All The Scales

William Zeitler

The "major" and the "minor" scales, and to a far lesser extent about a dozen 1 or so other scales have kept composers in the West busy for about 500 years now. Let's be generous and say we've really used about 20 different scales/modes.

But based on the Western system of notes (as exemplified by the piano keyboard), there are 1490 possible scales. 2 In other words, with the combined genius of medieval monks through Beethoven through Stravinsky and Coltrane, we've managed to explore roughly 1% of this musical terrain. (Admittedly not all of this terrain is equally musically fertile.)

Even limiting ourselves to the Western system (a rather arbitrary limitation), there remains an awful lot of musical territory to explore...

Introduction

All the Possible Scales and Modes:

(In each section of scales below, click on a note to hear the mode.)

  Number
of Scales 		Number of
Unique Modes
3-note Scales 1 1
4-note Scales 9 31
5-note Scales 31 155
6-note Scales 59 336
7-note Scales 59 413
8-note Scales 42 322
9-note Scales 19 165
10-note Scales 6 55
11-note Scales 1 11
12-note Scales 1 1
Total: 228 1490

Indices

1 the Major, the Minor, the other five Ecclesiastical modes (Dorian, Phrygian, Lydian, Mixolydian, Locrian), the Whole Tone scale, the two Diminished scales, a couple different Blues scales, the Pentatonic scale, the Chromatic scale – that's only 14 so far!

2A scale being defined as a series of notes, each of higher pitch than the previous, the entire series of pitches less than an octave (so the sequence can repeat itself at each octave), where the step between successive notes in the scale is no greater than a major third. The requirement of no step greater than a major third is somewhat arbitrary, but does allow us to include commonly used scales like the Pentatonic. Allowing steps greater than a major third significantly increases the number of possible scales.

Hopefully this little opus shows that even with a fairly restrictive definition of a scale — uses the Western equal-tempered chromatic scale, no steps greater than a major third — that there is still an enormous musical territory to explore. Making that musical territory even larger by relaxing any of these restrictions only emphasizes my thesis that we haven't begun to explore the realm of all possible music.

Copyright © 2005 William Zeitler