The Exciting Universe Of Music Theory

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Scale 3587

Scale 3587, 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{0,1,9,10,11}
Forte Number5-1
Rotational Symmetrynone
Reflection Axes5
Hemitonia4 (multihemitonic)
Cohemitonia3 (tricohemitonic)
prime: 31
Deep Scaleno
Interval Vector432100
Interval Spectrummn2s3d4
Distribution Spectra<1> = {1,8}
<2> = {2,9}
<3> = {3,10}
<4> = {4,11}
Spectra Variation5.6
Maximally Evenno
Myhill Propertyyes
Ridge Tones[10]


Modes are the rotational transformation of this scale. Scale 3587 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 3841
Scale 3841, Ian Ring Music Theory
3rd mode:
Scale 31
Scale 31, Ian Ring Music TheoryThis is the prime mode
4th mode:
Scale 2063
Scale 2063, Ian Ring Music Theory
5th mode:
Scale 3079
Scale 3079, Ian Ring Music Theory


The prime form of this scale is Scale 31

Scale 31Scale 31, Ian Ring Music Theory


The pentatonic modal family [3587, 3841, 31, 2063, 3079] (Forte: 5-1) is the complement of the heptatonic modal family [127, 2111, 3103, 3599, 3847, 3971, 4033] (Forte: 7-1)


The inverse of a scale is a reflection using the root as its axis. The inverse of 3587 is 2063

Scale 2063Scale 2063, Ian Ring Music Theory


T0 3587  T0I 2063
T1 3079  T1I 31
T2 2063  T2I 62
T3 31  T3I 124
T4 62  T4I 248
T5 124  T5I 496
T6 248  T6I 992
T7 496  T7I 1984
T8 992  T8I 3968
T9 1984  T9I 3841
T10 3968  T10I 3587
T11 3841  T11I 3079

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 3585Scale 3585, Ian Ring Music Theory
Scale 3589Scale 3589, Ian Ring Music Theory
Scale 3591Scale 3591, Ian Ring Music Theory
Scale 3595Scale 3595, Ian Ring Music Theory
Scale 3603Scale 3603, Ian Ring Music Theory
Scale 3619Scale 3619: Thanimic, Ian Ring Music TheoryThanimic
Scale 3651Scale 3651, Ian Ring Music Theory
Scale 3715Scale 3715, Ian Ring Music Theory
Scale 3843Scale 3843, Ian Ring Music Theory
Scale 3075Scale 3075, Ian Ring Music Theory
Scale 3331Scale 3331, Ian Ring Music Theory
Scale 2563Scale 2563, Ian Ring Music Theory
Scale 1539Scale 1539, 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.