The Exciting Universe Of Music Theory

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Scale 91

Scale 91, 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{0,1,3,4,6}
Forte Number5-10
Rotational Symmetrynone
Reflection Axesnone
enantiomorph: 2881
Hemitonia2 (dihemitonic)
Cohemitonia0 (ancohemitonic)
Deep Scaleno
Interval Vector223111
Interval Spectrumpmn3s2d2t
Distribution Spectra<1> = {1,2,6}
<2> = {3,7,8}
<3> = {4,5,9}
<4> = {6,10,11}
Spectra Variation4
Maximally Evenno
Maximal Area Setno
Interior Area1.366
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{0,3,6}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 91 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 2093
Scale 2093, Ian Ring Music Theory
3rd mode:
Scale 1547
Scale 1547, Ian Ring Music Theory
4th mode:
Scale 2821
Scale 2821, Ian Ring Music Theory
5th mode:
Scale 1729
Scale 1729, Ian Ring Music Theory


This is the prime form of this scale.


The pentatonic modal family [91, 2093, 1547, 2821, 1729] (Forte: 5-10) is the complement of the heptatonic modal family [607, 761, 1993, 2351, 3223, 3659, 3877] (Forte: 7-10)


The inverse of a scale is a reflection using the root as its axis. The inverse of 91 is 2881

Scale 2881Scale 2881, Ian Ring Music Theory


Only scales that are chiral will have an enantiomorph. Scale 91 is chiral, and its enantiomorph is scale 2881

Scale 2881Scale 2881, Ian Ring Music Theory


T0 91  T0I 2881
T1 182  T1I 1667
T2 364  T2I 3334
T3 728  T3I 2573
T4 1456  T4I 1051
T5 2912  T5I 2102
T6 1729  T6I 109
T7 3458  T7I 218
T8 2821  T8I 436
T9 1547  T9I 872
T10 3094  T10I 1744
T11 2093  T11I 3488

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 89Scale 89, Ian Ring Music Theory
Scale 93Scale 93, Ian Ring Music Theory
Scale 95Scale 95, Ian Ring Music Theory
Scale 83Scale 83, Ian Ring Music Theory
Scale 87Scale 87, Ian Ring Music Theory
Scale 75Scale 75, Ian Ring Music Theory
Scale 107Scale 107, Ian Ring Music Theory
Scale 123Scale 123, Ian Ring Music Theory
Scale 27Scale 27, Ian Ring Music Theory
Scale 59Scale 59, Ian Ring Music Theory
Scale 155Scale 155, Ian Ring Music Theory
Scale 219Scale 219: Istrian, Ian Ring Music TheoryIstrian
Scale 347Scale 347: Barimic, Ian Ring Music TheoryBarimic
Scale 603Scale 603: Aeolygimic, Ian Ring Music TheoryAeolygimic
Scale 1115Scale 1115: Superlocrian Hexamirror, Ian Ring Music TheorySuperlocrian Hexamirror
Scale 2139Scale 2139, 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.