Music Theory

Table of Contents

1. Interval

1.1. 12 Tone Equal Temperament

  • 12 TET
  • The frequency of each note is \(\sqrt[12]{2}\) times the previous note.

1.1.1. Name of Intervals

  • Minor 2nd
  • Major 2nd
  • Minor 3rd
  • Major 3rd
  • Perfect 4th
  • Tritone
  • Perfect 5th
  • Minor 6th
  • Major 6th
  • Minor 7th
  • Major 7th
  • Octave
  • Minor 9th
  • Major 9th
  • …

1.1.2. Dissonace

  • Minor 2nd, Major 2nd, Tritone, Minor 7th, Major 7th, … are considered to be dissonant with different degrees.
  • Tritone is at the exact middle of a scale, which enables Tritone substitution.

2. Chord

Learn EVERY Chord and Chord Symbol - The 7 Systems - YouTube

2.1. N

  • Major chord.
  • major 3rd - minor 3rd.

2.1.1. N7

  • Dominant 7th chord.
  • major 3rd - minor 3rd - minor 3rd.

2.1.2. NM7

  • Or NΔ7
  • Major 7th chord.
  • major 3rd - minor 3rd - major 3rd.

2.1.3. N6

  • Major 6th chord.
  • N(add6)

2.1.4. N6/9

  • Major 6 9 chord.
  • N6(add9)

2.1.5. N9

  • Dominant 9th chord.
  • N7(add9)

2.1.6. NM9

  • Or Nmaj9, NΔ9
  • Major 9th chord.
  • NΔ7(add9)

2.2. Nm

  • Or n, N-
  • Minor chord.
  • minor 3rd - major 3rd.

2.2.1. Nm7

  • Or N-7
  • Minor 7th chord.
  • minor 3rd - major 3rd - minor 3rd

2.2.2. NmM7

  • Or N-Δ7
  • Minor Major 7th chord.
  • minor 3rd - major 3rd - major 3rd

2.2.3. Nm6

  • Minor 6th chord.
  • N-(add6)

2.2.4. Nm6/9

  • Minor 6 9 chord.
  • Nm6(add9)

2.2.5. Nm9

  • Or Nmin9
  • Minor 9th chord.
  • N-7(add9)

2.3. Naug

  • Or N+
  • Augmented chord.
  • N(♯5)
  • major 3rd - major 3rd.

2.3.1. Naug7

  • Or N+7
  • Augmented 7th chord.
  • N(♯5,♭7)
  • major 3rd - major 3rd - major 2nd

2.4. Ndim

  • Or No
  • Diminished chord.
  • N-(♭5)
  • minor 3rd - minor 3rd

2.4.1. Nø7

  • Half-diminished 7th chord.
  • minor 3rd - minor-3rd - major 3rd
  • N-(♭5,♭7)

2.4.2. Ndim7

  • Or No7
  • Diminished 7th chord.
  • N-(♭5,♭♭7)
  • minor 3rd - minor 3rd - minor 3rd

2.5. Nsus4

  • Or Nsus
  • Suspended 4 chord.
  • N(omit3, add4)
  • perfect 4th - major 2nd

2.6. Nsus2

  • Suspended 2 chord.
  • N(omit3, add2)
  • major 2nd - perfect 4th

2.7. Extended chords

  • One can extends every 7th chord by:
    • (add 9) for 9th chord
    • (add 9, 11) for 11th chord
    • (add 9, 11, 13) for 13th chord.

2.7.1. Alterations

  • Sharpening or flattening of extensions are possible in any combination.
  • ♭9
  • ♯9
  • ♯11 (sometimes, ♭5)
  • ♭13 (sometimes, ♯5)
2.7.1.1. N7alt
  • Short for N7(♭9, ♯9, ♯11, ♭13). But one is to improvise with some of or all the altered notes.

2.8. Slash chords

  • Written as N/M.
  • Play N with M as the base note.
    • If note M is in N, then it represents inversion.
    • N could be the extension of M, in such case slash chord is used for notational convenience.

2.9. Polychords

  • Play M with N on top of that.
  • e.g. \[ \rm \frac{N}{M} \]

3. Scale

  • Scale is to tell which note to use to not sound off.

3.1. Diatonic

  • The notes are within the given scale.

3.2. Chromatic

  • The notes are outside of the scale.

3.3. Common Scales

Why 3 Minor Scales Exist (And How We Can Use Them) - YouTube

3.3.1. Major

3.3.2. Minor

  • Or Natural Minor
  • ♭VII, ♭III, ♭VI

3.3.3. C Minor Scale

Note Diatonic Chord
C Cm
D Do
E♭ E♭
F Fm
G Gm
A♭ A♭
B♭ B♭

3.3.4. Harmonic Minor

  • ♭III, ♭VI
  • This is to preserve the leading tone, VII.

3.3.5. C Harmonic Minor Scale

Note Diatonic Chord
C Cm
D Do
E♭ E♭+
F Fm
G G
A♭ A♭
B Bo

3.3.6. Melodic Minor

  • ♭III when ascending, ♭VII, ♭III, ♭VI when descending.
    • This is because we don't need leading tone when descending.
  • This is to remove the large gap between ♭VI and VII.

3.3.7. C Melodic Minor Scale

Note Diatonic Chord
C Cm
D Dm
E♭ E♭+
F F
G G
A Ao
B Bo

4. Key

  • The note that is the center of gravity.
    • Think of a song as a dance around this key.

5. Mode

  • Mode is a scale and a harmonic structure.
  • C Ionian = D Dorian = E Phrygian = …

5.1. Ionian

5.2. Dorian

  • ♭VII, ♭III

5.3. Phrygian

  • ♭VII, ♭III, ♭VI, ♭II

5.4. Lydian

  • ♯IV

5.5. Mixolydian

  • ♭VII

5.6. Aeolian

  • ♭VII, ♭III, ♭VI

5.7. Locrian

6. Chord Progression

7. Circle of Fifths

8. Tritone Substitution

9. Cadence

Cadence - Wikipedia

  • The end of phrase in which a full or partial resolution is achieved.

9.1. Jazz

  • ii9 - V13 - I6/9
    • Dm9 - G13 - C6/9

9.2. Pop

  • I - V - vi - IV

9.3. Inspirational

Corporate Music - How to Compose with no Soul - YouTube

  • IV - I - vi - V

chord_progression_IV-I-vi-V-1.png

9.4. Andalusian Cadence

  • vi - V - IV - III

9.5. Common Progression

  • 1-5-6-4. C, G, Am, F.
  • 6-4-1-5. Am, F, C, G.
  • 1-4-5-4. C, F, G, F.
  • 1-6-4-5. C, Am, F, G.
  • 2-5-1-6. Dm, G, C, Am.

10. Element

10.1. Tune

  • A piece of music

10.2. Phrase

  • Few bars of idea

10.3. Riff

  • The core idea of a tune

10.4. Lick

  • Quick phrase that acts as an embellishment

10.5. Vamp

  • Repeated chords
  • Usually melody is played over it.

10.6. Ostinato

Corporate Music - How to Compose with no Soul - YouTube

  • Persistently repetitive motif

11. Modal Interchange

It is a musical technique of temporarily changing 5 amidst a song.

12. Transposition

  • Transposing a piece means to rewrite the piece in another key.
  • How to Make a Musical Theme fit any Context - YouTube
    • Change based on the position of the notes within a scale
    • Change the notes based on the rises and falls of the intervals
      • The notes on the weak beats are not essential for the motif.
      • Insertion of Removal of notes are also possible.

13. Rhythm

Most rhythms don't have a recognized name

13.1. Son Clave

  • Bo Diddley Beat
  • son_clave.cropped_1722134548782_0.svg
    • Three Two Son Clave, Son Clave (3:2)
  • The version with bars exchanged is called Son Clave (2:3)
  • It is from the Latin music

13.2. Tresillo

  • Tresillo is spanish for triplet
  • tresillo.cropped_1722135354242_0.svg
  • Almost Triplet. Long(3) - Long(3) - Short(2)
  • Especially common among 2010 pop music.

13.3. Rumba Clave

  • rumba_clave.cropped_1722136697677_0.svg{:height 65, :width 418}

13.4. Standard African Bell Pattern

  • std_african_bell_pattern.cropped_1722136951747_0.svg
  • Likely to have influenced the shuffle groove

13.5. Swing

  • Whenever the eighth note is not evenly spaced, and the first ones are longer than the second ones.
  • The swing ratio is the ratio between the long and short notes.
  • Shuffle is 2 to 1 swing

13.5.1. Shuffle Groove

  • shuffle_groove.cropped_1722137451728_0.svg
  • Heart of the Blues, Jazz and later Rock music
  • It is a rhythm in 12/8 where we emphasize the first and third eighth note in each beat

13.5.2. Scotch Snap

  • Lombard Rhythm
  • scotch_snap.cropped_1722138054722_0.svg{:height 82, :width 421}
  • The name comes from the traditional Scottish music, and the Lombard comes from the baroque music.
  • It is also heard form the modern R&B and hip-hop music.

13.6. Bossa Nova

  • It makes use of various syncopated rhythms.
  • bossa_nova.cropped_1722138413849_0.svg
    • Archetypal Bossa Nova
    • 3 - 3 - 4 - 3 - 3

13.7. The Charleston

  • charleston.cropped_1722138725841_0.svg
  • Origianlly a song written for Charleston dance

13.8. Waltz

  • waltz.cropped_1722141018406_0.svg
  • Originally used for dancing

13.9. 5/4 Clave

  • 5_4_clave.cropped_1722141421601_0.svg
  • Famously featured in Mission Impossible

13.10. Polyrhythm

13.10.1. 3:2 Polyrhythm

  • Hemiola
  • Nice Cup of Tea

13.10.2. 4:3 Polyrhythm

  • Pass the god damn butter

13.11. Football Clap

  • England Chant
  • football_clap.cropped_1722142409588_0.svg
  • Shout England at the last two notes.

13.12. Shave and a Haircut, Two Bits

  • shave_and_a_haircut.cropped_1722142501999_0.svg
  • Rhythmic Call and Response
  • To give you a shave and a haircut, but not give you the two bits.

14. Instruments

14.1. Piano

  • The center C is called C4
    • My piano is tuned such that D4 = C4.

14.2. Double Base

15. Notations

15.1. Time Signature

15.1.1. Common time

common_time_symbol.png

  • Shorthand for 4/4.

15.1.2. Cut time

cut_time_symbol.png

  • Shorthand for 2/2.

15.2. Text

15.2.1. Rehearsal Mark

  • \(\fbox{A}\)
    • Letter A
  • \(\fbox{\,1\,}\)
    • Figure 1
  • Used to divide a score into movements.
  • It is useful for rehearsal.

15.3. History

Notation Must Die: The Battle For How We Read Music - YouTube

  • François-Auguste Gevaert(1828-1908) classified the musical notations into two categories: Phonetic notation,

15.3.1. Phonetic Notation

  • Chinese, Arabic, Hindi, Ancient Greek Notations.
  • Jianpu: Contemporary Chinese System for simple melodies.

15.3.2. Western Notation

15.3.2.1. Neumatic Notation
  • Started Out of Gregorian Chants to standardize its fragmentations across the continent.
  • Neumes: Squiggles indicating the quality of the note.
15.3.2.2. Nonantolian Notation
  • Northern Italy
  • Single, and later double, horizontal lines with vertical lines indicating pitches.
15.3.2.3. Guido
  • Guido made the nonantolian notation four horizontal lines, the staff lines, and placed neumes upon it. This system spread and it was standardized.
15.3.2.4. Mensural Notation
  • Polyphony emerged, and the rhythms needed to be notated.
  • Longa Brevis Semibrevis Minima Semiminima Fusa Semifusa
  • There's many competing systems.
  • Franco of Cologne introduced the prick of perfection that makes the brevis altera into brevis recta.
15.3.2.5. Standard Notation
  • Modern Standard that is descendant of all of these.

16. Music Composition

16.1. Chord Voicing

16.2. Structure

16.2.1. Harmony

16.2.2. Form

  • Such as sections

16.2.3. Narrative

  • Mainly, the melody.

17. References

Author: Jeemin Kim

Created: 2026-07-12 Sun 14:28