The Exciting Universe Of Music Theory

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Scale 215

Scale 215, 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{0,1,2,4,6,7}
Forte Number6-Z12
Rotational Symmetrynone
Reflection Axesnone
enantiomorph: 3425
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
Deep Scaleno
Interval Vector332232
Interval Spectrump3m2n2s3d3t2
Distribution Spectra<1> = {1,2,5}
<2> = {2,3,4,6}
<3> = {4,5,7,8}
<4> = {6,8,9,10}
<5> = {7,10,11}
Spectra Variation3.333
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
Major TriadsC{0,4,7}110.5
Diminished Triadsc♯°{1,4,7}110.5
Parsimonious Voice Leading Between Common Triads of Scale 215. Created by Ian Ring ©2019 C C c#° c#° C->c#°

Above is a graph showing opportunities for parsimonious voice leading between triads*. Each line connects two triads that have two common tones, while the third tone changes by one generic scale step.



Modes are the rotational transformation of this scale. Scale 215 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 2155
Scale 2155, Ian Ring Music Theory
3rd mode:
Scale 3125
Scale 3125, Ian Ring Music Theory
4th mode:
Scale 1805
Scale 1805, Ian Ring Music Theory
5th mode:
Scale 1475
Scale 1475, Ian Ring Music Theory
6th mode:
Scale 2785
Scale 2785, Ian Ring Music Theory


This is the prime form of this scale.


The hexatonic modal family [215, 2155, 3125, 1805, 1475, 2785] (Forte: 6-Z12) is the complement of the hexatonic modal family [335, 965, 1265, 2215, 3155, 3625] (Forte: 6-Z41)


The inverse of a scale is a reflection using the root as its axis. The inverse of 215 is 3425

Scale 3425Scale 3425, Ian Ring Music Theory


Only scales that are chiral will have an enantiomorph. Scale 215 is chiral, and its enantiomorph is scale 3425

Scale 3425Scale 3425, Ian Ring Music Theory


T0 215  T0I 3425
T1 430  T1I 2755
T2 860  T2I 1415
T3 1720  T3I 2830
T4 3440  T4I 1565
T5 2785  T5I 3130
T6 1475  T6I 2165
T7 2950  T7I 235
T8 1805  T8I 470
T9 3610  T9I 940
T10 3125  T10I 1880
T11 2155  T11I 3760

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 213Scale 213, Ian Ring Music Theory
Scale 211Scale 211, Ian Ring Music Theory
Scale 219Scale 219: Istrian, Ian Ring Music TheoryIstrian
Scale 223Scale 223, Ian Ring Music Theory
Scale 199Scale 199: Raga Nabhomani, Ian Ring Music TheoryRaga Nabhomani
Scale 207Scale 207, Ian Ring Music Theory
Scale 231Scale 231, Ian Ring Music Theory
Scale 247Scale 247, Ian Ring Music Theory
Scale 151Scale 151, Ian Ring Music Theory
Scale 183Scale 183, Ian Ring Music Theory
Scale 87Scale 87, Ian Ring Music Theory
Scale 343Scale 343: Ionorimic, Ian Ring Music TheoryIonorimic
Scale 471Scale 471: Dodian, Ian Ring Music TheoryDodian
Scale 727Scale 727: Phradian, Ian Ring Music TheoryPhradian
Scale 1239Scale 1239: Epaptian, Ian Ring Music TheoryEpaptian
Scale 2263Scale 2263: Lycrian, Ian Ring Music TheoryLycrian

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.