The Exciting Universe Of Music Theory

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Scale 2137

Scale 2137, 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{0,3,4,6,11}
Forte Number5-Z18
Rotational Symmetrynone
Reflection Axesnone
enantiomorph: 835
Hemitonia2 (dihemitonic)
Cohemitonia0 (ancohemitonic)
prime: 179
Deep Scaleno
Interval Vector212221
Interval Spectrump2m2n2sd2t
Distribution Spectra<1> = {1,2,3,5}
<2> = {3,4,6,7}
<3> = {5,6,8,9}
<4> = {7,9,10,11}
Spectra Variation3.2
Maximally Evenno
Myhill Propertyno
Ridge Tonesnone


Modes are the rotational transformation of this scale. Scale 2137 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 779
Scale 779, Ian Ring Music Theory
3rd mode:
Scale 2437
Scale 2437, Ian Ring Music Theory
4th mode:
Scale 1633
Scale 1633, Ian Ring Music Theory
5th mode:
Scale 179
Scale 179, Ian Ring Music TheoryThis is the prime mode


The prime form of this scale is Scale 179

Scale 179Scale 179, Ian Ring Music Theory


The pentatonic modal family [2137, 779, 2437, 1633, 179] (Forte: 5-Z18) is the complement of the heptatonic modal family [755, 815, 1945, 2425, 2455, 3275, 3685] (Forte: 7-Z18)


The inverse of a scale is a reflection using the root as its axis. The inverse of 2137 is 835

Scale 835Scale 835, Ian Ring Music Theory


Only scales that are chiral will have an enantiomorph. Scale 2137 is chiral, and its enantiomorph is scale 835

Scale 835Scale 835, Ian Ring Music Theory


T0 2137  T0I 835
T1 179  T1I 1670
T2 358  T2I 3340
T3 716  T3I 2585
T4 1432  T4I 1075
T5 2864  T5I 2150
T6 1633  T6I 205
T7 3266  T7I 410
T8 2437  T8I 820
T9 779  T9I 1640
T10 1558  T10I 3280
T11 3116  T11I 2465

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 2139Scale 2139, Ian Ring Music Theory
Scale 2141Scale 2141, Ian Ring Music Theory
Scale 2129Scale 2129: Raga Nigamagamini, Ian Ring Music TheoryRaga Nigamagamini
Scale 2133Scale 2133: Raga Kumurdaki, Ian Ring Music TheoryRaga Kumurdaki
Scale 2121Scale 2121, Ian Ring Music Theory
Scale 2153Scale 2153, Ian Ring Music Theory
Scale 2169Scale 2169, Ian Ring Music Theory
Scale 2073Scale 2073, Ian Ring Music Theory
Scale 2105Scale 2105, Ian Ring Music Theory
Scale 2201Scale 2201: Ionagitonic, Ian Ring Music TheoryIonagitonic
Scale 2265Scale 2265: Raga Rasamanjari, Ian Ring Music TheoryRaga Rasamanjari
Scale 2393Scale 2393: Zathimic, Ian Ring Music TheoryZathimic
Scale 2649Scale 2649: Aeolythimic, Ian Ring Music TheoryAeolythimic
Scale 3161Scale 3161: Kodimic, Ian Ring Music TheoryKodimic
Scale 89Scale 89, Ian Ring Music Theory
Scale 1113Scale 1113: Locrian Pentatonic 2, Ian Ring Music TheoryLocrian Pentatonic 2

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