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Scale 3967: "Soratic"

Scale 3967: Soratic, 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).

Common Names



Cardinality11 (undecatonic)
Pitch Class Set{0,1,2,3,4,5,6,8,9,10,11}
Forte Number11-1
Rotational Symmetrynone
Reflection Axes1
Hemitonia10 (multihemitonic)
Cohemitonia9 (multicohemitonic)
prime: 2047
Deep Scaleno
Interval Vector10101010105
Interval Spectrump10m10n10s10d10t5
Distribution Spectra<1> = {1,2}
<2> = {2,3}
<3> = {3,4}
<4> = {4,5}
<5> = {5,6}
<6> = {6,7}
<7> = {7,8}
<8> = {8,9}
<9> = {9,10}
<10> = {10,11}
Spectra Variation0.909
Maximally Evenyes
Maximal Area Setyes
Interior Area2.933
Myhill Propertyyes
Ridge Tones[2]

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♯{1,5,8}452.87
Minor Triadsc♯m{1,4,8}353
Augmented TriadsC+{0,4,8}552.9
Diminished Triads{0,3,6}253.3
Parsimonious Voice Leading Between Common Triads of Scale 3967. Created by Ian Ring ©2019 G# G# c°->G# B B c°->B C+ C+ c#m c#m C+->c#m E E C+->E fm fm C+->fm C+->G# am am C+->am C# C# c#m->C# A A c#m->A C#+ C#+ C#->C#+ C#->d° C#->fm dm dm C#+->dm F F C#+->F f#m f#m C#+->f#m C#+->A a#m a#m C#+->a#m d°->dm D D dm->D A# A# dm->A# D+ D+ D->D+ d#° d#° D->d#° D->f#m d#m d#m D+->d#m F# F# D+->F# D+->A# bm bm D+->bm d#°->d#m d#m->B E->f° g#m g#m E->g#m f°->fm fm->F f#° f#° F->f#° F->am f#°->f#m f#m->F# F#->a#m g#° g#° g#°->g#m g#°->bm g#m->G# g#m->B G#->a° a°->am am->A a#° a#° A->a#° a#°->a#m a#m->A# A#->b° b°->bm bm->B

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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 3967 can be rotated to make 10 other scales. The 1st mode is itself.

2nd mode:
Scale 4031
Scale 4031: Godatic, Ian Ring Music TheoryGodatic
3rd mode:
Scale 4063
Scale 4063: Eptatic, Ian Ring Music TheoryEptatic
4th mode:
Scale 4079
Scale 4079: Ionatic, Ian Ring Music TheoryIonatic
5th mode:
Scale 4087
Scale 4087: Aeolatic, Ian Ring Music TheoryAeolatic
6th mode:
Scale 4091
Scale 4091: Thydatic, Ian Ring Music TheoryThydatic
7th mode:
Scale 4093
Scale 4093: Aerycratic, Ian Ring Music TheoryAerycratic
8th mode:
Scale 2047
Scale 2047: Monatic, Ian Ring Music TheoryMonaticThis is the prime mode
9th mode:
Scale 3071
Scale 3071: Solatic, Ian Ring Music TheorySolatic
10th mode:
Scale 3583
Scale 3583: Zylatic, Ian Ring Music TheoryZylatic
11th mode:
Scale 3839
Scale 3839: Mixolatic, Ian Ring Music TheoryMixolatic


The prime form of this scale is Scale 2047

Scale 2047Scale 2047: Monatic, Ian Ring Music TheoryMonatic


The undecatonic modal family [3967, 4031, 4063, 4079, 4087, 4091, 4093, 2047, 3071, 3583, 3839] (Forte: 11-1) is the complement of the modal family [1] (Forte: 1-1)


The inverse of a scale is a reflection using the root as its axis. The inverse of 3967 is 4063

Scale 4063Scale 4063: Eptatic, Ian Ring Music TheoryEptatic


T0 3967  T0I 4063
T1 3839  T1I 4031
T2 3583  T2I 3967
T3 3071  T3I 3839
T4 2047  T4I 3583
T5 4094  T5I 3071
T6 4093  T6I 2047
T7 4091  T7I 4094
T8 4087  T8I 4093
T9 4079  T9I 4091
T10 4063  T10I 4087
T11 4031  T11I 4079

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 3965Scale 3965: Messiaen Mode 7 Inverse, Ian Ring Music TheoryMessiaen Mode 7 Inverse
Scale 3963Scale 3963: Aeoryllian, Ian Ring Music TheoryAeoryllian
Scale 3959Scale 3959: Katagyllian, Ian Ring Music TheoryKatagyllian
Scale 3951Scale 3951: Mathyllian, Ian Ring Music TheoryMathyllian
Scale 3935Scale 3935: Kataphyllian, Ian Ring Music TheoryKataphyllian
Scale 3903Scale 3903: Aeogyllian, Ian Ring Music TheoryAeogyllian
Scale 4031Scale 4031: Godatic, Ian Ring Music TheoryGodatic
Scale 4095Scale 4095: Chromatic, Ian Ring Music TheoryChromatic
Scale 3711Scale 3711: Dycryllian, Ian Ring Music TheoryDycryllian
Scale 3839Scale 3839: Mixolatic, Ian Ring Music TheoryMixolatic
Scale 3455Scale 3455: Ryptyllian, Ian Ring Music TheoryRyptyllian
Scale 2943Scale 2943: Dathyllian, Ian Ring Music TheoryDathyllian
Scale 1919Scale 1919: Rocryllian, Ian Ring Music TheoryRocryllian

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.