Music Theory Foundations

1Pitch, Notes, and Octaves

Western music names notes using seven letters:

After G, the sequence repeats:

Notes an octave apart have the same basic musical identity but occur in different registers.

In modern tuning:

• Moving up one octave doubles the frequency.
• Moving down one octave halves the frequency.
• An octave is divided into 12 equal semitones.

2Semitones and Whole Steps

In 12-tone equal temperament, the octave is divided into 12 equally sized semitones.

Half step = 1 semitone  ·  whole step = 2 semitones  ·  octave = 12 semitones.

Adjacent natural notes are usually a whole step apart. The exceptions are:

• B–C = half step
• E–F = half step

There is no separate piano key between B and C or between E and F because those pairs are already one semitone apart.

3The Chromatic Scale

Ascending from C, spelled with sharps:

The same pitches spelled with flats:

The complete sequence, showing both spellings:

4Accidentals

Examples:

• C♯ is one semitone above C.
• D♭ is one semitone below D.
• F𝄪 is two semitones above F.
• E𝄫 is two semitones below E.

5Enharmonic Equivalents

Examples:

• C♯ = D♭
• D♯ = E♭
• F♯ = G♭
• G♯ = A♭
• A♯ = B♭
• B♯ = C
• C♭ = B
• E♯ = F
• F♭ = E

Although enharmonic notes sound the same on a piano, their spellings reveal their musical functions.

6What Is an Interval?

Every interval has two parts:

1. A number: unison, second, third, fourth, and so forth
2. A quality: perfect, major, minor, augmented, or diminished

The number is determined by counting letter names inclusively.

Starting from C:

• C to C = unison
• C to D = second
• C to E = third
• C to F = fourth
• C to G = fifth
• C to A = sixth
• C to B = seventh
• C to the next C = octave

For example:

C to G is a fifth because five letter names are counted. A perfect fifth contains seven semitones.

7Simple Intervals

It may be spelled as:

• Augmented fourth: C–F♯
• Diminished fifth: C–G♭

These sound the same in equal temperament, but their spellings and musical functions differ.

8Perfect Intervals

The perfect interval family contains:

• Perfect unison
• Perfect fourth
• Perfect fifth
• Perfect octave

Perfect intervals do not have major or minor forms.

Changing a perfect interval by one semitone produces:

• Perfect enlarged by one semitone = augmented
• Perfect reduced by one semitone = diminished

Example:

9Major and Minor Intervals

Seconds, thirds, sixths, and sevenths belong to the major/minor interval family.

Within the same interval number:

• Major reduced by one semitone = minor
• Major enlarged by one semitone = augmented
• Minor enlarged by one semitone = major
• Minor reduced by one semitone = diminished

Example — four kinds of third, all spanning the letters C and E:

10Interval Identification

To identify an interval:

1. Count the letter names to determine the interval number.
2. Count the semitones to determine the interval quality.

11Compound Intervals

Examples:

• Major ninth = 14 semitones
• Major tenth = 16 semitones
• Perfect eleventh = 17 semitones
• Perfect twelfth = 19 semitones
• Major thirteenth = 21 semitones

Subtracting seven from a compound interval gives its related simple interval:

• Ninth → second
• Tenth → third
• Eleventh → fourth
• Twelfth → fifth
• Thirteenth → sixth

12Interval Inversions

Inverted interval numbers add to nine:

Interval qualities invert as follows:

• Major ↔ minor
• Perfect ↔ perfect
• Augmented ↔ diminished

Example:

• C up to E = major third
• E up to C = minor sixth

13What Is a Scale?

A scale provides a set of notes from which melodies and chords can be constructed.

14What Is a Key?

For example, music in the key of C major is centered on:

• The note C
• The C-major chord
• The notes and chords associated with the C-major scale

A piece in C major can contain notes outside the C-major scale. These are called chromatic notes. The piece remains in C major as long as C continues to function as its tonal center.

15Scale Degrees

Each note of a seven-note scale has a number and a functional name.

Scale degrees may be written with carets:

The corresponding movable-do solfège syllables are:

16The Major Scale

Every major scale follows the same pattern:

Measured in semitones from the tonic, the pattern is:

The C-major scale is:

Its step pattern, key to key:

• C to D = whole
• D to E = whole
• E to F = half
• F to G = whole
• G to A = whole
• A to B = whole
• B to C = half

17Correct Scale Spelling

18Natural Minor

The natural-minor pattern is:

Measured from the tonic:

The A natural-minor scale is:

19Harmonic Minor

A natural minor:

A harmonic minor:

Its pattern is:

The raised seventh creates a leading tone:

It also changes the chord built on the fifth degree from minor to major:

• E–G–B = E minor
• E–G♯–B = E major

This creates a stronger dominant-to-tonic resolution:

20Melodic Minor

In classical theory, the ascending melodic-minor scale raises the sixth and seventh degrees.

A melodic minor ascending:

When descending, classical melodic minor ordinarily returns to natural minor:

In jazz theory, melodic minor typically uses its ascending form in both directions:

21Relative Major and Minor

Examples:

• C major and A minor
• F major and D minor
• G major and E minor
• E♭ major and C minor

To find the relative minor of a major key:

• Begin on the major scale’s sixth degree, or
• Move down a minor third from the major tonic

To find the relative major of a minor key:

• Begin on the minor scale’s third degree, or
• Move up a minor third from the minor tonic

22Parallel Major and Minor

Examples:

• C major and C minor
• F major and F minor
• A major and A minor

23What Is a Chord?

Many basic Western chords are built by stacking thirds — selecting alternating notes from a scale.

24Triads

A triad contains three chord members:

1. Root
2. Third
3. Fifth

The root names the chord. The third usually determines whether the chord is major or minor. The fifth helps determine whether the chord is diminished or augmented.

25Four Types of Triads

Examples built on C:

• C major: C–E–G
• C minor: C–E♭–G
• C diminished: C–E♭–G♭
• C augmented: C–E–G♯

To turn a major triad into a minor triad, lower its third by one semitone:

26Chord Symbols

Common chord symbols include:

27What Does Diatonic Mean?

In C major, the diatonic notes are:

A diatonic chord in C major uses only those notes.

28Building a Triad on Each Scale Degree

To build a triad on a scale degree:

1. Choose the scale degree as the root.
2. Skip the next scale note.
3. Add the following note as the third.
4. Skip another scale note.
5. Add the following note as the fifth.

29Diatonic Triads in a Major Key

The triads in C major are:

The triad quality pattern in every major key is:

Or:

30Roman-Numeral Analysis

Roman numerals identify a chord’s scale degree and quality.

• Uppercase = major
• Lowercase = minor
• ° = diminished
• + = augmented

Examples:

• I = major chord on degree 1
• ii = minor chord on degree 2
• V = major chord on degree 5
• vii° = diminished chord on degree 7

Roman numerals allow the same progression to be described in any key. For example:

In C major:

In F major:

31Primary Chords

The three primary chords in a major key are:

• I — tonic
• IV — subdominant
• V — dominant

In C major:

32Diatonic Triads in Natural Minor

The triads in A natural minor are:

The natural-minor pattern is:

In tonal minor music, the seventh degree is frequently raised to create a stronger dominant chord. In A minor:

• E–G–B = E minor, or v
• E–G♯–B = E major, or V
• E–G♯–B–D = E7, or V7

The major V or dominant V7 strongly resolves to i:

33Root Position and Inversions

For C major:

A triad has two inversions.

All three contain the notes C, E, and G, so all three are C-major chords.

34Slash-Chord Notation

A slash chord is written as the chord symbol followed by a slash and the bass note.

• C = C major with C normally in the bass
• C/E = C major with E in the bass
• C/G = C major with G in the bass

35Chord Voicing

The same chord can be played:

• In different octaves
• With different notes doubled
• In close or widely spaced positions
• With different chord members on top
• In different inversions

Voicing changes the chord’s color and texture without necessarily changing its fundamental identity.

36Building Seventh Chords

Adding another stacked third to a triad creates a seventh chord:

1. Root
2. Third
3. Fifth
4. Seventh

Common seventh chords include:

• C7 = C–E–G–B♭
• Cmaj7 = C–E–G–B

37Diatonic Seventh Chords in Major

The seventh chords in C major are:

The pattern in every major key is:

Hear all of these in the diatonic explorer above — switch it to Sevenths.

38Tonic, Predominant, and Dominant Functions

Chords can be grouped according to the roles they perform.

The basic functional progression is:

In C major:

Or:

39The Dominant-to-Tonic Relationship

In C major:

• Tonic = C
• Dominant = G
• Dominant chord = G–B–D
• Dominant seventh = G–B–D–F

The dominant chord contains the leading tone B, which tends to resolve upward to C.

In G7:

• B tends to move up to C.
• F tends to move down to E.

These two movements create a strong resolution:

40The ii–V–I Progression

In C major:

• ii = D minor
• V = G major
• I = C major

With seventh chords:

The functions are:

• Dm7 = predominant
• G7 = dominant
• Cmaj7 = tonic

A ii–V change refers to the movement from ii to V, often as part of a complete ii–V–I progression.

41What Is a Cadence?

Cadences can sound:

• Final
• Partially complete
• Unfinished
• Unexpected

42Common Cadences

A half cadence is like a musical comma or question mark because the phrase ends on the dominant.

A perfect authentic cadence is like a musical period because it provides strong closure.

43What Is a Key Signature?

It indicates which notes are normally sharpened or flattened throughout the music.

A key signature does not, by itself, distinguish between a major key and its relative minor. Musical context determines which tonic is functioning as the tonal center.

44The Circle of Fifths

The circle of fifths organizes:

• Major keys
• Minor keys
• Key signatures
• The order of sharps and flats
• Closely related keys
• Dominant-to-tonic relationships

Moving clockwise raises each tonic by a perfect fifth:

Each clockwise step adds one sharp.

Moving counterclockwise raises each tonic by a perfect fourth, which is equivalent to moving down a perfect fifth:

Each counterclockwise step adds one flat.

45Major Keys and Relative Minors

Some keys occupy enharmonically equivalent positions:

• F♯ major and G♭ major
• C♯ major and D♭ major
• B major and C♭ major

They sound the same on an equal-tempered instrument but use different spellings and key signatures.

46Order of Sharps

Sharps are added in this order:

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Examples:

• G major: F♯
• D major: F♯, C♯
• A major: F♯, C♯, G♯
• E major: F♯, C♯, G♯, D♯

47Order of Flats

Flats are added in the reverse order:

Battle Ends And Down Goes Charles’ Father

Examples:

• F major: B♭
• B♭ major: B♭, E♭
• E♭ major: B♭, E♭, A♭
• A♭ major: B♭, E♭, A♭, D♭

48Finding a Major Key from Sharps

For a key signature containing sharps:

1. Find the final sharp.
2. Raise it by one semitone.
3. The resulting note is the major tonic.

49Finding a Major Key from Flats

For a key signature containing two or more flats:

1. Find the second-to-last flat.
2. That flat names the major key.

50Closely Related Keys

Keys next to each other on the circle of fifths differ by only one accidental.

C major’s neighboring keys are:

• G major: one sharp
• F major: one flat

Because neighboring keys share most of their notes and chords, movement between them usually sounds smooth.

51Dominant Motion Around the Circle

The circle also shows dominant-to-tonic movement.

Examples:

• G7 resolves to C.
• D7 resolves to G.
• A7 resolves to D.
• E7 resolves to A.

A progression can chain these resolutions:

This moves counterclockwise around the circle by descending fifths.

§The Whole Map

The concepts build on one another in this order:

1. Pitch describes how high or low a sound is.
2. The octave is divided into 12 semitones.
3. Notes receive letter names and may be changed by accidentals.
4. Letter names and semitone distances determine intervals.
5. Patterns of whole and half steps create scales.
6. A key organizes notes and chords around a tonic.
7. Notes within a scale are assigned scale degrees.
8. Stacking thirds on scale degrees creates triads.
9. Adding another third creates seventh chords.
10. Roman numerals describe chords relative to the key.
11. Chords perform tonic, predominant, and dominant functions.
12. Functions produce progressions such as ii–V–I.
13. Progressions create tension, resolution, and cadences.
14. The circle of fifths organizes keys, signatures, relatives, and dominant relationships.

Essential Patterns to Memorize