The Exciting Universe Of Music Theory

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Scale 3115

Scale 3115, 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{0,1,3,5,10,11}
Forte Number6-9
Rotational Symmetrynone
Reflection Axesnone
enantiomorph: 2695
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 Triadsa♯m{10,1,5}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 3115 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 3605
Scale 3605, Ian Ring Music Theory
3rd mode:
Scale 1925
Scale 1925, Ian Ring Music Theory
4th mode:
Scale 1505
Scale 1505, Ian Ring Music Theory
5th mode:
Scale 175
Scale 175, Ian Ring Music TheoryThis is the prime mode
6th mode:
Scale 2135
Scale 2135, Ian Ring Music Theory


The prime form of this scale is Scale 175

Scale 175Scale 175, Ian Ring Music Theory


The hexatonic modal family [3115, 3605, 1925, 1505, 175, 2135] (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 3115 is 2695

Scale 2695Scale 2695, Ian Ring Music Theory


Only scales that are chiral will have an enantiomorph. Scale 3115 is chiral, and its enantiomorph is scale 2695

Scale 2695Scale 2695, Ian Ring Music Theory


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

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 3113Scale 3113, Ian Ring Music Theory
Scale 3117Scale 3117, Ian Ring Music Theory
Scale 3119Scale 3119, Ian Ring Music Theory
Scale 3107Scale 3107, Ian Ring Music Theory
Scale 3111Scale 3111, Ian Ring Music Theory
Scale 3123Scale 3123, Ian Ring Music Theory
Scale 3131Scale 3131, Ian Ring Music Theory
Scale 3083Scale 3083, Ian Ring Music Theory
Scale 3099Scale 3099, Ian Ring Music Theory
Scale 3147Scale 3147: Ryrimic, Ian Ring Music TheoryRyrimic
Scale 3179Scale 3179: Daptian, Ian Ring Music TheoryDaptian
Scale 3243Scale 3243: Mela Rupavati, Ian Ring Music TheoryMela Rupavati
Scale 3371Scale 3371: Aeolylian, Ian Ring Music TheoryAeolylian
Scale 3627Scale 3627: Kalian, Ian Ring Music TheoryKalian
Scale 2091Scale 2091, Ian Ring Music Theory
Scale 2603Scale 2603: Gadimic, Ian Ring Music TheoryGadimic
Scale 1067Scale 1067, 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.