The Exciting Universe Of Music Theory

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Scale 3131

Scale 3131, 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).


Cardinality7 (heptatonic)
Pitch Class Set{0,1,3,4,5,10,11}
Forte Number7-5
Rotational Symmetrynone
Reflection Axesnone
enantiomorph: 2951
Hemitonia5 (multihemitonic)
Cohemitonia3 (tricohemitonic)
prime: 239
Deep Scaleno
Interval Vector543342
Interval Spectrump4m3n3s4d5t2
Distribution Spectra<1> = {1,2,5}
<2> = {2,3,6}
<3> = {3,4,7}
<4> = {5,8,9}
<5> = {6,9,10}
<6> = {7,10,11}
Spectra Variation3.429
Maximally Evenno
Maximal Area Setno
Interior Area1.933
Myhill Propertyno
Ridge Tonesnone

Harmonic Chords

Common Triads

These are the common triads (major, minor, augmented and diminished) that you can create from members of this scale.

* Pitches are shown with C as the root

Triad TypeTriad*Pitch ClassesDegreeEccentricityCloseness Centrality
Minor Triadsa♯m{10,1,5}110.5
Diminished Triadsa♯°{10,1,4}110.5
Parsimonious Voice Leading Between Common Triads of Scale 3131. Created by Ian Ring ©2019 a#° a#° a#m a#m a#°->a#m

Above is a graph showing opportunities for parsimonious voice leading between triads*. Each line connects two triads that have two common tones, while the third tone changes by one generic scale step.



Modes are the rotational transformation of this scale. Scale 3131 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 3613
Scale 3613, Ian Ring Music Theory
3rd mode:
Scale 1927
Scale 1927, Ian Ring Music Theory
4th mode:
Scale 3011
Scale 3011, Ian Ring Music Theory
5th mode:
Scale 3553
Scale 3553, Ian Ring Music Theory
6th mode:
Scale 239
Scale 239, Ian Ring Music TheoryThis is the prime mode
7th mode:
Scale 2167
Scale 2167, Ian Ring Music Theory


The prime form of this scale is Scale 239

Scale 239Scale 239, Ian Ring Music Theory


The heptatonic modal family [3131, 3613, 1927, 3011, 3553, 239, 2167] (Forte: 7-5) is the complement of the pentatonic modal family [143, 481, 2119, 3107, 3601] (Forte: 5-5)


The inverse of a scale is a reflection using the root as its axis. The inverse of 3131 is 2951

Scale 2951Scale 2951, Ian Ring Music Theory


Only scales that are chiral will have an enantiomorph. Scale 3131 is chiral, and its enantiomorph is scale 2951

Scale 2951Scale 2951, Ian Ring Music Theory


T0 3131  T0I 2951
T1 2167  T1I 1807
T2 239  T2I 3614
T3 478  T3I 3133
T4 956  T4I 2171
T5 1912  T5I 247
T6 3824  T6I 494
T7 3553  T7I 988
T8 3011  T8I 1976
T9 1927  T9I 3952
T10 3854  T10I 3809
T11 3613  T11I 3523

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 3129Scale 3129, Ian Ring Music Theory
Scale 3133Scale 3133, Ian Ring Music Theory
Scale 3135Scale 3135, Ian Ring Music Theory
Scale 3123Scale 3123, Ian Ring Music Theory
Scale 3127Scale 3127, Ian Ring Music Theory
Scale 3115Scale 3115, Ian Ring Music Theory
Scale 3099Scale 3099, Ian Ring Music Theory
Scale 3163Scale 3163: Rogian, Ian Ring Music TheoryRogian
Scale 3195Scale 3195: Raryllic, Ian Ring Music TheoryRaryllic
Scale 3259Scale 3259, Ian Ring Music Theory
Scale 3387Scale 3387: Aeryptyllic, Ian Ring Music TheoryAeryptyllic
Scale 3643Scale 3643: Kydyllic, Ian Ring Music TheoryKydyllic
Scale 2107Scale 2107, Ian Ring Music Theory
Scale 2619Scale 2619: Ionyrian, Ian Ring Music TheoryIonyrian
Scale 1083Scale 1083, Ian Ring Music Theory

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.