The Exciting Universe Of Music Theory

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Scale 3331

Scale 3331, 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.

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{0,1,8,10,11}
Forte Number5-2
Rotational Symmetrynone
Reflection Axesnone
enantiomorph: 2071
Hemitonia3 (trihemitonic)
Cohemitonia2 (dicohemitonic)
prime: 47
Deep Scaleno
Interval Vector332110
Interval Spectrumpmn2s3d3
Distribution Spectra<1> = {1,2,7}
<2> = {2,3,8,9}
<3> = {3,4,9,10}
<4> = {5,10,11}
Spectra Variation5.2
Maximally Evenno
Myhill Propertyno
Ridge Tonesnone


Modes are the rotational transformation of this scale. Scale 3331 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 3713
Scale 3713, Ian Ring Music Theory
3rd mode:
Scale 61
Scale 61, Ian Ring Music Theory
4th mode:
Scale 1039
Scale 1039, Ian Ring Music Theory
5th mode:
Scale 2567
Scale 2567, Ian Ring Music Theory


The prime form of this scale is Scale 47

Scale 47Scale 47, Ian Ring Music Theory


The pentatonic modal family [3331, 3713, 61, 1039, 2567] (Forte: 5-2) is the complement of the heptatonic modal family [191, 2017, 2143, 3119, 3607, 3851, 3973] (Forte: 7-2)


The inverse of a scale is a reflection using the root as its axis. The inverse of 3331 is 2071

Scale 2071Scale 2071, Ian Ring Music Theory


Only scales that are chiral will have an enantiomorph. Scale 3331 is chiral, and its enantiomorph is scale 2071

Scale 2071Scale 2071, Ian Ring Music Theory


T0 3331  T0I 2071
T1 2567  T1I 47
T2 1039  T2I 94
T3 2078  T3I 188
T4 61  T4I 376
T5 122  T5I 752
T6 244  T6I 1504
T7 488  T7I 3008
T8 976  T8I 1921
T9 1952  T9I 3842
T10 3904  T10I 3589
T11 3713  T11I 3083

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 3329Scale 3329, Ian Ring Music Theory
Scale 3333Scale 3333, Ian Ring Music Theory
Scale 3335Scale 3335, Ian Ring Music Theory
Scale 3339Scale 3339, Ian Ring Music Theory
Scale 3347Scale 3347: Synimic, Ian Ring Music TheorySynimic
Scale 3363Scale 3363: Rogimic, Ian Ring Music TheoryRogimic
Scale 3395Scale 3395, Ian Ring Music Theory
Scale 3459Scale 3459, Ian Ring Music Theory
Scale 3075Scale 3075, Ian Ring Music Theory
Scale 3203Scale 3203, Ian Ring Music Theory
Scale 3587Scale 3587, Ian Ring Music Theory
Scale 3843Scale 3843, Ian Ring Music Theory
Scale 2307Scale 2307, Ian Ring Music Theory
Scale 2819Scale 2819, Ian Ring Music Theory
Scale 1283Scale 1283, 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, and MIDI playback by MIDI.js. Bibliography