The Exciting Universe Of Music Theory

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Scale 2131

Scale 2131, 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).


Cardinality5 (pentatonic)
Pitch Class Set{0,1,4,6,11}
Forte Number5-14
Rotational Symmetrynone
Reflection Axesnone
enantiomorph: 2371
Hemitonia2 (dihemitonic)
Cohemitonia1 (uncohemitonic)
prime: 167
Deep Scaleno
Interval Vector221131
Interval Spectrump3mns2d2t
Distribution Spectra<1> = {1,2,3,5}
<2> = {2,4,5,6,7}
<3> = {5,6,7,8,10}
<4> = {7,9,10,11}
Spectra Variation3.6
Maximally Evenno
Maximal Area Setno
Interior Area1.683
Myhill Propertyno
Ridge Tonesnone

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 2131 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 3113
Scale 3113, Ian Ring Music Theory
3rd mode:
Scale 901
Scale 901, Ian Ring Music Theory
4th mode:
Scale 1249
Scale 1249, Ian Ring Music Theory
5th mode:
Scale 167
Scale 167, Ian Ring Music TheoryThis is the prime mode


The prime form of this scale is Scale 167

Scale 167Scale 167, Ian Ring Music Theory


The pentatonic modal family [2131, 3113, 901, 1249, 167] (Forte: 5-14) is the complement of the heptatonic modal family [431, 1507, 1933, 2263, 2801, 3179, 3637] (Forte: 7-14)


The inverse of a scale is a reflection using the root as its axis. The inverse of 2131 is 2371

Scale 2371Scale 2371, Ian Ring Music Theory


Only scales that are chiral will have an enantiomorph. Scale 2131 is chiral, and its enantiomorph is scale 2371

Scale 2371Scale 2371, Ian Ring Music Theory


T0 2131  T0I 2371
T1 167  T1I 647
T2 334  T2I 1294
T3 668  T3I 2588
T4 1336  T4I 1081
T5 2672  T5I 2162
T6 1249  T6I 229
T7 2498  T7I 458
T8 901  T8I 916
T9 1802  T9I 1832
T10 3604  T10I 3664
T11 3113  T11I 3233

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 2129Scale 2129: Raga Nigamagamini, Ian Ring Music TheoryRaga Nigamagamini
Scale 2133Scale 2133: Raga Kumurdaki, Ian Ring Music TheoryRaga Kumurdaki
Scale 2135Scale 2135, Ian Ring Music Theory
Scale 2139Scale 2139, Ian Ring Music Theory
Scale 2115Scale 2115, Ian Ring Music Theory
Scale 2123Scale 2123, Ian Ring Music Theory
Scale 2147Scale 2147, Ian Ring Music Theory
Scale 2163Scale 2163, Ian Ring Music Theory
Scale 2067Scale 2067, Ian Ring Music Theory
Scale 2099Scale 2099: Raga Megharanji, Ian Ring Music TheoryRaga Megharanji
Scale 2195Scale 2195: Zalitonic, Ian Ring Music TheoryZalitonic
Scale 2259Scale 2259: Raga Mandari, Ian Ring Music TheoryRaga Mandari
Scale 2387Scale 2387: Paptimic, Ian Ring Music TheoryPaptimic
Scale 2643Scale 2643: Raga Hamsanandi, Ian Ring Music TheoryRaga Hamsanandi
Scale 3155Scale 3155: Ladimic, Ian Ring Music TheoryLadimic
Scale 83Scale 83, Ian Ring Music Theory
Scale 1107Scale 1107: Mogitonic, Ian Ring Music TheoryMogitonic

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.