The Exciting Universe Of Music Theory

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Scale 2115

Scale 2115, 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).


Cardinality4 (tetratonic)
Pitch Class Set{0,1,6,11}
Forte Number4-6
Rotational Symmetrynone
Reflection Axes0
Hemitonia2 (dihemitonic)
Cohemitonia1 (uncohemitonic)
prime: 135
Deep Scaleno
Interval Vector210021
Interval Spectrump2sd2t
Distribution Spectra<1> = {1,5}
<2> = {2,6,10}
<3> = {7,11}
Spectra Variation4
Maximally Evenno
Maximal Area Setno
Interior Area1
Myhill Propertyno
Ridge Tones[0]

Common Triads

There are no common triads (major, minor, augmented and diminished) that can be formed using notes in this scale.


Modes are the rotational transformation of this scale. Scale 2115 can be rotated to make 3 other scales. The 1st mode is itself.

2nd mode:
Scale 3105
Scale 3105, Ian Ring Music Theory
3rd mode:
Scale 225
Scale 225, Ian Ring Music Theory
4th mode:
Scale 135
Scale 135, Ian Ring Music TheoryThis is the prime mode


The prime form of this scale is Scale 135

Scale 135Scale 135, Ian Ring Music Theory


The tetratonic modal family [2115, 3105, 225, 135] (Forte: 4-6) is the complement of the octatonic modal family [495, 1935, 2295, 3015, 3195, 3555, 3645, 3825] (Forte: 8-6)


The inverse of a scale is a reflection using the root as its axis. The inverse of 2115 is itself, because it is a palindromic scale!

Scale 2115Scale 2115, Ian Ring Music Theory


T0 2115  T0I 2115
T1 135  T1I 135
T2 270  T2I 270
T3 540  T3I 540
T4 1080  T4I 1080
T5 2160  T5I 2160
T6 225  T6I 225
T7 450  T7I 450
T8 900  T8I 900
T9 1800  T9I 1800
T10 3600  T10I 3600
T11 3105  T11I 3105

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 2113Scale 2113, Ian Ring Music Theory
Scale 2117Scale 2117: Raga Sumukam, Ian Ring Music TheoryRaga Sumukam
Scale 2119Scale 2119, Ian Ring Music Theory
Scale 2123Scale 2123, Ian Ring Music Theory
Scale 2131Scale 2131, Ian Ring Music Theory
Scale 2147Scale 2147, Ian Ring Music Theory
Scale 2051Scale 2051, Ian Ring Music Theory
Scale 2083Scale 2083, Ian Ring Music Theory
Scale 2179Scale 2179, Ian Ring Music Theory
Scale 2243Scale 2243, Ian Ring Music Theory
Scale 2371Scale 2371, Ian Ring Music Theory
Scale 2627Scale 2627, Ian Ring Music Theory
Scale 3139Scale 3139, Ian Ring Music Theory
Scale 67Scale 67, Ian Ring Music Theory
Scale 1091Scale 1091, 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.