The Exciting Universe Of Music Theory

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Scale 3135

Scale 3135, 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).


Cardinality8 (octatonic)
Pitch Class Set{0,1,2,3,4,5,10,11}
Forte Number8-1
Rotational Symmetrynone
Reflection Axes1.5
Hemitonia7 (multihemitonic)
Cohemitonia6 (multicohemitonic)
prime: 255
Deep Scaleno
Interval Vector765442
Interval Spectrump4m4n5s6d7t2
Distribution Spectra<1> = {1,5}
<2> = {2,6}
<3> = {3,7}
<4> = {4,8}
<5> = {5,9}
<6> = {6,10}
<7> = {7,11}
Spectra Variation3.5
Maximally Evenno
Maximal Area Setno
Interior Area2
Myhill Propertyyes
Ridge Tones[3]

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 TriadsA♯{10,2,5}221
Minor Triadsa♯m{10,1,5}221
Diminished Triadsa♯°{10,1,4}131.5
Parsimonious Voice Leading Between Common Triads of Scale 3135. Created by Ian Ring ©2019 a#° a#° a#m a#m a#°->a#m A# A# a#m->A# A#->b°

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.

Central Verticesa♯m, A♯
Peripheral Verticesa♯°, b°


Modes are the rotational transformation of this scale. Scale 3135 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3615
Scale 3615, Ian Ring Music Theory
3rd mode:
Scale 3855
Scale 3855, Ian Ring Music Theory
4th mode:
Scale 3975
Scale 3975, Ian Ring Music Theory
5th mode:
Scale 4035
Scale 4035, Ian Ring Music Theory
6th mode:
Scale 4065
Scale 4065, Ian Ring Music Theory
7th mode:
Scale 255
Scale 255, Ian Ring Music TheoryThis is the prime mode
8th mode:
Scale 2175
Scale 2175, Ian Ring Music Theory


The prime form of this scale is Scale 255

Scale 255Scale 255, Ian Ring Music Theory


The octatonic modal family [3135, 3615, 3855, 3975, 4035, 4065, 255, 2175] (Forte: 8-1) is the complement of the tetratonic modal family [15, 2055, 3075, 3585] (Forte: 4-1)


The inverse of a scale is a reflection using the root as its axis. The inverse of 3135 is 3975

Scale 3975Scale 3975, Ian Ring Music Theory


T0 3135  T0I 3975
T1 2175  T1I 3855
T2 255  T2I 3615
T3 510  T3I 3135
T4 1020  T4I 2175
T5 2040  T5I 255
T6 4080  T6I 510
T7 4065  T7I 1020
T8 4035  T8I 2040
T9 3975  T9I 4080
T10 3855  T10I 4065
T11 3615  T11I 4035

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 3133Scale 3133, Ian Ring Music Theory
Scale 3131Scale 3131, Ian Ring Music Theory
Scale 3127Scale 3127, Ian Ring Music Theory
Scale 3119Scale 3119, Ian Ring Music Theory
Scale 3103Scale 3103, Ian Ring Music Theory
Scale 3167Scale 3167: Thynyllic, Ian Ring Music TheoryThynyllic
Scale 3199Scale 3199: Thaptygic, Ian Ring Music TheoryThaptygic
Scale 3263Scale 3263: Pyrygic, Ian Ring Music TheoryPyrygic
Scale 3391Scale 3391: Aeolynygic, Ian Ring Music TheoryAeolynygic
Scale 3647Scale 3647: Eporygic, Ian Ring Music TheoryEporygic
Scale 2111Scale 2111, Ian Ring Music Theory
Scale 2623Scale 2623: Aerylyllic, Ian Ring Music TheoryAerylyllic
Scale 1087Scale 1087, 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.