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Scale 3143: "Polimic"

Scale 3143: Polimic, 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



Cardinality6 (hexatonic)
Pitch Class Set{0,1,2,6,10,11}
Forte Number6-Z37
Rotational Symmetrynone
Reflection Axes0
Hemitonia4 (multihemitonic)
Cohemitonia3 (tricohemitonic)
prime: 287
Deep Scaleno
Interval Vector432321
Interval Spectrump2m3n2s3d4t
Distribution Spectra<1> = {1,4}
<2> = {2,5,8}
<3> = {3,6,9}
<4> = {4,7,10}
<5> = {8,11}
Spectra Variation4
Maximally Evenno
Maximal Area Setno
Interior Area1.866
Myhill Propertyno
Ridge Tones[0]

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 TriadsF♯{6,10,1}121
Minor Triadsbm{11,2,6}121
Augmented TriadsD+{2,6,10}210.67
Parsimonious Voice Leading Between Common Triads of Scale 3143. Created by Ian Ring ©2019 D+ D+ F# F# D+->F# bm bm D+->bm

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 VerticesD+
Peripheral VerticesF♯, bm


Modes are the rotational transformation of this scale. Scale 3143 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 3619
Scale 3619: Thanimic, Ian Ring Music TheoryThanimic
3rd mode:
Scale 3857
Scale 3857: Ponimic, Ian Ring Music TheoryPonimic
4th mode:
Scale 497
Scale 497: Kadimic, Ian Ring Music TheoryKadimic
5th mode:
Scale 287
Scale 287: Gynimic, Ian Ring Music TheoryGynimicThis is the prime mode
6th mode:
Scale 2191
Scale 2191: Thydimic, Ian Ring Music TheoryThydimic


The prime form of this scale is Scale 287

Scale 287Scale 287: Gynimic, Ian Ring Music TheoryGynimic


The hexatonic modal family [3143, 3619, 3857, 497, 287, 2191] (Forte: 6-Z37) is the complement of the hexatonic modal family [119, 1799, 2107, 2947, 3101, 3521] (Forte: 6-Z4)


The inverse of a scale is a reflection using the root as its axis. The inverse of 3143 is itself, because it is a palindromic scale!

Scale 3143Scale 3143: Polimic, Ian Ring Music TheoryPolimic


T0 3143  T0I 3143
T1 2191  T1I 2191
T2 287  T2I 287
T3 574  T3I 574
T4 1148  T4I 1148
T5 2296  T5I 2296
T6 497  T6I 497
T7 994  T7I 994
T8 1988  T8I 1988
T9 3976  T9I 3976
T10 3857  T10I 3857
T11 3619  T11I 3619

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 3141Scale 3141: Kanitonic, Ian Ring Music TheoryKanitonic
Scale 3139Scale 3139, Ian Ring Music Theory
Scale 3147Scale 3147: Ryrimic, Ian Ring Music TheoryRyrimic
Scale 3151Scale 3151: Pacrian, Ian Ring Music TheoryPacrian
Scale 3159Scale 3159: Stocrian, Ian Ring Music TheoryStocrian
Scale 3175Scale 3175: Eponian, Ian Ring Music TheoryEponian
Scale 3079Scale 3079, Ian Ring Music Theory
Scale 3111Scale 3111, Ian Ring Music Theory
Scale 3207Scale 3207, Ian Ring Music Theory
Scale 3271Scale 3271: Mela Raghupriya, Ian Ring Music TheoryMela Raghupriya
Scale 3399Scale 3399: Zonian, Ian Ring Music TheoryZonian
Scale 3655Scale 3655: Mathian, Ian Ring Music TheoryMathian
Scale 2119Scale 2119, Ian Ring Music Theory
Scale 2631Scale 2631: Macrimic, Ian Ring Music TheoryMacrimic
Scale 1095Scale 1095: Phrythitonic, Ian Ring Music TheoryPhrythitonic

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.