The Exciting Universe Of Music Theory

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Scale 2087

Scale 2087, 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{0,1,2,5,11}
Forte Number5-4
Rotational Symmetrynone
Reflection Axesnone
enantiomorph: 3203
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
Maximal Area Setno
Interior Area1.25
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{11,2,5}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 2087 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 3091
Scale 3091, Ian Ring Music Theory
3rd mode:
Scale 3593
Scale 3593, Ian Ring Music Theory
4th mode:
Scale 961
Scale 961, Ian Ring Music Theory
5th mode:
Scale 79
Scale 79, Ian Ring Music TheoryThis is the prime mode


The prime form of this scale is Scale 79

Scale 79Scale 79, Ian Ring Music Theory


The pentatonic modal family [2087, 3091, 3593, 961, 79] (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 2087 is 3203

Scale 3203Scale 3203, Ian Ring Music Theory


Only scales that are chiral will have an enantiomorph. Scale 2087 is chiral, and its enantiomorph is scale 3203

Scale 3203Scale 3203, Ian Ring Music Theory


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

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 2085Scale 2085, Ian Ring Music Theory
Scale 2083Scale 2083, Ian Ring Music Theory
Scale 2091Scale 2091, Ian Ring Music Theory
Scale 2095Scale 2095, Ian Ring Music Theory
Scale 2103Scale 2103, Ian Ring Music Theory
Scale 2055Scale 2055, Ian Ring Music Theory
Scale 2071Scale 2071, Ian Ring Music Theory
Scale 2119Scale 2119, Ian Ring Music Theory
Scale 2151Scale 2151, Ian Ring Music Theory
Scale 2215Scale 2215: Ranimic, Ian Ring Music TheoryRanimic
Scale 2343Scale 2343: Tharimic, Ian Ring Music TheoryTharimic
Scale 2599Scale 2599: Malimic, Ian Ring Music TheoryMalimic
Scale 3111Scale 3111, Ian Ring Music Theory
Scale 39Scale 39, Ian Ring Music Theory
Scale 1063Scale 1063, 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.