Music Theory

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Notation

Staff
The music staff is a set of five horizontal lines and four spaces on which musical notes are written.

Note
A note is a symbol that represents a specific pitch and duration in music. Notes are placed on the staff to show which sound to play and for how long.

Pitch
Pitch refers to how high or low a sound is. It is determined by the frequency of the sound wave; higher frequencies produce higher pitches, and lower frequencies produce lower pitches.

Musical Alphabet
The musical alphabet consists of seven letters: A, B, C, D, E, F, and G. These letters repeat in order across the musical scale.

Clef
A clef is a symbol placed at the beginning of the staff that indicates the pitch of the notes on the lines and spaces. It helps to identify which notes are represented by the notes on the staff.

Treble Clef
The treble clef, also known as the G clef, spirals around the second line of the staff, which represents the note G. It is used for higher-pitched instruments and voices, such as the violin, flute, and right hand of the piano.

Bass Clef
The bass clef, also known as the F clef, marks the fourth line of the staff as the note F. It is used for lower-pitched instruments and voices, such as the cello, bassoon, and left hand of the piano.

Whole Tone (Whole Step)
- An interval of two semitones.
- Example: From C to D (C → C# → D).
- In scale: The distance between C and D is a whole tone.

Semitone (Half Step)
- The smallest interval in Western music, equal to one fret on a guitar or one key on a piano (black or white).
- Example: From C to C# (or Db), or from E to F.
- In scale: The distance from E to F is a semitone.

Accidental
- A symbol (sharp, flat, or natural) used to alter the pitch of a note outside the key signature.
- Example: If you see a # or b next to a note like F#, it’s an accidental.

Sharp (#)
- Raises a note by one semitone.
- Example: F# is one semitone higher than F.

Flat (b)
- Lowers a note by one semitone.
- Example: Bb is one semitone lower than B.

Natural (♮)
- Cancels a previous sharp or flat, returning the note to its original pitch.
- Example: If a note was F# and you see a natural sign, it becomes F again.

Double Sharp (𝄪)
- Raises a note by two semitones (a whole step).
- Example: C𝄪 is two semitones higher than C, which sounds like D.

Double Flat (𝄫)
- Lowers a note by two semitones.
- Example: B𝄫 is two semitones lower than B, which sounds like A.

Chromatic Semitone
- The semitone between two notes that are spelled differently but sound the same (enharmonic).
- Example: C# and Db are enharmonic equivalents, both a chromatic semitone apart.

Diatonic Semitone
- The semitone between two notes in the same diatonic scale, which are spelled differently.
- B to C are two notes with different spelling and are a diatonic semitone apart.

Enharmonic Equivalent Notes
- Two notes that sound the same but are written differently.
- Example: C# and Db, or F# and Gb.

Keys

The illustration shown above is the circle of fifths. It moves in fifths clockwise from C to G, D, A, E, B, F#, and so on. Moving counterclockwise from C to F, Bb, Eb, Ab, Db, Gb, and so forth, the circle progresses in fourths. The keys shown in green inside the circle represent the minor keys. Some keys are enharmonic equivalents, meaning they sound the same but are written differently; for example, B and Cb are enharmonic equivalents, as are F# and Gb, and C# and Db. Similarly, D# and Eb are enharmonic equivalents, and A# and Bb are also enharmonic equivalents.

Major Keys:

- C major — no sharps or flats
- G major — 1 sharp (F#)
- D major — 2 sharps (F#, C#)
- A major — 3 sharps (F#, C#, G#)
- E major — 4 sharps (F#, C#, G#, D#)
- B major — 5 sharps (F#, C#, G#, D#, A#)
- F# major — 6 sharps (F#, C#, G#, D#, A#, E#)
- C# major — 7 sharps (F#, C#, G#, D#, A#, E#, B#)

- F major — 1 flat (Bb)
- Bb major — 2 flats (Bb, Eb)
- Eb major — 3 flats (Bb, Eb, Ab)
- Ab major — 4 flats (Bb, Eb, Ab, Db)
- Db major — 5 flats (Bb, Eb, Ab, Db, Gb)
- Gb major — 6 flats (Bb, Eb, Ab, Db, Gb, Cb
- Cb major — 7 flats (Bb, Eb, Ab, Db, Gb, Cb, Fb)

Minor Keys:

- A minor — no sharps or flats
- E minor — 1 sharp (F#)
- B minor — 2 sharps (F#, C#)
- F# minor — 3 sharps (F#, C#, G#)
- C# minor — 4 sharps (F#, C#, G#, D#)
- G# minor — 5 sharps (F#, C#, G#, D#, A#)
- D# minor — 6 sharps (F#, C#, G#, D#, A#, E#)

- A# minor — 7 sharps (F#, C#, G#, D#, A#, E#, B#)

- D minor — 1 flat (Bb)
- G minor — 2 flats (Bb, Eb)
- C minor — 3 flats (Bb, Eb, Ab)
- F minor — 4 flats (Bb, Eb, Ab, Db)
- Bb minor — 5 flats (Bb, Eb, Ab, Db, Gb)
- Eb minor — 6 flats (Bb, Eb, Ab, Db, Gb, Cb)
- Ab minor — 7 flats (Bb, Eb, Ab, Db, Gb, Cb, Fb)

Scale Degree Names

1. Tonic — the first and home note of the scale
2. Supertonic — the second note, just above the tonic
3. Mediant — the third note, halfway between the tonic and dominant
4. Subdominant — the fourth note, below the dominant and above the tonic
5. Dominant — the fifth note, strongly leading back to the tonic
6. Submediant — the sixth note, halfway between the subdominant and the octave
7. Leading tone (or Subtonic in natural minor) — the seventh note, leading up to the tonic (a half step below the tonic in major and harmonic minor; a whole step below in natural minor)

Scales

A scale is a sequence of musical notes arranged in ascending or descending order, spanning an octave.

Major Scale
A major scale is a specific type of scale characterized by a bright, happy sound. It consists of seven notes plus the octave, following a particular pattern of intervals (whole and half steps).

To construct a major scale starting from a root note:
1. Follow the pattern of intervals: Whole, Whole, Half, Whole, Whole, Whole, Half (W-W-H-W-W-W-H).
2. Starting from your root note, move through the notes according to this pattern.

Example:*
Constructing a C Major Scale:
- Start on C
- Move a whole step up to D
- Whole step up to E
- Half step up to F*
- Whole step up to G
- Whole step up to A
- Whole step up to B
- Half step up to C (octave)
C — D — E — F — G — A — B — C

Natural Minor Scale

The natural minor scale is a basic minor scale with a specific pattern of whole and half steps.
- Pattern: W - H - W - W - H - W - W (where W = whole step, H = half step)
- It can be derived from the major scale by lowering the 3rd, 6th, and 7th scale degrees by a half step.

Example in A minor:

- Start on A
- Move a whole step up to B
- Whole step up to C
- Half step up to D
- Whole step up to E
- Whole step up to F
- Whole step up to G
- Half step up to A (octave)

A — B — C — D — E — F — G — A

(This is the same as the C major scale starting from A)

Harmonic Minor Scale
The harmonic minor raises the 7th degree of the natural minor scale by a half step to create a leading tone.
- Pattern: W - H - W - W - H - 1.5W - H
(where 1.5W means a step and a half, or a whole step plus a half step)

Same as the natural minor but with the 7th degree raised by a half step.

Example in A harmonic minor:

- Start on A
- Move a whole step up to B
- Whole step up to C
- Half step up to D
- Whole step up to E
- Whole step up to F
- Half step up to G♯ (raised 7th degree)
- Half step up to A (octave)

A — B — C — D — E — F — G♯ — A

Melodic Minor Scale
The melodic minor scale raises both the 6th and 7th degrees by a half step when ascending, but reverts to the natural minor form when descending.
- (ascending): W - H - W - W - W - W - H
- (descending): Same as natural minor

- Ascending: Raise 6th and 7th degrees of the natural minor
- Descending: Use the natural minor form

Example in A melodic minor (ascending):

- Start on A
- Move a whole step up to B
- Whole step up to C
- W half step up to D
- W whole step up to E
- W whole step up to F♯ (raised 6th)
- W whole step up to G♯ (raised 7th)
- Half step up to A (octave)

A — B — C — D — E — F♯ — G♯ — A

Descending A Melodic Minor Scale:

- When descending, it reverts to the natural minor form:
A — G — F — E — D — C — B — A

Relative Major and Minor Scales
The major key that shares the same key signature (sharps/flats) as a minor key is called the relative major. It is located a major sixth above the minor key’s tonic.

The minor key that shares the same key signature as a major key is called the relative minor. It is located a minor sixth (or a whole step down) below the major key’s tonic.

- To find the relative major of a minor key, go up a minor third (3 semitones) from the minor key’s tonic.
- To find the relative minor of a major key, go down a minor third from the major key’s tonic.

List of All Major and Their Relative Minors

C major is the relative major of A minor, since both keys have no sharps or flats in their key signatures.

Tonic Major and Minor Scales

Tonic major and minor scales are scales that share the same root note (called the tonic) but differ in their mode — one is a major scale, and the other is a minor scale. These are also known as parallel major and minor scales.

- Tonic Major Scale: The major scale that starts on a specific note.
- Tonic Minor Scale: The natural minor scale that starts on the same note.

For example:
- C Major and C Minor*are parallel scales because they both start on C.
- They share the same tonic note (C) but differ in their structure and sound.

List of All Tonic Major and Minor (Parallel) Scales
C Major C Natural Minor
C# Major / Db Major C# Natural Minor / Db Natural Minor
D Major D Natural Minor
D# Major / Eb Major D# Natural Minor / Eb Natural Minor
E Major E Natural Minor
F Major F Natural Minor
F# Major / Gb Major F# Natural Minor / Gb Natural Minor
G Major G Natural Minor
G# Major / Ab Major G# Natural Minor / Ab Natural Minor
A Major A Natural Minor
A# Major / Bb Major A# Natural Minor / Bb Natural Minor
B Major B Natural Minor

Modes

The major scale modes are different scales derived from the major scale by starting on different degrees (notes). There are seven modes in total, each with its own unique sound and pattern.

The Seven Major Scale Modes

Starting from the Ionian mode (the major scale), the modes are:

1. Ionian (Major Scale)
2. Dorian
3. Phrygian
4. Lydian
5. Mixolydian
6. Aeolian (Natural Minor Scale)
7. Locrian

How to Write Each Mode (with Example in C)

Let's use the C major scale (C-D-E-F-G-A-B-C) to illustrate each mode:

1. Ionian (Major Scale)
- Notes: C-D-E-F-G-A-B-C
- Pattern: Whole, Whole, Half, Whole, Whole, Whole, Half

2. Dorian (Start on the 2nd degree of the major scale)
- Notes: D-E-F-G-A-B-C-D
- Pattern: Whole, Half, Whole, Whole, Whole, Half, Whole

3. Phrygian (Start on the 3rd degree)
- Notes: E-F-G-A-B-C-D-E
- Pattern: Half, Whole, Whole, Whole, Half, Whole, Whole

4. Lydian (Start on the 4th degree)
- Notes: F-G-A-B-C-D-E-F
- Pattern: Whole, Whole, Whole, Half, Whole, Whole, Half

5. Mixolydian (Start on the 5th degree)
- Notes: G-A-B-C-D-E-F-G
- Pattern: Whole, Whole, Half, Whole, Whole, Half, Whole

6. Aeolian (Natural Minor) (Start on the 6th degree)
- Notes: A-B-C-D-E-F-G-A
- Pattern: Whole, Half, Whole, Whole, Half, Whole, Whole

7. Locrian (Start on the 7th degree)
- Notes: B-C-D-E-F-G-A-B
- Pattern: Half, Whole, Whole, Half, Whole, Whole, Whole

Intervals

An interval is the distance in pitch between two notes. It is measured in steps, and it defines how far apart two notes are.

Qualities of Intervals
Intervals can be described by their quality and number:

- Perfect (P): Used for unisons, fourths, fifths, and octaves.
- Major (M): Used for seconds, thirds, sixths, and sevenths.
- Minor (m): The lowered (flatted) version of major intervals, found in minor scales.
- Augmented (A): A raised interval, larger than perfect or major.
- Diminished (d): A lowered interval, smaller than perfect or minor.

Intervals Found in the Major Scale
The major scale contains specific intervals between the root and other notes:
Unison | C — C |
Major Second | C — D |
Major Third | C — E |
Perfect Fourth | C — F |
Perfect Fifth | C — G |
Major Sixth C — A |
Major Seventh | C — B |
Octave | C — C |

The major scale includes unison, major seconds, major thirds, perfect fourths, perfect fifths, major sixths, major sevenths, and octaves.

Triad

A triad is a three-note chord built by stacking two intervals of thirds on top of a root note.

Types of Triads

1. Major Triad:
- Root, Major third, Perfect fifth

2. Minor Triad:
- Root, Minor third, Perfect fifth

3. Diminished Triad:
- Root, Minor third, Diminished fifth (one semitone lower than perfect)

4. Augmented Triad:
- Root, Major third, Augmented fifth (raised by one semitone)

Inversions of Triads
Inversions are different arrangements of the notes in a triad

- Root position: The root note is the lowest.
- First inversion: The third of the triad is in the bass.
- Second inversion: The fifth of the triad is in the bass.

Triads from the Major Scale

- I (Tonic) chord: Major triad built on the 1st degree
- ii (Supertonic) chord: Minor triad built on the 2nd degree
- iii (Mediant) chord: Minor triad built on the 3rd degree
- IV (Subdominant) chord: Major triad built on the 4th degree
- V (Dominant) chord: Major triad built on the 5th degree
- vi (Submediant) chord: Minor triad built on the 6th degree
- vii° (Leading tone) chord: Diminished triad built on the 7th degree

Example the C Major Scale:
- C major (I)
- D minor (ii)
- E minor (iii)
- F major (IV)
- G major (V)
- A minor (vi)
- B diminished (vii°)