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THE CHORD / SCALE DICTIONARY
This is a work in progress. Currently lists only jazz names, classical names will be added later.
The chord/scale dictionary lets you look up any chord or scale by its notes and find out its name. The dictionary includes colloquial names, for research purposes. If you only know the C-E-G-Bb-D# chord as a dom7-sharp-9 chord, you won't find much about it if you google it. But if you know its colloquial name, the Hendrix chord, you can find out much more. Colloquial names include classical and jazz names: the Italian 6th chord, the double dim chord, the phrygian chord, etc. Occasionally, a song, genre or ethnic group associated with the chord or scale is listed.
THE FORMAT
The lefthand columns are more mathematical and the righthand columns are more musical. Example:
354 435 0-4-7 1-M3-5 C-E-G C "major"
The final digit of the gap number is derived from an assumed octave (0-4-7 is really 0-4-7-12). The digits of a gap number always add up to 12. The gap number is rotated by successively making the first digit last (435 --> 354 --> 543). The index number column comes first because the dictionary is sorted by index number.
For a scale, rather than a gap between notes there is a scale step. The major pentatonic scale CDEGAC has elements 1-M2-M3-5-M6, element numbers 0-2-4-7-9, a gap number 22323 and an index number 22323. The line between chords and scales is fuzzy; this scale can also be consided to be a C6/9 chord.
Scales have modes (C major = A minor) and chords have homonyms (C6 = Am7). Homonyms and modes are grouped together, so you can easily find alternate interpretations of your chord/scale. This is why the dictionary is sorted by index number, because every group of homonyms/modes has the same index number. The larger the index number, the more evenly distributed around the octave the notes of the chord/scale are, and the more common the chord/scale will usually be. For this reason index numbers are sorted high to low.
Within a group, homonyms/modes are sorted most common first and least common last, with obscure ones in parentheses. The first homonym/mode has a C root/tonic and the others have the appropriate root/tonic. Only 1 of the 12 possible chords is listed, e.g., Cm represents the minor chord in general, and stands for Dbm, Dm, Ebm, Em, etc.
Certain chords imply a missing root. For example, play C major, F major, C major and B diminished. In this context, to Western ears, the Bdim triad sounds like a G7 tetrad, even though no G note was played. G7 is a rootless homonym of Bdim. In fact G7 is a more common interpretation of the notes B-D-F than Bdim. Rootless homonyms can be used to find bass notes or suggest arrangements. Rootless homonyms are listed among the other homonyms as "no1" chords. Every chord has 12 possible roots, and 12 possible homonyms, but unlikely ones are omitted from the dictionary.
The jazz name can be affected by the voicing. For example, the difference between C9sus4 and C11no3 is whether the F note is voiced low or high.
Dyads are defined analogous to triads, tetrads, etc. as two pitch classes, not two pitches as some theory textbooks assert. Thus the 0-7 interval contains exactly two pitches, but the 0-7 dyad may contain more (e.g. C3-G3-C4-G4-C5). Likewise C3-C4-C5 is a monad. The term "chord" is expanded from its traditional meaning to include monads and dyads.
The "Intervals" section omits the index number and gap number columns, and is sorted by interval size. This section also lists how each interval would appear in a chord name, e.g. 0-2 appears as either sus2 or 9. Obscure intervals that are never used in chord names, such as aug 3rd or dim 4th, are omitted.
Gap numbers and index numbers have digits that are really numbers, but the numbers 10 and 11 can't be digits. Therefore two dyad groups (2A and 1B) and one triad group (11A) require using A for 10 and B for 11 in the gap and index numbers.
HOW TO LOOK UP A CHORD OR SCALE
First octave-reduce all chord notes so that the 9th becomes a 2nd, the 11th becomes a 4th, etc. Then use one of these two methods:
1st method: If you know the root/tonic of your chord/scale, search for the elements (or element numbers) using control-F. Element numbers are safer because they avoid the 4 ambiguities (A2/m3, A4/d5, A5/m6 and M6/d7). Transpose the chord/scale as needed. Omit the leading "1-" or "0-" to also find rootless versions of your chord. If your chord is rootless, beware, not all rootless homonyms are listed.
2nd method: Find the gap number and search for that. Or, rotate the gap number to find the index number, look up the index number in the first column, and look for the gap number in the homonym/mode group. Because of rootless homonyms, a single gap number may appear multiple times in a homonym group. Transpose as needed.
For D-F-A, the 1st method gives 1-m3-P5 = 0-3-7. Search the triads for "1-m3-P5" or "0-3-7" to get Cm. Transpose the chord from C to D to get Dm. To find (D)-F-A, search the dyads for "m3-P5" or "3-7" to get Am,no1. Transpose the chord from A to D to get Dm,no1.
The 2nd method gives D-F = 3 semitones, F-A = 4 and A-D = 5, making 345 for the gap number and in this case also the index number. Look up this number in the first column. Look for 345 in the 2nd column, the homonym group. It appears as Cm and AbM7no1 and F9no1,3. Transpose from the rooted homonym, from C to D, up a M2 to get Dm. Transpose the rootless Ab and F homonyms similarly to get BbM7no1 and G9no1,3.
BACKGROUND INFO, MISC NOTES, MATHY STUFF
There are 351 possible combinations of the 12 notes. 2101 combinations if including rooted homonyms and modes.
Only 2048 if accounting for symmetrical chords/scales like dim7 or the whole tone scale. But that wouldn't
shorten the dictionary, because symmetrical chords/scales are listed with all possible roots/tonics. Including
rootless homonyms increases the number of entries. With every possible root considered, the theoretical maximum
is 351 x 12 = 4212 combinations. But tonicless scales are pointless, so there are under 4000 entries total.
1 monad
6 dyads, 11 counting rooted homonyms
19 triads, 55 counting rooted homonyms
43 tetrads, 165 counting rooted homonyms
66 pentads, 330 counting rooted homonyms/modes
80 hexads, 462 counting rooted homonyms/modes
66 heptads, 462 counting rooted homonyms/modes
43 octatonic scales, 330 counting modes
19 nonatonic scales, 165 counting modes
6 decatonic scales, 55 counting modes
1 11-note scale, 11 counting modes
1 12-note scale
groups homonyms/modes symmetrical chords/scales
1 1 1
2 6 12 - 1 = 11 66
3 19 57 - 2 = 55 444
4 43 172 - 7 = 165 3333, 2424, 1515
5 66 330
6 80 480 - 18 = 462 222222, 131313, 132132, 123123, 114114
7 66 462
8 43 344 - 14 = 330 12121212, 11221122, 11131113
9 19 171 - 6 = 165 112112112
10 6 60 - 5 = 55 1111211112
11 1 11
12 1 1
--- ---- --
351 2101 - 53 = 2048
Apparently no one has ever compiled a dictionary of all 4000 chords/scales. Some related attempts:
www.stevenjacks.com/conservatory/resources/scales-and-chords/ (useless made-up names)
www.allthescales.org (more useless made-up names)
en.wikipedia.org/wiki/Forte_number (I hate these!)
www.tedgreene.com/images/lessons/v_system/14_The_43_Four-Note_Qualities.pdf (very good, but tetrads only)
solomonsmusic.net/pcsets.htm (good, but no homonyms or modes)
www.e-chords.com/chord-dictionary.htm (Good start, but put in C5-/7 or C4/9 and you get a wrong keyboard, missing a black key!
Uses a different convention: C7sus4no5 is called C4/7, C/9 is called C9, and C9 is called C7/9)
jguitar.com/chorddictionary.jsp (Good, but doesn't group homonyms, and lists obscure homonyms like 354 and 534 separately)
format questions:
Make 1st homonym be a C-rooted chord even if it's rootless?
336 4-7-10 M3-5-m7 (Ab)-C-Eb-Gb Ab7no1
" 0-3-6 1-m3-d5 C-Eb-Gb Cdim
becomes
336 4-7-10 M3-5-m7 (C)-E-G-Bb C7no1
" 0-3-6 1-m3-d5 E-G-Bb Edim
disadvantage: no longer true that every chord contains the C note
advantage: the dom7no1 chord looks more like the dom7 chord
Omit obscure homonyms like 354 and 534?
disadvantage: someone might search for 354 or 534
Add a "gaps" column between "435" and "0-4-7", "M3-m3-4"?
disadvantage: less searchable because of ambiguities like A4 vs. d5
Rotate gap numbers to get the largest index number, and list index numbers small to large?
that makes blocks defined by the largest gap/step, better for scales, worse for chords
THE CHORD / SCALE DICTIONARY
Intervals
Monads and Dyads
Triads
Tetrads
Pentads / Pentatonic Scales
Hexads / Hexatonic Scales
Heptads / Heptatonic Scales
Octatonic Scales
Nonatonic Scales
Decatonic Scales
11-note Scales
12-note Scales
Chord abbreviations:
M = maj = major
m = min = minor
# = aug = augmented
b = dim = diminished
2 = sus2 = suspended 2nd
4 = sus4 = suspended 4th
7 = dom7 = dominant 7th
/ = add = added
Chord symbols:
+ (plus sign) = augmented (e.g. C+ = Caug)
- (minus sign) = minor (e.g. C- = Cm)
Δ (delta sign) = major (e.g. CΔ7 = CM7)
7 (seven with cross-stroke) = major 7th (e.g. C7 = CM7)
o (circle) = dim or dim7 (e.g. Co = Cdim or Cdim7, Co7 = Cdim7)
ø (circle with slash) = half-dim (e.g. Cø or Cø7 = Cm7b5)
Top
Intervals:
element #s name(s) notes written in chord as
0 unison C assumed to be present, absence indicated by no1
0-1 m2 or m9 C-Db b9 (never b2)
0-2 M2 or M9 C-D sus2 or 9
0-3 m3 C-Eb m
" A2 or A9 C-D# #9 (never #2)
0-4 M3 C-E assumed to be present, if absent, m or sus2 or sus4 or no3
0-5 4 or 11 C-F sus4 or 11
0-6 A4 or A11 C-F# #11 (never #4)
" d5 C-Gb b5
0-7 5 C-G assumed to be present, if absent, #5 or b5 or no5
0-8 A5 C-G# #5 or aug
" m6 or m13 C-Ab b13 (never b6)
0-9 M6 or M13 C-A 6 or 13
" d7 C-Bbb dim7 (only used when d5 is present)
0-10 m7 C-Bb 7 ("A" in gap numbers and index numbers)
0-11 M7 C-B M7 ("B" in gap numbers and index numbers)
0-12 8 C-C assumed to be present
Top
Monads and Dyads:
index # gap # element #s elements notes jazz name colloquial name
-- -- 0 1 C C5no5? (used in gyil music)
66 66 0-6 1-d5 C-Gb Cdim,no3
" " " F#-C F#dim,no3
" 4-10 1-M3-m7 (Ab)-C-Gb Ab7no1no5
" " " (D)-F#-C D7no1no5
57 75 0-7 1-5 C-G C5 "power chord"
(57) 0-5 1-4 G-C G4no5
48 48 0-4 1-M3 C-E Cno5
" 3-7 m3-5 (A)-C-E Am,no1
(84) 0-8 1-A5 E-B# Eaug,no3
39 39 0-3 1-m3 C-Eb Cm,no5
" 4-7 M3-5 (Ab)-C-Eb Ab,no1
(93) 0-9 1-M6 Eb-C Eb6no3,5
2A 2A 0-2 1-M2 C-D Csus2no5
A2 0-10 1-m7 D-C D7no3,5
2A 5-7 4-5 (G)-C-D G4no1
1B B1 0-11 1-M7 C-B CM7no3,5
(1B) 0-1 1-m2 B-C B(b9)no3,5
Top
Triads:
To do: expand groups in the "1" block
index # gap # element #s elements notes jazz name colloquial name
444 444 0-4-8 1-M3-A5 C-E-G# Caug
" " " E-G#-B# Eaug
" " " Ab-C-E Abaug
" 3-7-11 m3-5-M7 (A)-C-E-G# AmM7no1
" " " (C#)-E-G#-B# C#mM7no1
" " " (F)-Ab-C-E FmM7no1
354 435 0-4-7 1-M3-5 C-E-G C major (or just C)
" 3-7-10 m3-5-m7 (A)-C-E-G Am7no1
354 2-5-10 M2-4-m7 (D)-E-G-C D11no1,3,5
(543) 0-5-9 1-4-M6 G-C-E G6sus4no5
(354) 0-3-8 1-m3-A5 E-G-B# Em(#5)?
345 345 0-3-7 1-m3-5 C-Eb-G Cm
" 4-7-11 M3-5-M7 (Ab)-C-Eb-G AbM7no1
534 2-7-10 M2-5-m7 (F)-G-C-Eb F9no1,3
453 0-4-9 1-M3-M6 Eb-G-C Eb6no5
(534) 0-5-8 1-4-A5 G-C-D# Gaug,sus4?
336 336 4-7-10 M3-5-m7 (Ab)-C-Eb-Gb Ab7no1
" 0-3-6 1-m3-d5 C-Eb-Gb Cdim
363 0-3-9 1-m3-d7 Eb-Gb-Dbb Ebdim7no5
633 0-6-9 1-d5-d7 F#-C-Eb F#dim7no3
336 3-6-9 m3-d5-d7 (A)-C-Eb-Gb Adim7no1
273 732 0-7-10 1-5-m7 C-G-Bb C7no3
(273) 0-2-9 1-M2-M6 Bb-C-G Bb6sus2no5
(327) 0-3-5 1-m3-4 G-Bb-C Gm/11no5
327 2-5-7 M2-4-5 (F)-G-Bb-C Fsus4/9no1
264 426 0-4-6 1-M3-d5 C-E-Gb C(b5)? "flat five"
(642) 0-6-10 1-d5-m7 Gb-Dbb-Fb ?
(264) 0-2-8 1-M2-A5 E-F#-B# ?
255 525 0-5-7 1-4-5 C-F-G Csus = C4 = Csus4
255 0-2-7 1-M2-5 F-G-C Fsus2 = F2
552 0-5-10 1-4-m7 G-C-F G7sus4no5
246 462 0-4-10 1-M3-m7 C-E-Bb C7no5
246 1-3-7 m2-m3-5 (A)-Bb-C-E Am(b9)no1
(246) 0-2-6 1-M2-d5 Bb-C-Fb Bbsus2(b5)?
(624) 0-6-8 1-d5-m6? 1-A4-A5?
237 372 0-3-10 1-m3-m7 C-Eb-Bb Cm7no5
723 0-7-9 1-5-M6 Eb-Bb-C Eb6no3
237 2-4-7 M2-M3-5 (Ab)-Bb-C-Eb Ab/9no1
(237) 0-2-5 1-M2-4 Bb-C-Eb ?
228 228 0-2-4 1-M2-M3 C-D-E C/9no5
282 0-2-10 1-M2-m7 D-E-C D9no3no5 or D7sus2no5
(822) 0-8-10 1-A5-m7 E-B#-D Eaug7no3
228 3-5-7 m3-4-5 (A)-C-D-E Am/11no1
192 219 0-2-3 1-M2-m3 C-D-Eb Cm/9no5 = Ab(#11)no1
183 318 0-3-4 1-A2-M3 C-D#-E C(#9)no5 = Ab(b13)no1
174 741 0-7-11 1-5-M7 C-G-B CM7no3
165 165 0-1-7 1-d2-5 C-Db-G C5(b9)
156 615 0-6-7 1-A4-5 C-F#-G C5(#11)
147 471 0-4-11 1-M3-M7 C-E-B CM7no5
138 381 0-3-11 1-m3-M7 C-Eb-B CmM7no5
129 291 0-2-11 1-M2-M8 C-D-B CM9no3no5
11A (dissonant)
Top
Tetrads:
no JH = not included in James Hober's list
* = check with JH
To do: expand groups in the "1" block
index # gap # element #s elements notes jazz name colloquial name
3333 3333 0-3-6-9 1-m3-d5-d7 C-Eb-Gb-Bbb Cdim7 "dim" (incorrectly)
" " " D#-F#-A-C D#dim7 "
" " " F#-A-C-Eb F#dim7 "
" " " A-C-Eb-Gb Adim7 "
" 1-4-7-10 m2-M3-5-m7 (B)-C-D#-F#-A B7(b9)no1
" " " (D)-Eb-F#-A-C D7(b9)no1
" " " (F)-Gb-A-C-Eb F7(b9)no1
" " " (G#)-A-B#-D#-F# G#7(b9)no1
" 2-5-8-11 M2-4-m6-M7 (Bb)-C-Eb-Gb-A Bbdim7 ext "dim7 extension"
" " " (C#)-D#-F#-A-B# C#dim7 ext "
" " " (E)-F#-A-C-D# Edim7 ext "
" " " (G)-A-C-Eb-F# Gdim7 ext "
2433 4332 0-4-7-10 1-M3-5-m7 C-E-G-Bb C7 classical "major-minor 7th"
3243 1-4-6-10 m2-M3-d5-m7 (F#)-G-A#-C-E F#7(b5,b9)no1
2433 1-3-7-10 m2-m3-5-m7 (A)-Bb-C-E-G Am7(b9)no1
3324 0-3-6-8 1-m3-d5-m6 E-G-Bb-C Edim(b6)
* 3324 1-4-7-9 m2-M3-5-M6 (Eb)-Fb-G-Bb-C Eb6(b9)no1
2433 0-2-6-9 1-M2-d5-d7 Bb-C-Fb-Abb Bbdim7/9no3 (or Bbdim7sus2?)
or 1-M2-A4-M6 Bb-C-E-G Bb6/9(#11)no3,5
3243 2-5-7-11 M2-4-5-M7 (F)-G-Bb-C-E FM9sus4no1
no JH (3243) 0-3-5-9 1-m3-4-M6 G-Bb-C-E Gm6/11no5
2424 4242 0-4-6-10 1-M3-d5-m7 C-E-Gb-Bb C7(b5)
" " " F#-A#-C-E F#7(b5)
2424 2-4-8-10 M2-M3-A5-m7 (Ab)-Bb-C-E-Gb Abaug9no1
" " " (D)-E-F#-A#-C Daug9no1
" 0-2-6-8 1-M2-A4-A5 E-F#-A#-B# Eaug9(#11)no3,7
" " " Bb-C-E-F# Bbaug9(#11)no3,7
no JH (2424) 1-3-7-9 m2-m3-5-M6 (A)-Bb-C-E-F# Am6(b9)no1
no JH " " " (D#)-E-F#-A#-B# D#m6(b9)no1
2343 3432 0-3-7-10 1-m3-5-m7 C-Eb-G-Bb Cm7
4323 0-4-7-9 1-M3-5-M6 Eb-G-Bb-C Eb6
2343 2-4-7-11 M2-M3-5-M7 (Ab)-Bb-C-Eb-G AbM9no1
3234 2-5-7-10 M2-4-5-m7 (F)-G-Bb-C-Eb F9sus4no1 or F11no1,3
4323 2-6-9-11 M2-A4-M6-M7 (Db)-Eb-G-Bb-C DbM13(#11)no1,3,5
2343 0-2-5-9 1-M2-4-M6 Bb-C-Eb-G Bb6/9sus4no5
" 1-3-6-10 m2-m3-d5-m7 (A)-Bb-C-Eb-G Am7(b5,b9)no1
4323 1-5-8-10 m2-4-A5-m7 (D)-Eb-G-A#-C D11(b9,#5)no1,3
* 3234 0-3-5-8 1-m3-4-A5 G-Bb-C-D# Gm/11(#5)
2334 3423 0-3-7-9 1-m3-5-M6 C-Eb-G-A Cm6
3342 0-3-6-10 1-m3-d5-m7 A-C-Eb-G Am7(b5) "half-dim"
2334 2-4-7-10 M2-M3-5-m7 (F)-G-A-C-Eb F9no1
3423 1-4-8-10 m2-M3-A5-m7 (B)-C-D#-F##-A Baug7(b9)no1
4233 1-5-7-10 m2-4-5-m7 (D)-Eb-G-A-C D11(b9)no1,3
" 0-4-6-9 1-M3-d5-M6 Eb-G-Bbb-C Eb6(b5)
* 3423 2-5-9-11 M2-4-M6-M7 (Bb)-C-Eb-G-A BbM13no1,3,5
no JH (2334) 0-2-5-8 1-M2-4-m6 G-A-C-Eb G11(b13)no3,5,7
2325 5232 0-5-7-10 1-4-5-m7 C-F-G-Bb C7sus4
2325 2-4-7-9 M2-M3-5-M6 (Eb)-F-G-Bb-C Eb6/9no1
2523 0-2-7-9 1-M2-5-M6 Bb-C-F-G Bb6sus2 or Bb6/9no3
3252 0-3-5-10 1-A2-4-m7 G-A#-C-F G7sus4no5(#9)
or 1-m3-4-m7 G-Bb-C-F Gm7/11no5
* 2523 2-4-9-11 M2-M3-M6-M7 (Ab)-Bb-C-F-G AbM9/13no1,5
2325 0-2-5-7 1-M2-4-5 F-G-Bb-C F4/9
" 4-6-9-11 M3-d5-M6-M7 (Db)-F-Abb-Bb-C DbM7(b5)/6no1
or M3-A4-M6-M7 (Db)-F-G-Bb-C DbM7(#11)/6no1,5
" 1-3-6-8 m2-m3-d5-m6 (E)-F-G-Bb-C Edim(b9,b13)no1
2523 1-3-8-10 m2-m3-A5-m7 (A)-Bb-C-E#-G Am7(#5,b9)no1
2253 2253 0-2-4-9 1-M2-M3-M6 C-D-E-A C6/9no5
2532 0-2-7-10 1-M2-5-m7 D-E-A-C D7sus2 or D9no3
2253 2-4-6-11 M2-M3-d5-M7 (Bb)-C-D-Fb-A BbM9(b5)no1
or M2-M3-A4-M7 (Bb)-C-D-E-A BbM9(#11)no1,5
3225 0-3-5-7 1-m3-4-5 A-C-D-E Am/11
" 3-6-8-10 m3-d5-m6-m7 (F#)-A-C-D-E F#m7(b5,b13)no1
or A2-d5-m6-m7 (F#)-G##-C-D-E F#7(b5,#9,b13)no1,3
5322 0-5-8-10 1-4-A5-m7 E-A-C-D E7sus4(#5)
2253 1-3-5-10 m2-m3-4-m7 (B)-C-D-E-A Bm7/11(b9)no1,5
3225 1-4-6-8 m2-M3-A4-A5 (Ab)-Bbb-C-D-E Abaug(b9,#11)no1
" 4-7-9-11 M3-5-M6-M7 (F)-A-C-D-E FM7/13no1
" 2-5-7-9 M2-4-5-M6 (G)-A-C-D-E G6/9sus4no1
2244 4422 0-4-8-10 1-M3-A5-m7 C-E-G#-Bb Caug7
2244 2-4-6-10 M2-M3-d5-m7 (F#)-G#-A#-C-E F#9(b5)no1
2442 0-2-6-10 1-M2-d5-m7 Bb-C-Fb-Ab Bb9(b5)no3
4224 2-6-8-10 M2-d5-m6-m7 (D)-E-Ab-Bb-C D9(b5,b13)no1,3
" 0-4-6-8 1-M3-A4-A5 E-G#-A#-B# Eaug(#11)
2244 0-2-4-8 1-M2-M3-A5 Ab-Bb-C-E Abaug/9
2235 2235 0-2-4-7 1-M2-M3-5 C-D-E-G C/9
" 3-5-7-10 m3-4-5-m7 (A)-C-D-E-G Am7/11no1
2352 0-2-5-10 1-m2-4-m7 D-E-G-C D9sus4no5 or D11no3,5
3522 0-3-8-10 1-m3-A5-m7 E-G-B#-D Em7(#5)
* 5223 2-7-9-11 M2-5-M6-M7 (F)-G-C-D-E FM9/13no1,3
" 1-6-8-10 m2-A4-A5-m7 (F#)-G-B#-C##-E F#aug7(b9,#11)no1,3
or m2-d5-m6-m7 (F#)-G-C-D-E F#7(b5,b9,b13)no1,3
2235 2-4-6-9 M2-M3-d5-M6 (Bb)-C-D-Fb-G Bb6/9(b5)no1
5223 0-5-7-9 1-4-5-M6 G-C-D-E G6sus4
2235 1-3-5-8 m2-m3-4-A5 (B)-C-D-E-F## Bm11(b9,#5)no1,7
2226 2262 0-2-4-10 1-M2-M3-m7 C-D-E-Bb C9no5
2226 4-6-8-10 M3-A4-A5-m7 (Gb)-Bb-C-D-Fb Gbaug7(#11)no1 (JH has this as F# too)
2622 0-2-8-10 1-M2-A5-m7 D-E-A#-C D9(#5)no3
6222 0-6-8-10 1-A4-A5-m7 E-A#-B#-D Eaug7(#11)no3
2226 2-4-6-8 M2-M3-A4-A5 (Ab)-Bb-C-D-E Abaug/9(#11)no1
" 0-2-4-6 1-M2-M3-d5 Bb-C-D-Fb Bb/9(b5)
1722 2172 0-2-3-10 1-M2-m3-m7 C-D-Eb-Bb Cm9no5
1632 2163 0-2-3-9 1-M2-m3-M6 C-D-Eb-A Cm6/9no5
1623 3162 0-3-4-10 1-A2-M3-m7 C-D#-E-Bb C7(#9)no5 "Hendrix chord no 5"
1542 2154 2-4-5-10 M2-M3-4-m7 (Bb)-C-D-Eb-Ab Bb11no1,5
1533 3315 0-3-6-7 1-m3-A4-5 C-Eb-F#-G Cm(#11)
1524 4152 0-4-5-10 1-M3-4-m7 C-E-F-Bb C7/11no5 = FM7sus4
1515 1515 3-4-9-10 A2-M3-M6-m7 (A)-B#-C#-F#-G A7/13(#9)no1,5 = Eb7/13(#9)no1,5
1452 2145 0-2-3-7 1-M2-m3-5 C-D-Eb-G Cm/9 = G4(b13)
1443 4431 0-4-8-11 1-M3-A5-M7 C-E-G#-B CaugM7 = E(b13) = Abaug(#9)
1434 4341 0-4-7-11 1-M3-5-M7 C-E-G-B CM7
1425 4251 0-4-6-11 1-M3-d5-M7 C-E-Gb-B CM7(b5) = Bsus4(b9)
1416 4161 0-4-5-11 1-M3-4-M7 C-E-F-B CM7/11no5
1362 1362 0-1-4-10 1-m2-M3-m7 C-Db-E-Bb C7(b9)no5
1353 3135 0-3-4-7 1-A2-M3-5 C-D#-E-G C(#9)
1344 3441 0-3-7-11 1-m3-5-M7 C-Eb-G-B CmM7 "minor-major 7th"
1335 3351 0-3-6-11 1-m3-d5-M7 C-Eb-Gb-B CmM7(b5) = B(b9) "dim major 7th"
1326 6132 0-6-7-10 1-A4-5-m7 C-F#-G-Bb C7(#11)no3 = GmM7/11no5
1317 7131 0-7-8-11 1-5-m6-M7 C-G-Ab-B CM7(b13)no3 = AbM7(#9)no5
1272
1263
1254 2541 0-2-7-11 1-M2-5-M7 C-D-G-B CM7sus2? CM9(no3)? = G/11
1245
1236
1227
1218
1182 dissonant
1173 "
1164 "
1155 "
1146 "
1137 "
1128 "
1119 "
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Pentads / pentatonic scales:
To do: expand groups in the "1" block
index # gap # element #s elements notes jazz name colloquial name
22323 22323 0-2-4-7-9 1-M2-M3-5-M6 C-D-E-G-A C6/9 C major pentatonic
32232 0-3-5-7-10 1-m3-4-5-m7 A-C-D-E-G Am7/11 A minor pentatonic
23232 0-2-5-7-10 1-M2-4-5-m7 D-E-G-A-C D9sus4? D11no3?
23223 0-2-5-7-9 1-M2-4-5-M6 G-A-C-D-E G6/9sus4? G13no3,7?
(32322) 0-3-5-8-10 1-m3-4-A5-m7 E-G-A-B#-D Em7/11(#5)
23223 2-4-7-9-11 M2-M3-5-M6-M7 (F)-G-A-C-D-E FM9/13no1
22233 22332 0-2-4-7-10 1-M2-M3-5-m7 C-D-E-G-Bb C9 (waGogo scale)
32223 0-3-5-7-9 1-m3-4-5-M6 G-Bb-C-D-E Gm6/11
(22233) 0-2-4-6-9 1-M2-M3-d5-M6 Bb-C-D-Fb-G Bb6/9(b5)
(23322) 0-2-5-8-10 1-M2-4-m6-m7 D-E-G-Bb-C D11(b13)no3,5
(33222) 0-3-6-8-10 1-m3-d5-m6-m7 E-G-Bb-C-D Em7/6(b5)
22233 1-3-5-7-10 m2-m3-4-5-m7 (A)-Bb-C-D-E-G Am11(b9)no1
22224 22242 0-2-4-6-10 1-M2-M3-d5-m7 C-D-E-Gb-Bb C9(b5)
22422 0-2-4-8-10 1-M2-M3-A5-m7 D-E-F#-A#-C D9(#5)? Daug9?
(22224) 0-2-4-6-8 1-M2-M3-A4-A5 Bb-C-D-E-F# Bbaug9(#11)no7
(42222) 0-4-6-8-10 1-M3-A4-A5-m7 Gb-Bb-C-D-Fb Gbaug7(#11)
(24222) 0-2-6-8-10 1-M2-A4-A5-m7 E-F#-A#-B#-D E9(#5,#11)no3
15222 22152 0-2-4-5-10 1-M2-M3-4-m7 C-D-E-F-Bb C11no5
22215 0-2-4-6-7 1-M2-M3-A4-5 Bb-C-D-E-F Bb/9(#11)
52221 0-5-7-9-11 1-4-5-M6-M7 F-Bb-C-D-E FM13no3,9
(15222) 0-1-6-8-10 1-m2-d5-m6-m7 E-F-Bb-C-D ?
(21522) 0-2-3-8-10 1-M2-m3-m6-m7 D-E-F-Bb-C Dm9(b13)no5
14322 21432 0-2-3-7-10 1-M2-m3-5-m7 C-D-Eb-G-Bb Cm9
43221 0-4-7-9-11 1-M3-5-6-M7 Eb-G-Bb-C-D Eb6(M7)? EbM7/6?
32214 0-3-5-7-8 1-m3-4-5-m6 G-Bb-C-D-Eb Gm/11(b13)
(22143) 0-2-4-5-9 1-M2-M3-4-M6 Bb-C-D-Eb-G Bb11no5,7
(14322) 0-1-5-8-10 1-m2-4-m6-m7 D-Eb-G-Bb-C ?
22143 2-4-6-7-11 M2-M3-A4-5-M7 (Ab)-Bb-C-D-Eb-G AbM9(#11)no1?
14232 21423 0-2-3-7-9 1-M2-m3-5-M6 C-D-Eb-G-A Cm6/9
14232 0-1-5-7-10 1-m2-4-5-m7 D-Eb-G-A-C D7sus4(b9)
(42321) 0-4-6-9-11 1-M3-d5-M6-M7 Eb-G-Bbb-C-D EbM7/13(b5)
(23214) 0-2-5-7-8 1-M2-4-5-m6 G-A-C-D-Eb G4/9(b13)?
(32142) 0-3-5-6-10 1-m3-4-d5-m7 A-C-D-Eb-G Am7/11(b5)
23214 2-4-7-9-10 M2-M3-5-M6-m7 (F)-G-A-C-D-Eb F9/13no1
14223 22314 0-2-4-7-8 1-M2-M3-5-m6 C-D-E-G-Ab C/9(b13)
42231 0-4-6-8-11 1-M3-A4-A5-M7 Ab-C-D-E-G Abaug(M7,#11)?
(14223) 0-1-5-7-9 1-m2-4-5-M6 G-Ab-C-D-E G6sus4(b9)
(31422) 0-3-4-8-10 1-A2-M3-A5-m7 E-F##-G#-B#-D Eaug7(#9)
(23142) 0-2-5-6-10 1-M2-4-d5-m7 D-E-G-Ab-C D11(b5)no3
(14223) 2-3-7-9-11 M2-m3-5-M6-M7 (F)-G-Ab-C-D-E FmM7aad9,13no1?
14142 21414 0-2-3-7-8 1-M2-m3-5-m6 C-D-Eb-G-Ab Cm/9(b13) (Japanese scale)
42141 0-4-6-7-11 1-M3-A4-5-M7 Ab-C-D-Eb-G AbM7(#11)
14214 0-1-5-7-8 1-m2-4-5-m6 G-Ab-C-D-Eb G4(b9,b13)
(41421) 0-4-5-9-11 1-M3-4-M6-M7 Eb-G-Ab-C-D EbM13no5,9
(14142) 0-1-5-6-10 1-m2-4-d5-m7 D-Eb-G-Ab-C D11(b5,b9)no3?
14214 2-3-7-9-10 M2-m3-5-M6-m7 (F)-G-Ab-C-D-Eb Fm9/13no1
13422
13332 13332 0-1-4-7-10 1-m2-M3-5-m7 C-Db-E-G-Bb C7(b9) "flat 9", classical "dom minor 9th"
13323 31332 0-3-4-7-10 1-A2-M3-5-m7 C-D#-E-G-Bb C7(#9) "Hendrix chord"
13314
13242
13233
13224
13215
13152
13143
13134
12612
12522
12513
12432
12423
12414 41241 0-4-5-7-11 1-M3-4-5-M7 C-E-F-G-B CM7/11 (SE asian scale)
12342
12333 33123 0-3-6-7-9 1-m3-A4-5-M6 C-Eb-F#-G-A Cm6(#11)
12324
12315
12252
12243
12234 22341 0-2-4-7-11 1-M2-M3-5-M7 C-D-E-G-B CM9
12225
12216
12162
12153
12144
12135
12126
(dissonant)
11712
11622
11613
11532
11523
11514
11442
11433
11424
11415
11352
11343
11334
11325
11316
11262
11253
11244
11235
11226
11217
11172
(really dissonant)
11163
11154
11145
11136
11127
11118
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Hexads / hexatonic scales:
222222 222222 0-2-4-6-8-10 1-M2-M3-A4-A5-m7 C-D-E-F#-G#-Bb C whole tone scale
132132 symmetric
131313 symmetric
123123 symmetric
114114 symmetric
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Heptads / heptatonic scales:
1221222 2212221 0-2-4-5-7-9-11 1-M2-M3-4-5-M6-M7 C-D-E-F-G-A-B C major scale
2122122 0-2-3-5-7-8-10 1-M2-m3-4-5-m6-m7 A-B-C-D-E-F-G A minor scale
2122212 0-2-3-5-7-9-10 1-M2-m3-4-5-M6-m7 D-E-F-G-A-B-C D dorian scale
1222122 0-1-3-5-7-8-10 1-m2-m3-4-5-m6-m7 E-F-G-A-B-C-D E phrygian scale
2221221 0-2-4-6-7-9-11 1-M2-M3-A4-5-M6-M7 F-G-A-B-C-D-E F lydian scale
2212212 0-2-4-5-7-9-10 1-M2-M3-4-5-M6-m7 G-A-B-C-D-E-F G mixoydian scale
(2122212) 0-2-3-5-7-9-10 1-m2-m3-4-d5-m6-m7 B-C-D-E-F-G-A B locrian scale
1212213 2122131 0-2-3-5-7-8-11 1-M2-m3-4-5-m6-M7 C-D-Eb-F-G-Ab-B C harmonic minor scale
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Octotonic scales:
12121212 21212121 0-2-3-5-6-8-9-11 1-M2-m3-4-b5-A5-M6-M7 C-D-Eb-F-Gb-G#-A-B C ? scale
12121212 0-1-3-4-6-7-9-10 1-m2-m3-M3-A4-5-M6-m7 C-Db-Eb-E-F#-G-A-Bb C ? scale
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Nonotonic scales:
Top
Decatonic scales:
Top
11-note scales:
11111111112 11111111112 0-1-2-3-4-5-6-7-8-9-10 C-Db-D-Eb-E-F-Gb-G-Ab-A-Bb ?
11111111121 0-1-2-3-4-5-6-7-8-9-11
11111111211 0-1-2-3-4-5-6-7-8-10-11
11111112111 0-1-2-3-4-5-6-7-9-10-11
11111121111 0-1-2-3-4-5-6-8-9-10-11
11111211111 0-1-2-3-4-5-7-8-9-10-11
11112111111 0-1-2-3-4-6-7-8-9-10-11
11121111111 0-1-2-3-5-6-7-8-9-10-11
11211111111 0-1-2-4-5-6-7-8-9-10-11
12111111111 0-1-3-4-5-6-7-8-9-10-11
21111111111 0-2-3-4-5-6-7-8-9-10-11
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12-note scales:
111111111111 111111111111 0-1-2-3-4-5-6-7-8-9-10-11 C-Db-D-Eb-E-F-Gb-G-Ab-A-Bb-B C chromatic scale