The Exciting Universe Of Music Theory

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Scale 231

Scale 231, Ian Ring Music Theory

Bracelet Diagram

The bracelet shows tones that are in this scale, starting from the top (12 o'clock), going clockwise in ascending semitones. The "i" icon marks imperfect tones that do not have a tone a fifth above. Dotted lines indicate axes of symmetry.

Tonnetz Diagram

Tonnetz diagrams are popular in Neo-Riemannian theory. Notes are arranged in a lattice where perfect 5th intervals are from left to right, major third are northeast, and major 6th intervals are northwest. Other directions are inverse of their opposite. This diagram helps to visualize common triads (they're triangles) and circle-of-fifth relationships (horizontal lines).


Cardinality6 (hexatonic)
Pitch Class Set{0,1,2,5,6,7}
Forte Number6-Z6
Rotational Symmetrynone
Reflection Axes3.5
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Deep Scaleno
Interval Vector421242
Interval Spectrump4m2ns2d4t2
Distribution Spectra<1> = {1,3,5}
<2> = {2,4,6}
<3> = {5,7}
<4> = {6,8,10}
<5> = {7,9,11}
Spectra Variation3
Maximally Evenno
Maximal Area Setno
Interior Area1.75
Myhill Propertyno
Ridge Tones[7]

Common Triads

There are no common triads (major, minor, augmented and diminished) that can be formed using notes in this scale.


Modes are the rotational transformation of this scale. Scale 231 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 2163
Scale 2163, Ian Ring Music Theory
3rd mode:
Scale 3129
Scale 3129, Ian Ring Music Theory
4th mode:
Scale 903
Scale 903, Ian Ring Music Theory
5th mode:
Scale 2499
Scale 2499, Ian Ring Music Theory
6th mode:
Scale 3297
Scale 3297, Ian Ring Music Theory


This is the prime form of this scale.


The hexatonic modal family [231, 2163, 3129, 903, 2499, 3297] (Forte: 6-Z6) is the complement of the hexatonic modal family [399, 483, 2247, 2289, 3171, 3633] (Forte: 6-Z38)


The inverse of a scale is a reflection using the root as its axis. The inverse of 231 is 3297

Scale 3297Scale 3297, Ian Ring Music Theory


T0 231  T0I 3297
T1 462  T1I 2499
T2 924  T2I 903
T3 1848  T3I 1806
T4 3696  T4I 3612
T5 3297  T5I 3129
T6 2499  T6I 2163
T7 903  T7I 231
T8 1806  T8I 462
T9 3612  T9I 924
T10 3129  T10I 1848
T11 2163  T11I 3696

Nearby Scales:

These are other scales that are similar to this one, created by adding a tone, removing a tone, or moving one note up or down a semitone.

Scale 229Scale 229, Ian Ring Music Theory
Scale 227Scale 227, Ian Ring Music Theory
Scale 235Scale 235, Ian Ring Music Theory
Scale 239Scale 239, Ian Ring Music Theory
Scale 247Scale 247, Ian Ring Music Theory
Scale 199Scale 199: Raga Nabhomani, Ian Ring Music TheoryRaga Nabhomani
Scale 215Scale 215, Ian Ring Music Theory
Scale 167Scale 167, Ian Ring Music Theory
Scale 103Scale 103, Ian Ring Music Theory
Scale 359Scale 359: Bothimic, Ian Ring Music TheoryBothimic
Scale 487Scale 487: Dynian, Ian Ring Music TheoryDynian
Scale 743Scale 743: Chromatic Hypophrygian Inverse, Ian Ring Music TheoryChromatic Hypophrygian Inverse
Scale 1255Scale 1255: Chromatic Mixolydian, Ian Ring Music TheoryChromatic Mixolydian
Scale 2279Scale 2279: Dyrian, Ian Ring Music TheoryDyrian

This scale analysis was created by Ian Ring, Canadian Composer of works for Piano, and total music theory nerd. The software used to generate this analysis is an open source project at GitHub. Scale notation generated by VexFlow, graph visualization by Graphviz, and MIDI playback by MIDI.js. Some scale names used on this and other pages are ©2005 William Zeitler ( used with permission.

Pitch spelling algorithm employed here is adapted from a method by Uzay Bora, Baris Tekin Tezel, and Alper Vahaplar. (An algorithm for spelling the pitches of any musical scale) Contact authors Patent owner: Dokuz Eylül University, Used with Permission. Contact TTO

Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography. Special thanks to Richard Repp for helping with technical accuracy.