Show tooltips...
📝
Start tutorial

The Division of Nine

There are twelve musical notes. When three notes are played, that leaves nine unplayed.
Now, consider all the ways to divide the number nine using only two or three digits. There are exactly eleven such divisions:
18  27  36  45 117  126  135  144 225  234 333
Each of these combinations forms the root of a triad family — a set of chords that share similar tonal properties.
Within the triad hierarchy, shifting from one family to another during a chord progression adds new layers of depth and color to the harmony.
------------------------------------------------
Colored shapes represent different triad categories. Each category contains several triads that all share the same three notes.

For example, let's look at the group 1621. It includes the triads 62 - 21 - 16. Whichever of these chords you choose, the same three notes are always present, but placed differently across the keyboard, resulting in different interval structures each time.
In other words, the harmonic feeling remains the same, though the balance changes depending on the voicing.
------------------------------------------------
Please refer to the division of nine chart below that shows all existing triads. Triads in grey, considered as too dissonant - until now - are therefore excluded.
G♭ / E♭ D♭ / B♭ A♭ / F E♭ / C B♭ / G F / D C / A G / E D / B A / F# E / C# B / G# F# / D# M/m
E♭ B♭ F C G D A E B F# C# G# D# M
E♭ B♭ F C G D A E B F# C# G# D# H
234 225 333 126 135 144 27 36
2342
 3243
 2252
 3333
 1261
 6216
 3513
 5315
 4144
 2702
 7207
 3603
 6306
23 32 22 33 12 62 35 53 41 27 72 36 63
34 24 25 26 21 51 31 14 70 20 60 30
42 43 52 61 16 13 15 44 02 07 03 06
Cm7
D♭m7
Dm7
E♭m7
Em7
Fm7
G♭m7
Gm7
A♭m7
Am7
B♭m7
Bm7
C7
D♭7
D7
E♭7
E7
F7
G♭7
G7
A♭7
A7
B♭7
B7
Cmaj7
D♭maj7
Dmaj7
E♭maj7
Emaj7
Fmaj7
G♭maj7
Gmaj7
A♭maj7
Amaj7
B♭maj7
Bmaj7
Cm7(♭5)
D♭m7(♭5)
Dm7(♭5)
E♭m7(♭5)
Em7(♭5)
Fm7(♭5)
G♭m7(♭5)
Gm7(♭5)
A♭m7(♭5)
Am7(♭5)
B♭m7(♭5)
Bm7(♭5)
Cm(maj7)
D♭m(maj7)
Dm(maj7)
E♭m(maj7)
Em(maj7)
Fm(maj7)
G♭m(maj7)
Gm(maj7)
A♭m(maj7)
Am(maj7)
B♭m(maj7)
Bm(maj7)
Cdim7
D♭dim7
Ddim7
E♭dim7
Edim7
Fdim7
G♭dim7
Gdim7
A♭dim7
Adim7
B♭dim7
Bdim7
Cmaj7(#5)
D♭maj7(#5)
Dmaj7(#5)
E♭maj7(#5)
Emaj7(#5)
Fmaj7(#5)
G♭maj7(#5)
Gmaj7(#5)
A♭maj7(#5)
Amaj7(#5)
B♭maj7(#5)
Bmaj7(#5)