how many beats are in each measure.
• The bottom number tells which note value gets one beat: 4 means the quarter note, 2 means the half note, 8 means the eighth note.

So 4/4 means four beats per measure, quarter note gets the beat. 3/4 means three beats per measure, quarter gets the beat (the waltz feel). 2/4 means two beats per measure, quarter gets the beat.

Simple meter families

When the beat divides naturally into two equal parts, the meter is simple. Simple meters are grouped by how many beats fill a bar:

The first beat of each measure carries the strongest natural accent. That downbeat is what gives meter its pulse and lets listeners feel where each bar begins.

Compound meter and 6/8

6/8 is the classic point of confusion. Its bottom number 8 says the eighth note is the base unit, and the top number 6 says there are six eighths per bar. But at any normal tempo you do not feel six even beats, you feel two, each divided into three eighths: ONE-two-three, FOUR-five-six. Meters whose beat divides into three are called compound. So 6/8 is felt as compound duple: two big beats, each a dotted quarter. This lilting, rolling feel is why 6/8 suits jigs and many ballads.

Common time

You will often see a large "C" instead of the numbers 4/4; this stands for common time and means exactly 4/4. A "C" with a vertical slash means cut time (2/2): two beats per bar with the half note getting the beat, used for brisk marches.

The keyboard as a map

The piano keyboard is the clearest picture of how pitch is organized, so music theory leans on it even for non-pianists. The keys repeat in a pattern of white and black keys. Look at the black keys: they come in alternating groups of two and three. That grouping is your compass.

The white key immediately to the left of any group of two black keys is always C. From there the white keys ascend by letter: C, D, E, then F, G, A, B, then back to C, forever. So D sits between the two black keys of the group of two; F is just left of the group of three; and so on.

Half steps and whole steps

The smallest distance between two adjacent keys on the piano, counting both white and black keys, is a half step (also called a semitone). It is the atom of Western pitch. A whole step (a whole tone) is simply two half steps.

Here is the crucial subtlety. Between most white-key neighbors there is a black key in between, so those white keys are a whole step apart. But two pairs of white keys have no black key between them: E to F, and B to C. Those two pairs are only a half step apart. Memorizing "E-F and B-C are half steps" prevents countless errors later, because scales are built from precise sequences of half and whole steps.

Naming the black keys

The black keys take their names from the white keys next to them, using accidentals:

• A sharp (#) raises a note by one half step. The black key just right of C is C sharp.
• A flat (b) lowers a note by one half step. That same black key is also D flat, because it is one half step below D.
• A natural cancels a previous sharp or flat, returning to the plain white-key note.

Enharmonic equivalents

Because C sharp and D flat are the very same key, they are enharmonic equivalents: two spellings for one pitch. Which spelling you use depends on the musical context, especially the key you are in, a distinction that becomes important when we build scales in the next module. For now, hold onto three facts: the keyboard repeats in groups of two and three black keys; a half step is the nearest neighbor; and E-F and B-C are the natural half steps.

What a scale is

A scale is an ordered ladder of pitches spanning one octave, arranged by a fixed pattern of steps. The major scale is the foundation of Western tonal music, the bright, familiar "do re mi fa sol la ti do." Its sound comes entirely from one pattern of half and whole steps.

The major-scale formula

Starting from any note (the first degree), a major scale follows this sequence of steps to reach the octave:

W - W - H - W - W - W - H

where W is a whole step and H is a half step. That is seven steps that take you through eight notes, landing back on the starting letter one octave up. The two half steps always fall between degrees 3-4 and degrees 7-8.

Building C major

Start on C and apply the formula, using the keyboard where E-F and B-C are the natural half steps:

C major uses only white keys and needs no sharps or flats, which is why it is the natural starting point.

Building G major (a worked example)

Now start on G: G (W) A (W) B (H) C (W) D (W) E (W) F? Applying the sixth step, a whole step above E is F sharp, not F. So the scale is G A B C D E F# G. The one sharp is exactly what keeps the half steps in the required spots (B-C and F#-G). This is the general principle: to preserve the W-W-H-W-W-W-H pattern from a new starting note, you must raise or lower certain notes with sharps or flats.

Scale degrees have names

Each of the seven degrees has a functional name you will use constantly:

The tonic (degree 1) and dominant (degree 5) are the two most important pitches; nearly all harmony orbits them. The leading tone (degree 7) sits just a half step under the tonic and creates the strong pull home that gives major keys their sense of resolution.

Practice building major scales from several starting notes, always checking that your half steps land between 3-4 and 7-8. If they do, the scale is correct; if not, you have missed a sharp or flat.

Why key signatures exist

We saw that G major always needs F sharp. Rather than write a sharp in front of every F throughout the piece, we place it once, at the start of every staff, in a key signature: a collection of sharps or flats, just after the clef, that applies to those notes for the whole piece. The key signature tells you the key and saves enormous clutter.

The order is fixed

Sharps and flats always appear in a strict order, never random. The sharps enter in this sequence:

F# - C# - G# - D# - A# - E# - B# (Father Charles Goes Down And Ends Battle)

The flats enter in the exact reverse order:

Bb - Eb - Ab - Db - Gb - Cb - Fb (Battle Ends And Down Goes Charles' Father)

A key with one sharp has F#; two sharps means F# and C#; and so on down the list. A key with one flat has Bb; two flats means Bb and Eb; and so on.

The circle of fifths

The circle of fifths arranges all twelve keys so that each step clockwise moves up a perfect fifth and adds one sharp, while each step counterclockwise moves down a fifth and adds one flat. C major sits at the top with zero sharps and zero flats:

Notice the pattern in the sharp column: starting at C, going up a fifth to G adds F#; up another fifth to D adds C#; each new key keeps all the previous sharps and adds exactly one more, the next in the "Father Charles" order.

Two quick tricks

• Finding the key from sharps: the last sharp in the signature is the leading tone; the tonic is one half step above it. If the last sharp is F#, the key is G major (a half step above F#).
• Finding the key from flats: the second-to-last flat names the major key directly. With flats Bb-Eb-Ab, the second-to-last is Eb, so the key is E flat major. (The single-flat key, F major, you simply memorize.)

Relative connection

Every major key signature is shared by one minor key, its relative minor, which we explore next. For now, the takeaway is that a key signature is a compact label: it fixes which notes are sharp or flat throughout, and the circle of fifths lets you recall any key's signature without memorizing all fifteen separately.

The other side of tonality

If major sounds bright and open, minor sounds darker, more serious or plaintive. The difference is again just a rearrangement of half and whole steps, centered on a lowered third degree.

The natural minor formula

The natural minor scale follows this step pattern:

W - H - W - W - H - W - W

The half steps now fall between degrees 2-3 and 5-6. Compared to a major scale on the same starting note, natural minor has a lowered 3rd, 6th, and 7th degree. That lowered third is the single most important ingredient of the minor sound.

Building A minor

Apply the pattern from A: A (W) B (H) C (W) D (W) E (H) F (W) G (W) A. The result is A B C D E F G A, all white keys, no accidentals. That is not a coincidence.

Relative major and minor

A minor uses the same notes as C major; they share the empty key signature. A minor is the relative minor of C major, and C is the relative major of A minor. Every major key has a relative minor that starts on its sixth degree (the submediant). The sixth degree of C major is A, so A minor is its relative. To find any relative minor, count down three half steps from the major tonic, or equivalently up to the sixth degree.

Three forms of minor

Minor comes in three closely related forms because composers wanted a stronger pull to the tonic than natural minor provides:

• Natural minor uses the key signature exactly, with a lowered 7th. Its 7th is a whole step below the tonic, so it lacks a strong leading tone.
• Harmonic minor raises the 7th degree by a half step to create a leading tone that pulls firmly up to the tonic. In A minor this makes the 7th G sharp. This creates a distinctive wide gap (an augmented second) between degrees 6 and 7.
• Melodic minor smooths that gap by raising both the 6th and 7th degrees when ascending, then traditionally lowering them back to natural minor when descending. In A minor: ascending A B C D E F# G# A, descending A G F E D C B A.

Why this matters

You will meet the raised 7th constantly in minor-key harmony, because the leading tone is what makes the dominant chord pull home. When you analyze minor-key music, expect to see that raised 7th appear as an accidental, since the key signature only supplies the natural (lowered) version. Master natural minor first as the backbone, then treat harmonic and melodic minor as the two adjustments composers make to strengthen or smooth the approach to the tonic.

What an interval is

An interval is the distance between two pitches. Every interval has two parts to its name: a number (how many letter names it spans) and a quality (its exact size in half steps). Getting both right is a core skill, because chords, scales, and harmony are all described in terms of intervals.

Step 1: the number

To find the number, count the letter names from the lower note to the upper note, including both ends. From C to E you count C-D-E, that is three letters, so it is some kind of third. From C to G you count C-D-E-F-G, five letters, a fifth. A note to itself is a unison (1), and an octave (spanning eight letters) is an 8th. The number ignores sharps and flats; C to E and C to E flat are both "thirds."

Step 2: the quality

The number alone is not enough, because a third can be bigger or smaller by a half step. Quality pins down the exact size. Intervals fall into two families:

• Perfect intervals: the unison, 4th, 5th, and octave. These sound stable and are labeled perfect (P).
• Major/minor intervals: the 2nd, 3rd, 6th, and 7th. These come in a larger major (M) and a smaller minor (m) form, one half step apart.

Two more qualities modify these: augmented (A) is one half step larger than perfect or major, and diminished (d) is one half step smaller than perfect or minor.

Interval sizes in half steps

The surest way to name quality is to count half steps. This table lists the common intervals within an octave:

Worked example

Name the interval from C to E flat. First the number: C-D-E is three letters, so it is a third. Now the quality: C to E flat is 3 half steps (C to C# to D to Eb). Three half steps in a third is a minor third. Contrast C to E natural, which is 4 half steps, a major third. The single half-step difference flips the whole character from bright to dark.

The tritone

The interval of exactly 6 half steps (three whole tones) is the famous tritone. It is enharmonically both an augmented 4th and a diminished 5th, and it sounds tense and unstable, which composers exploit to drive music toward resolution. It sits right at the middle of the octave.

Practice by naming intervals two ways, first count letters for the number, then count half steps for the quality. When both agree, you have the full name, such as "minor sixth" or "perfect fifth."

From intervals to chords

A chord is three or more notes sounded together. The most basic chord is the triad: three notes built by stacking two thirds. Start on a note called the root, add the note a third above it (the third), and add another third on top (the fifth). Because we learned intervals in the last module, chords are now just intervals stacked up.

Four qualities from two thirds

A triad's quality depends on which kinds of thirds you stack, major (4 half steps) or minor (3 half steps). There are four combinations:

Read the pattern: a major triad is a major third on the bottom with a minor third on top, and it sounds bright and stable. A minor triad flips them, minor third on the bottom, major on top, and sounds darker. A diminished triad stacks two minor thirds and sounds tense (its outer interval is a tritone). An augmented triad stacks two major thirds and sounds suspended and unsettled.

Worked example

Build a G major triad. Root is G. A major third above G is B (G to B is 4 half steps). A minor third above B is D (B to D is 3 half steps). So the G major triad is G - B - D. To make it G minor, lower the third to B flat: G - Bb - D. Notice the fifth (D) does not change between major and minor; only the middle note moves. That middle note, the third, is what determines major versus minor quality.

Naming from the root

The root gives the chord its letter name, so a triad built on F is an "F chord," and its quality (major, minor, and so on) is added: "F major," "F minor." The three chord tones are simply the root, third, and fifth. Even when a chord is voiced with notes in a different vertical order (called an inversion), it is still named by its root and quality.

Practice building all four qualities on several roots. Ask yourself two questions each time: is the lower third major or minor, and is the upper third major or minor? Those two answers name the quality every time.

Chords that belong to a key

If you build a triad on each note of a scale, using only notes from that scale, you get the diatonic chords of the key: its natural chord family. These seven chords are the palette most tonal music is built from, and their qualities follow a fixed pattern.

Roman numerals

We label diatonic chords with Roman numerals matching the scale degree of their root. Crucially, the case of the numeral shows the quality:

• Uppercase (I, IV, V) means a major triad.
• Lowercase (ii, iii, vi) means a minor triad.
• A lowercase numeral with a small circle (vii°) means a diminished triad.

The major-key pattern

Build a triad on every degree of C major, using only white keys, and the qualities come out in this fixed order:

The quality pattern for every major key is therefore: major, minor, minor, major, major, minor, diminished (I ii iii IV V vi vii°). This never changes, whatever the key, because the scale's fixed step pattern forces it. In G major, the same pattern gives G(I), Am(ii), Bm(iii), C(IV), D(V), Em(vi), F#°(vii°).

The minor-key family

Building triads on the natural minor scale gives a different but equally fixed pattern. Using A natural minor (all white keys, so the chords are the same seven triads as C major, but reordered from A):

So natural minor gives: minor, diminished, major, minor, minor, major, major (i ii° III iv v VI VII). Note that the v chord is minor here. In practice composers often raise the leading tone (harmonic minor) to make chord V major, giving it a strong pull back to i, an adjustment you will see constantly.

Why this matters

Knowing the diatonic family lets you predict which chords "belong" in a key and label any chord by function. When you see a chord progression written as Roman numerals, you can instantly translate it into real notes for any key, and you can hear why some chords feel like home (I) and others feel like they want to move (V, vii°). This is the direct bridge to progressions, our final topic.

Chords in motion

A single chord is static; music comes alive when chords move in a progression, an ordered series of chords over time. Progressions are not random. In tonal music, chords take on functions that create a sense of departure and return around the home chord.

The three main functions

• Tonic (I) is home, the point of rest and resolution. Music tends to begin and end here.
• Dominant (V) is the pole of tension. Built on the fifth degree, it contains the leading tone (degree 7), which strains upward to the tonic. V wants to resolve to I more than any other chord.
• Subdominant (IV) is the pre-dominant, a gentle move away from home that often sets up the dominant.

These three chords, I, IV, and V, are the primary chords of a key. Remarkably, they contain every note of the scale between them, so a huge amount of music, from folk songs to pop to hymns, uses little more than these three.

The I-IV-V-I progression

The classic progression I - IV - V - I tells a complete little story: rest (I), step away (IV), build tension (V), return home (I). In C major that is C - F - G - C. Listen for how the G chord (V) feels unfinished and how arriving on C (I) feels like an exhale. That pull comes from the leading tone B inside the G chord resolving up a half step to C, the tonic.

Cadences: musical punctuation

A cadence is a chord progression that ends a phrase, like punctuation ending a sentence. The two most important:

• Authentic cadence (V - I): the strongest ending. Moving from the dominant to the tonic gives a firm, conclusive "period." When both chords are in root position and the melody lands on the tonic, it is a perfect authentic cadence, the most final-sounding of all.
• Plagal cadence (IV - I): a softer, gentler close, famous as the "Amen" ending of hymns. It resolves to the tonic without the sharp leading-tone pull of the dominant.

Other progressions add color, but nearly all resolve, sooner or later, through a dominant back to tonic. That tension-and-release between V and I is the engine of tonal harmony.

Common progressions to know

Beyond I-IV-V-I, a few progressions appear everywhere. The I - V - vi - IV progression underlies countless pop songs. The ii - V - I is the backbone of jazz harmony, using the subdominant-function ii chord to approach V. In every case, notice the pull toward the dominant and the eventual return to tonic. Learn to hear that gravitational pull, and you can predict and understand most of the harmony you encounter.

Two dimensions of music

Music combines a horizontal dimension, one note after another in time, and a vertical dimension, notes sounding together. The horizontal is melody; the vertical is harmony. A great song is a conversation between the two: a memorable tune supported by chords that give it depth and direction.

What makes a melody

A melody is a succession of single pitches that the ear follows as a coherent line, the part you hum. Melodies are shaped by:

• Contour: the overall shape of the line as it rises and falls. Melodies that move mostly by step (to adjacent scale notes) sound smooth and singable; those that leap (larger intervals) sound more dramatic. Most good melodies balance steps and leaps.
• Phrasing: melodies breathe in phrases, musical sentences that reach a small point of rest, much as spoken sentences do. Phrases often come in balanced pairs: a question phrase answered by a matching one.
• Range: the distance from the lowest to the highest note. Singable melodies usually stay within a comfortable range, often about an octave.

Chord tones and non-chord tones

When a melody plays over a chord, its notes fall into two groups. Chord tones belong to the current chord (its root, third, or fifth) and sound consonant and settled. Non-chord tones do not belong to the chord; they create momentary tension that resolves to a chord tone. The most common non-chord tone is the passing tone, a note that steps between two chord tones to fill a gap smoothly. Non-chord tones are what keep a melody from being a dull outline of the chords, they add motion and expression.

Harmonizing a melody

To harmonize a melody is to choose chords that support it. A simple, reliable method:

1. Identify the key and its diatonic chords (from Module 6).
2. For each strong beat, look at the melody note and pick a diatonic chord that contains that note as a chord tone.
3. Favor the primary chords I, IV, and V, and aim to end phrases with a cadence (usually V - I).

Worked example. Harmonize the opening of a tune in C major whose first strong-beat notes are C, then G, then C. The note C appears in both the C chord (C-E-G) and the F chord (F-A-C); the note G appears in both the C chord and the G chord. A clean choice: C over the first C (I), G chord over the G (V), and C chord over the final C (I). That yields I - V - I, C - G - C, a satisfying tonic-dominant-tonic frame with a strong authentic cadence at the end.

Putting it all together

Everything in this course now connects. Pitch on the staff and the keyboard gives you notes; rhythm and meter place them in time; scales and keys organize which notes belong together; intervals measure their distances; triads and diatonic chords stack them into harmony; and progressions and cadences move that harmony through tension and rest beneath a singable melody. That is the complete loop of tonal music, and you now have the tools to read it, write it, and understand why it works.