Theory reference tables

Generated tables you can trust: intervals, key signatures, diatonic chords in every key, chord formulas, scale formulas, and chord-scale pairings.

Every table on this page is produced by the course's theory engine at build time, and the engine is tested against standard theory (see the project README). Bookmark it.

Intervals

Symbol	Name	Semitones	From C	Inversion
P1	perfect unison	0	C → C	P8
m2	minor second	1	C → Db	M7
M2	major second	2	C → D	m7
m3	minor third	3	C → Eb	M6
M3	major third	4	C → E	m6
P4	perfect fourth	5	C → F	P5
A4	augmented fourth	6	C → F#	d5
P5	perfect fifth	7	C → G	P4
m6	minor sixth	8	C → Ab	M3
M6	major sixth	9	C → A	m3
m7	minor seventh	10	C → Bb	M2
M7	major seventh	11	C → B	m2
P8	perfect octave	12	C → C	P8

Key signatures

Major key	Relative minor	Signature	Accidentals in order
C major	A minor	—	—
G major	E minor	1 ♯	F#
D major	B minor	2 ♯	F# C#
A major	F# minor	3 ♯	F# C# G#
E major	C# minor	4 ♯	F# C# G# D#
B major	G# minor	5 ♯	F# C# G# D# A#
F# major	D# minor	6 ♯	F# C# G# D# A# E#
C# major	A# minor	7 ♯	F# C# G# D# A# E# B#
F major	D minor	1 ♭	Bb
Bb major	G minor	2 ♭	Bb Eb
Eb major	C minor	3 ♭	Bb Eb Ab
Ab major	F minor	4 ♭	Bb Eb Ab Db
Db major	Bb minor	5 ♭	Bb Eb Ab Db Gb
Gb major	Eb minor	6 ♭	Bb Eb Ab Db Gb Cb
Cb major	Ab minor	7 ♭	Bb Eb Ab Db Gb Cb Fb

Diatonic seventh chords in every major key

Major keys
Key	Imaj7	ii7	iii7	IVmaj7	V7	vi7	viiø7
C	Cmaj7	Dm7	Em7	Fmaj7	G7	Am7	Bm7b5
F	Fmaj7	Gm7	Am7	Bbmaj7	C7	Dm7	Em7b5
Bb	Bbmaj7	Cm7	Dm7	Ebmaj7	F7	Gm7	Am7b5
Eb	Ebmaj7	Fm7	Gm7	Abmaj7	Bb7	Cm7	Dm7b5
Ab	Abmaj7	Bbm7	Cm7	Dbmaj7	Eb7	Fm7	Gm7b5
Db	Dbmaj7	Ebm7	Fm7	Gbmaj7	Ab7	Bbm7	Cm7b5
Gb	Gbmaj7	Abm7	Bbm7	Cbmaj7	Db7	Ebm7	Fm7b5
B	Bmaj7	C#m7	D#m7	Emaj7	F#7	G#m7	A#m7b5
E	Emaj7	F#m7	G#m7	Amaj7	B7	C#m7	D#m7b5
A	Amaj7	Bm7	C#m7	Dmaj7	E7	F#m7	G#m7b5
D	Dmaj7	Em7	F#m7	Gmaj7	A7	Bm7	C#m7b5
G	Gmaj7	Am7	Bm7	Cmaj7	D7	Em7	F#m7b5

Diatonic chords of the minor scales (A as the example tonic)

Diatonic seventh chords in A minor
Degree	Chord	Notes
i7	Am7	A C E G
iiø7	Bm7b5	B D F A
bIIImaj7	Cmaj7	C E G B
iv7	Dm7	D F A C
v7	Em7	E G B D
bVImaj7	Fmaj7	F A C E
bVII7	G7	G B D F

Diatonic seventh chords in A harmonic minor
Degree	Chord	Notes
i(maj7)	AmMaj7	A C E G#
iiø7	Bm7b5	B D F A
bIII+maj7	Cmaj7#5	C E G# B
iv7	Dm7	D F A C
V7	E7	E G# B D
bVImaj7	Fmaj7	F A C E
vii°7	G#dim7	G# B D F

Diatonic seventh chords in A melodic minor
Degree	Chord	Notes
i(maj7)	AmMaj7	A C E G#
ii7	Bm7	B D F# A
bIII+maj7	Cmaj7#5	C E G# B
IV7	D7	D F# A C
V7	E7	E G# B D
viø7	F#m7b5	F# A C E
viiø7	G#m7b5	G# B D F#

ii–V–I in every key

Major ii–V–I
Key	ii7	V7	Imaj7
C	Dm7	G7	Cmaj7
F	Gm7	C7	Fmaj7
Bb	Cm7	F7	Bbmaj7
Eb	Fm7	Bb7	Ebmaj7
Ab	Bbm7	Eb7	Abmaj7
Db	Ebm7	Ab7	Dbmaj7
Gb	Abm7	Db7	Gbmaj7
B	C#m7	F#7	Bmaj7
E	F#m7	B7	Emaj7
A	Bm7	E7	Amaj7
D	Em7	A7	Dmaj7
G	Am7	D7	Gmaj7

Minor ii–V–i (dominant written with b9)
Key	iiø7	V7b9	i(maj7)
C	Dm7b5	G7b9	CmMaj7
F	Gm7b5	C7b9	FmMaj7
Bb	Cm7b5	F7b9	BbmMaj7
Eb	Fm7b5	Bb7b9	EbmMaj7
Ab	Bbm7b5	Eb7b9	AbmMaj7
Db	Ebm7b5	Ab7b9	DbmMaj7
Gb	Abm7b5	Db7b9	GbmMaj7
B	C#m7b5	F#7b9	BmMaj7
E	F#m7b5	B7b9	EmMaj7
A	Bm7b5	E7b9	AmMaj7
D	Em7b5	A7b9	DmMaj7
G	Am7b5	D7b9	GmMaj7

Secondary dominants and tritone substitutes in every key

Secondary dominants and bII7 (tritone sub of V7)
Key	V7/ii	V7/iii	V7/IV	V7/V	V7/vi	bII7
C	A7	B7	C7	D7	E7	Db7
F	D7	E7	F7	G7	A7	Gb7
Bb	G7	A7	Bb7	C7	D7	Cb7
Eb	C7	D7	Eb7	F7	G7	Fb7
Ab	F7	G7	Ab7	Bb7	C7	Bbb7
Db	Bb7	C7	Db7	Eb7	F7	Ebb7
Gb	Eb7	F7	Gb7	Ab7	Bb7	Abb7
B	G#7	A#7	B7	C#7	D#7	C7
E	C#7	D#7	E7	F#7	G#7	F7
A	F#7	G#7	A7	B7	C#7	Bb7
D	B7	C#7	D7	E7	F#7	Eb7
G	E7	F#7	G7	A7	B7	Ab7

Chord formulas

Symbol	Name	Formula	Notes
C	major triad	1 3 5	C E G
Cm	minor triad	1 b3 5	C Eb G
Cdim	diminished triad	1 b3 b5	C Eb Gb
Caug	augmented triad	1 3 #5	C E G#
Csus4	suspended 4th	1 4 5	C F G
Csus2	suspended 2nd	1 2 5	C D G
C6	major sixth	1 3 5 6	C E G A
Cm6	minor sixth	1 b3 5 6	C Eb G A
C6/9	six-nine	1 3 5 6 9	C E G A D
Cmaj7	major seventh	1 3 5 7	C E G B
C7	dominant seventh	1 3 5 b7	C E G Bb
Cm7	minor seventh	1 b3 5 b7	C Eb G Bb
Cm7b5	half-diminished (minor seven flat five)	1 b3 b5 b7	C Eb Gb Bb
Cdim7	diminished seventh	1 b3 b5 bb7	C Eb Gb A
CmMaj7	minor-major seventh	1 b3 5 7	C Eb G B
Cmaj7#5	major seventh sharp five	1 3 #5 7	C E G# B
C7#5	dominant seventh sharp five	1 3 #5 b7	C E G# Bb
C7b5	dominant seventh flat five	1 3 b5 b7	C E Gb Bb
C7sus4	dominant seventh sus4	1 4 5 b7	C F G Bb
Cmaj9	major ninth	1 3 5 7 9	C E G B D
C9	dominant ninth	1 3 5 b7 9	C E G Bb D
Cm9	minor ninth	1 b3 5 b7 9	C Eb G Bb D
C7b9	dominant seven flat nine	1 3 5 b7 b9	C E G Bb Db
C7#9	dominant seven sharp nine	1 3 5 b7 #9	C E G Bb D#
C7#11	dominant seven sharp eleven	1 3 5 b7 #11	C E G Bb F#
Cmaj7#11	major seven sharp eleven	1 3 5 7 #11	C E G B F#
C11	dominant eleventh	1 3 5 b7 9 11	C E G Bb D F
Cm11	minor eleventh	1 b3 5 b7 9 11	C Eb G Bb D F
C13	dominant thirteenth	1 3 5 b7 9 13	C E G Bb D A
Cmaj13	major thirteenth	1 3 5 7 9 13	C E G B D A
Cm13	minor thirteenth	1 b3 5 b7 9 13	C Eb G Bb D A
C13b9	thirteen flat nine	1 3 5 b7 b9 13	C E G Bb Db A
C7b13	seven flat thirteen	1 3 5 b7 b13	C E G Bb Ab
C7b9b13	seven flat nine flat thirteen	1 3 5 b7 b9 b13	C E G Bb Db Ab
C7#9#5	seven sharp nine sharp five	1 3 #5 b7 #9	C E G# Bb D#
C7alt	altered dominant	1 3 b7 b9 #9 b13	C E Bb Db D# Ab

Scale formulas

Scale	Formula	Notes from C	Typical chords
Major (Ionian)	1 2 3 4 5 6 7	C D E F G A B	maj7, maj9, 6, 6/9
Dorian	1 2 b3 4 5 6 b7	C D Eb F G A Bb	m7, m9, m6, m11
Phrygian	1 b2 b3 4 5 b6 b7	C Db Eb F G Ab Bb	m7, 7sus4b9
Lydian	1 2 3 #4 5 6 7	C D E F# G A B	maj7, maj7#11, maj9#11, maj13#11
Mixolydian	1 2 3 4 5 6 b7	C D E F G A Bb	7, 9, 13, 7sus4
Aeolian (natural minor)	1 2 b3 4 5 b6 b7	C D Eb F G Ab Bb	m7, m9, m11
Locrian	1 b2 b3 4 b5 b6 b7	C Db Eb F Gb Ab Bb	m7b5
Melodic minor (jazz minor)	1 2 b3 4 5 6 7	C D Eb F G A B	mMaj7, m6, m6/9, mMaj9
Dorian b2 (Phrygian natural 6)	1 b2 b3 4 5 6 b7	C Db Eb F G A Bb	7sus4b9, m7
Lydian augmented	1 2 3 #4 #5 6 7	C D E F# G# A B	maj7#5, maj7#11#5
Lydian dominant	1 2 3 #4 5 6 b7	C D E F# G A Bb	7#11, 9#11, 13#11, 7
Mixolydian b6 (Hindu)	1 2 3 4 5 b6 b7	C D E F G Ab Bb	7b13, 9b13
Locrian natural 2 (half-diminished scale)	1 2 b3 4 b5 b6 b7	C D Eb F Gb Ab Bb	m7b5, m9b5
Altered (Super Locrian)	1 b2 b3 3 b5 b6 b7	C Db Eb E Gb Ab Bb	7alt, 7#5, 7b9#5, 7#9#5
Harmonic minor	1 2 b3 4 5 b6 7	C D Eb F G Ab B	mMaj7, m
Phrygian dominant (Mixolydian b9 b13)	1 b2 3 4 5 b6 b7	C Db E F G Ab Bb	7b9, 7b9b13, 7b13
Harmonic major	1 2 3 4 5 b6 7	C D E F G Ab B	maj7, maj7b13
Whole tone	1 2 3 #4 #5 b7	C D E F# G# Bb	7#5, 7b5, 9#5, aug
Diminished (whole-half)	1 2 b3 4 b5 b6 bb7 7	C D Eb F Gb Ab A B	dim7, dim
Dominant diminished (half-whole)	1 b2 b3 3 #4 5 6 b7	C Db Eb E F# G A Bb	7b9, 7#9, 13b9, 7b9#11
Major pentatonic	1 2 3 5 6	C D E G A	maj, 6, 6/9
Minor pentatonic	1 b3 4 5 b7	C Eb F G Bb	m7, m
Blues scale	1 b3 4 b5 5 b7	C Eb F Gb G Bb	m7, m
Major blues scale	1 2 b3 3 5 6	C D Eb E G A	maj, 6
Bebop dominant	1 2 3 4 5 6 b7 7	C D E F G A Bb B	7, 9, 13
Bebop major	1 2 3 4 5 #5 6 7	C D E F G G# A B	maj7, 6, maj9
Bebop Dorian (minor)	1 2 b3 3 4 5 6 b7	C D Eb E F G A Bb	m7, m9
Bebop melodic minor	1 2 b3 4 5 #5 6 7	C D Eb F G G# A B	mMaj7, m6

Modes of the major scale and of melodic minor

Modes of C Major (Ionian)
Mode	Name	Formula	Notes	Chords
1	C Major (Ionian)	1 2 3 4 5 6 7	C D E F G A B	maj7, maj9, 6
2	D Dorian	1 2 b3 4 5 6 b7	D E F G A B C	m7, m9, m6
3	E Phrygian	1 b2 b3 4 5 b6 b7	E F G A B C D	m7, 7sus4b9
4	F Lydian	1 2 3 #4 5 6 7	F G A B C D E	maj7, maj7#11, maj9#11
5	G Mixolydian	1 2 3 4 5 6 b7	G A B C D E F	7, 9, 13
6	A Aeolian (natural minor)	1 2 b3 4 5 b6 b7	A B C D E F G	m7, m9, m11
7	B Locrian	1 b2 b3 4 b5 b6 b7	B C D E F G A	m7b5

Modes of C Melodic minor (jazz minor)
Mode	Name	Formula	Notes	Chords
1	C Melodic minor (jazz minor)	1 2 b3 4 5 6 7	C D Eb F G A B	mMaj7, m6, m6/9
2	D Dorian b2 (Phrygian natural 6)	1 b2 b3 4 5 6 b7	D Eb F G A B C	7sus4b9, m7
3	Eb Lydian augmented	1 2 3 #4 #5 6 7	Eb F G A B C D	maj7#5, maj7#11#5
4	F Lydian dominant	1 2 3 #4 5 6 b7	F G A B C D Eb	7#11, 9#11, 13#11
5	G Mixolydian b6 (Hindu)	1 2 3 4 5 b6 b7	G A B C D Eb F	7b13, 9b13
6	A Locrian natural 2 (half-diminished scale)	1 2 b3 4 b5 b6 b7	A B C D Eb F G	m7b5, m9b5
7	B Altered (Super Locrian)	1 b2 b3 3 b5 b6 b7	B C D D# F G A	7alt, 7#5, 7b9#5

Chord–scale pairings

Chord	Notes	Scales that contain every chord tone
Cmaj7	C E G B	C Major (Ionian), C Lydian, C Harmonic major, C Bebop major
Cmaj7#11	C E G B F#	C Lydian
C6	C E G A	C Major (Ionian), C Major pentatonic, C Major blues scale, C Bebop major
Cm7	C Eb G Bb	C Dorian, C Phrygian, C Aeolian (natural minor), C Dorian b2 (Phrygian natural 6), C Minor pentatonic, C Blues scale, C Bebop Dorian (minor)
Cm6	C Eb G A	C Dorian, C Melodic minor (jazz minor), C Bebop melodic minor
CmMaj7	C Eb G B	C Melodic minor (jazz minor), C Harmonic minor, C Bebop melodic minor
Cm7b5	C Eb Gb Bb	C Locrian, C Locrian natural 2 (half-diminished scale)
C7	C E G Bb	C Mixolydian, C Lydian dominant, C Bebop dominant
C7sus4	C F G Bb	C Mixolydian
C7#11	C E G Bb F#	C Lydian dominant
C7b9	C E G Bb Db	C Phrygian dominant (Mixolydian b9 b13), C Dominant diminished (half-whole)
C7#9	C E G Bb D#	C Dominant diminished (half-whole)
C7alt	C E Bb Db D# Ab	C Altered (Super Locrian)
C7#5	C E G# Bb	C Altered (Super Locrian), C Whole tone
C13	C E G Bb D A	C Mixolydian, C Bebop dominant
C13b9	C E G Bb Db A	C Dominant diminished (half-whole)
Cdim7	C Eb Gb A	C Diminished (whole-half)
Cmaj7#5	C E G# B	C Lydian augmented