The Exciting Universe Of Music Theory

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Scale 2135

Scale 2135, 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{0,1,2,4,6,11}
Forte Number6-9
Rotational Symmetrynone
Reflection Axesnone
enantiomorph: 3395
Hemitonia3 (trihemitonic)
Cohemitonia2 (dicohemitonic)
prime: 175
Deep Scaleno
Interval Vector342231
Interval Spectrump3m2n2s4d3t
Distribution Spectra<1> = {1,2,5}
<2> = {2,3,4,6,7}
<3> = {3,4,5,7,8,9}
<4> = {5,6,8,9,10}
<5> = {7,10,11}
Spectra Variation4
Maximally Evenno
Maximal Area Setno
Interior Area1.866
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
Minor Triadsbm{11,2,6}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 2135 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 3115
Scale 3115, Ian Ring Music Theory
3rd mode:
Scale 3605
Scale 3605, Ian Ring Music Theory
4th mode:
Scale 1925
Scale 1925, Ian Ring Music Theory
5th mode:
Scale 1505
Scale 1505, Ian Ring Music Theory
6th mode:
Scale 175
Scale 175, Ian Ring Music TheoryThis is the prime mode


The prime form of this scale is Scale 175

Scale 175Scale 175, Ian Ring Music Theory


The hexatonic modal family [2135, 3115, 3605, 1925, 1505, 175] (Forte: 6-9) is the complement of the hexatonic modal family [175, 1505, 1925, 2135, 3115, 3605] (Forte: 6-9)


The inverse of a scale is a reflection using the root as its axis. The inverse of 2135 is 3395

Scale 3395Scale 3395, Ian Ring Music Theory


Only scales that are chiral will have an enantiomorph. Scale 2135 is chiral, and its enantiomorph is scale 3395

Scale 3395Scale 3395, Ian Ring Music Theory


T0 2135  T0I 3395
T1 175  T1I 2695
T2 350  T2I 1295
T3 700  T3I 2590
T4 1400  T4I 1085
T5 2800  T5I 2170
T6 1505  T6I 245
T7 3010  T7I 490
T8 1925  T8I 980
T9 3850  T9I 1960
T10 3605  T10I 3920
T11 3115  T11I 3745

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 2133Scale 2133: Raga Kumurdaki, Ian Ring Music TheoryRaga Kumurdaki
Scale 2131Scale 2131, Ian Ring Music Theory
Scale 2139Scale 2139, Ian Ring Music Theory
Scale 2143Scale 2143, Ian Ring Music Theory
Scale 2119Scale 2119, Ian Ring Music Theory
Scale 2127Scale 2127, Ian Ring Music Theory
Scale 2151Scale 2151, Ian Ring Music Theory
Scale 2167Scale 2167, Ian Ring Music Theory
Scale 2071Scale 2071, Ian Ring Music Theory
Scale 2103Scale 2103, Ian Ring Music Theory
Scale 2199Scale 2199: Dyptimic, Ian Ring Music TheoryDyptimic
Scale 2263Scale 2263: Lycrian, Ian Ring Music TheoryLycrian
Scale 2391Scale 2391: Molian, Ian Ring Music TheoryMolian
Scale 2647Scale 2647: Dadian, Ian Ring Music TheoryDadian
Scale 3159Scale 3159: Stocrian, Ian Ring Music TheoryStocrian
Scale 87Scale 87, Ian Ring Music Theory
Scale 1111Scale 1111: Sycrimic, Ian Ring Music TheorySycrimic

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.