The Exciting Universe Of Music Theory

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Scale 3597

Scale 3597, 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{0,2,3,9,10,11}
Forte Number6-Z3
Rotational Symmetrynone
Reflection Axesnone
enantiomorph: 1551
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
prime: 111
Deep Scaleno
Interval Vector433221
Interval Spectrump2m2n3s3d4t
Distribution Spectra<1> = {1,2,6}
<2> = {2,3,7}
<3> = {3,4,8,9}
<4> = {5,9,10}
<5> = {6,10,11}
Spectra Variation4.333
Maximally Evenno
Maximal Area Setno
Interior Area1.433
Myhill Propertyno
Ridge Tonesnone

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
Diminished Triads{9,0,3}000

Since there is only one common triad in this scale, there are no opportunities for parsimonious voice leading between triads.


Modes are the rotational transformation of this scale. Scale 3597 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 1923
Scale 1923, Ian Ring Music Theory
3rd mode:
Scale 3009
Scale 3009, Ian Ring Music Theory
4th mode:
Scale 111
Scale 111, Ian Ring Music TheoryThis is the prime mode
5th mode:
Scale 2103
Scale 2103, Ian Ring Music Theory
6th mode:
Scale 3099
Scale 3099, Ian Ring Music Theory


The prime form of this scale is Scale 111

Scale 111Scale 111, Ian Ring Music Theory


The hexatonic modal family [3597, 1923, 3009, 111, 2103, 3099] (Forte: 6-Z3) is the complement of the hexatonic modal family [159, 993, 2127, 3111, 3603, 3849] (Forte: 6-Z36)


The inverse of a scale is a reflection using the root as its axis. The inverse of 3597 is 1551

Scale 1551Scale 1551, Ian Ring Music Theory


Only scales that are chiral will have an enantiomorph. Scale 3597 is chiral, and its enantiomorph is scale 1551

Scale 1551Scale 1551, Ian Ring Music Theory


T0 3597  T0I 1551
T1 3099  T1I 3102
T2 2103  T2I 2109
T3 111  T3I 123
T4 222  T4I 246
T5 444  T5I 492
T6 888  T6I 984
T7 1776  T7I 1968
T8 3552  T8I 3936
T9 3009  T9I 3777
T10 1923  T10I 3459
T11 3846  T11I 2823

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 3599Scale 3599, Ian Ring Music Theory
Scale 3593Scale 3593, Ian Ring Music Theory
Scale 3595Scale 3595, Ian Ring Music Theory
Scale 3589Scale 3589, Ian Ring Music Theory
Scale 3605Scale 3605, Ian Ring Music Theory
Scale 3613Scale 3613, Ian Ring Music Theory
Scale 3629Scale 3629: Boptian, Ian Ring Music TheoryBoptian
Scale 3661Scale 3661: Mixodorian, Ian Ring Music TheoryMixodorian
Scale 3725Scale 3725: Kyrian, Ian Ring Music TheoryKyrian
Scale 3853Scale 3853, Ian Ring Music Theory
Scale 3085Scale 3085, Ian Ring Music Theory
Scale 3341Scale 3341, Ian Ring Music Theory
Scale 2573Scale 2573, Ian Ring Music Theory
Scale 1549Scale 1549, 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.