The Exciting Universe Of Music Theory

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Scale 3111

Scale 3111, 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{0,1,2,5,10,11}
Forte Number6-Z36
Rotational Symmetrynone
Reflection Axesnone
enantiomorph: 3207
Hemitonia4 (multihemitonic)
Cohemitonia3 (tricohemitonic)
prime: 159
Deep Scaleno
Interval Vector433221
Interval Spectrump2m2n3s3d4t
Distribution Spectra<1> = {1,3,5}
<2> = {2,4,6,8}
<3> = {3,5,7,9}
<4> = {4,6,8,10}
<5> = {7,9,11}
Spectra Variation4.333
Maximally Evenno
Maximal Area Setno
Interior Area1.75
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 TriadsA♯{10,2,5}210.67
Minor Triadsa♯m{10,1,5}121
Diminished Triads{11,2,5}121
Parsimonious Voice Leading Between Common Triads of Scale 3111. Created by Ian Ring ©2019 a#m 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♯
Peripheral Verticesa♯m, b°


Modes are the rotational transformation of this scale. Scale 3111 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 3603
Scale 3603, Ian Ring Music Theory
3rd mode:
Scale 3849
Scale 3849, Ian Ring Music Theory
4th mode:
Scale 993
Scale 993, Ian Ring Music Theory
5th mode:
Scale 159
Scale 159, Ian Ring Music TheoryThis is the prime mode
6th mode:
Scale 2127
Scale 2127, Ian Ring Music Theory


The prime form of this scale is Scale 159

Scale 159Scale 159, Ian Ring Music Theory


The hexatonic modal family [3111, 3603, 3849, 993, 159, 2127] (Forte: 6-Z36) is the complement of the hexatonic modal family [111, 1923, 2103, 3009, 3099, 3597] (Forte: 6-Z3)


The inverse of a scale is a reflection using the root as its axis. The inverse of 3111 is 3207

Scale 3207Scale 3207, Ian Ring Music Theory


Only scales that are chiral will have an enantiomorph. Scale 3111 is chiral, and its enantiomorph is scale 3207

Scale 3207Scale 3207, Ian Ring Music Theory


T0 3111  T0I 3207
T1 2127  T1I 2319
T2 159  T2I 543
T3 318  T3I 1086
T4 636  T4I 2172
T5 1272  T5I 249
T6 2544  T6I 498
T7 993  T7I 996
T8 1986  T8I 1992
T9 3972  T9I 3984
T10 3849  T10I 3873
T11 3603  T11I 3651

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 3109Scale 3109, Ian Ring Music Theory
Scale 3107Scale 3107, Ian Ring Music Theory
Scale 3115Scale 3115, Ian Ring Music Theory
Scale 3119Scale 3119, Ian Ring Music Theory
Scale 3127Scale 3127, Ian Ring Music Theory
Scale 3079Scale 3079, Ian Ring Music Theory
Scale 3095Scale 3095, Ian Ring Music Theory
Scale 3143Scale 3143: Polimic, Ian Ring Music TheoryPolimic
Scale 3175Scale 3175: Eponian, Ian Ring Music TheoryEponian
Scale 3239Scale 3239: Mela Tanarupi, Ian Ring Music TheoryMela Tanarupi
Scale 3367Scale 3367: Moptian, Ian Ring Music TheoryMoptian
Scale 3623Scale 3623: Aerocrian, Ian Ring Music TheoryAerocrian
Scale 2087Scale 2087, Ian Ring Music Theory
Scale 2599Scale 2599: Malimic, Ian Ring Music TheoryMalimic
Scale 1063Scale 1063, 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.