The Exciting Universe Of Music Theory

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Scale 3129

Scale 3129, 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{0,3,4,5,10,11}
Forte Number6-Z6
Rotational Symmetrynone
Reflection Axes1.5
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
prime: 231
Deep Scaleno
Interval Vector421242
Interval Spectrump4m2ns2d4t2
Distribution Spectra<1> = {1,3,5}
<2> = {2,4,6}
<3> = {5,7}
<4> = {6,8,10}
<5> = {7,9,11}
Spectra Variation3
Maximally Evenno
Maximal Area Setno
Interior Area1.75
Myhill Propertyno
Ridge Tones[3]

Common Triads

There are no common triads (major, minor, augmented and diminished) that can be formed using notes in this scale.


Modes are the rotational transformation of this scale. Scale 3129 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 903
Scale 903, Ian Ring Music Theory
3rd mode:
Scale 2499
Scale 2499, Ian Ring Music Theory
4th mode:
Scale 3297
Scale 3297, Ian Ring Music Theory
5th mode:
Scale 231
Scale 231, Ian Ring Music TheoryThis is the prime mode
6th mode:
Scale 2163
Scale 2163, Ian Ring Music Theory


The prime form of this scale is Scale 231

Scale 231Scale 231, Ian Ring Music Theory


The hexatonic modal family [3129, 903, 2499, 3297, 231, 2163] (Forte: 6-Z6) is the complement of the hexatonic modal family [399, 483, 2247, 2289, 3171, 3633] (Forte: 6-Z38)


The inverse of a scale is a reflection using the root as its axis. The inverse of 3129 is 903

Scale 903Scale 903, Ian Ring Music Theory


T0 3129  T0I 903
T1 2163  T1I 1806
T2 231  T2I 3612
T3 462  T3I 3129
T4 924  T4I 2163
T5 1848  T5I 231
T6 3696  T6I 462
T7 3297  T7I 924
T8 2499  T8I 1848
T9 903  T9I 3696
T10 1806  T10I 3297
T11 3612  T11I 2499

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 3131Scale 3131, Ian Ring Music Theory
Scale 3133Scale 3133, Ian Ring Music Theory
Scale 3121Scale 3121, Ian Ring Music Theory
Scale 3125Scale 3125, Ian Ring Music Theory
Scale 3113Scale 3113, Ian Ring Music Theory
Scale 3097Scale 3097, Ian Ring Music Theory
Scale 3161Scale 3161: Kodimic, Ian Ring Music TheoryKodimic
Scale 3193Scale 3193: Zathian, Ian Ring Music TheoryZathian
Scale 3257Scale 3257: Mela Calanata, Ian Ring Music TheoryMela Calanata
Scale 3385Scale 3385: Chromatic Phrygian, Ian Ring Music TheoryChromatic Phrygian
Scale 3641Scale 3641: Thocrian, Ian Ring Music TheoryThocrian
Scale 2105Scale 2105, Ian Ring Music Theory
Scale 2617Scale 2617: Pylimic, Ian Ring Music TheoryPylimic
Scale 1081Scale 1081, 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.