The Exciting Universe Of Music Theory

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Scale 3091

Scale 3091, 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{0,1,4,10,11}
Forte Number5-4
Rotational Symmetrynone
Reflection Axesnone
enantiomorph: 2311
Hemitonia3 (trihemitonic)
Cohemitonia2 (dicohemitonic)
prime: 79
Deep Scaleno
Interval Vector322111
Interval Spectrumpmn2s2d3t
Distribution Spectra<1> = {1,3,6}
<2> = {2,4,7,9}
<3> = {3,5,8,10}
<4> = {6,9,11}
Spectra Variation4.8
Maximally Evenno
Myhill Propertyno
Ridge Tonesnone


Modes are the rotational transformation of this scale. Scale 3091 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 3593
Scale 3593, Ian Ring Music Theory
3rd mode:
Scale 961
Scale 961, Ian Ring Music Theory
4th mode:
Scale 79
Scale 79, Ian Ring Music TheoryThis is the prime mode
5th mode:
Scale 2087
Scale 2087, Ian Ring Music Theory


The prime form of this scale is Scale 79

Scale 79Scale 79, Ian Ring Music Theory


The pentatonic modal family [3091, 3593, 961, 79, 2087] (Forte: 5-4) is the complement of the heptatonic modal family [223, 1987, 2159, 3041, 3127, 3611, 3853] (Forte: 7-4)


The inverse of a scale is a reflection using the root as its axis. The inverse of 3091 is 2311

Scale 2311Scale 2311: Raga Kumarapriya, Ian Ring Music TheoryRaga Kumarapriya


Only scales that are chiral will have an enantiomorph. Scale 3091 is chiral, and its enantiomorph is scale 2311

Scale 2311Scale 2311: Raga Kumarapriya, Ian Ring Music TheoryRaga Kumarapriya


T0 3091  T0I 2311
T1 2087  T1I 527
T2 79  T2I 1054
T3 158  T3I 2108
T4 316  T4I 121
T5 632  T5I 242
T6 1264  T6I 484
T7 2528  T7I 968
T8 961  T8I 1936
T9 1922  T9I 3872
T10 3844  T10I 3649
T11 3593  T11I 3203

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 3089Scale 3089, Ian Ring Music Theory
Scale 3093Scale 3093, Ian Ring Music Theory
Scale 3095Scale 3095, Ian Ring Music Theory
Scale 3099Scale 3099, Ian Ring Music Theory
Scale 3075Scale 3075, Ian Ring Music Theory
Scale 3083Scale 3083, Ian Ring Music Theory
Scale 3107Scale 3107, Ian Ring Music Theory
Scale 3123Scale 3123, Ian Ring Music Theory
Scale 3155Scale 3155: Ladimic, Ian Ring Music TheoryLadimic
Scale 3219Scale 3219: Ionaphimic, Ian Ring Music TheoryIonaphimic
Scale 3347Scale 3347: Synimic, Ian Ring Music TheorySynimic
Scale 3603Scale 3603, Ian Ring Music Theory
Scale 2067Scale 2067, Ian Ring Music Theory
Scale 2579Scale 2579, Ian Ring Music Theory
Scale 1043Scale 1043, 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. Some scale names used on this and other pages are ©2005 William Zeitler ( Peruse this Bibliography.