The Exciting Universe Of Music Theory

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Scale 3125

Scale 3125, 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{0,2,4,5,10,11}
Forte Number6-Z12
Rotational Symmetrynone
Reflection Axesnone
enantiomorph: 1415
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
prime: 215
Deep Scaleno
Interval Vector332232
Interval Spectrump3m2n2s3d3t2
Distribution Spectra<1> = {1,2,5}
<2> = {2,3,4,6}
<3> = {4,5,7,8}
<4> = {6,8,9,10}
<5> = {7,10,11}
Spectra Variation3.333
Maximally Evenno
Maximal Area Setno
Interior Area1.866
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}110.5
Diminished Triads{11,2,5}110.5
Parsimonious Voice Leading Between Common Triads of Scale 3125. Created by Ian Ring ©2019 A# 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.



Modes are the rotational transformation of this scale. Scale 3125 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 1805
Scale 1805, Ian Ring Music Theory
3rd mode:
Scale 1475
Scale 1475, Ian Ring Music Theory
4th mode:
Scale 2785
Scale 2785, Ian Ring Music Theory
5th mode:
Scale 215
Scale 215, Ian Ring Music TheoryThis is the prime mode
6th mode:
Scale 2155
Scale 2155, Ian Ring Music Theory


The prime form of this scale is Scale 215

Scale 215Scale 215, Ian Ring Music Theory


The hexatonic modal family [3125, 1805, 1475, 2785, 215, 2155] (Forte: 6-Z12) is the complement of the hexatonic modal family [335, 965, 1265, 2215, 3155, 3625] (Forte: 6-Z41)


The inverse of a scale is a reflection using the root as its axis. The inverse of 3125 is 1415

Scale 1415Scale 1415, Ian Ring Music Theory


Only scales that are chiral will have an enantiomorph. Scale 3125 is chiral, and its enantiomorph is scale 1415

Scale 1415Scale 1415, Ian Ring Music Theory


T0 3125  T0I 1415
T1 2155  T1I 2830
T2 215  T2I 1565
T3 430  T3I 3130
T4 860  T4I 2165
T5 1720  T5I 235
T6 3440  T6I 470
T7 2785  T7I 940
T8 1475  T8I 1880
T9 2950  T9I 3760
T10 1805  T10I 3425
T11 3610  T11I 2755

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 3127Scale 3127, Ian Ring Music Theory
Scale 3121Scale 3121, Ian Ring Music Theory
Scale 3123Scale 3123, Ian Ring Music Theory
Scale 3129Scale 3129, Ian Ring Music Theory
Scale 3133Scale 3133, Ian Ring Music Theory
Scale 3109Scale 3109, Ian Ring Music Theory
Scale 3117Scale 3117, Ian Ring Music Theory
Scale 3093Scale 3093, Ian Ring Music Theory
Scale 3157Scale 3157: Zyptimic, Ian Ring Music TheoryZyptimic
Scale 3189Scale 3189: Aeolonian, Ian Ring Music TheoryAeolonian
Scale 3253Scale 3253: Mela Naganandini, Ian Ring Music TheoryMela Naganandini
Scale 3381Scale 3381: Katanian, Ian Ring Music TheoryKatanian
Scale 3637Scale 3637: Raga Rageshri, Ian Ring Music TheoryRaga Rageshri
Scale 2101Scale 2101, Ian Ring Music Theory
Scale 2613Scale 2613: Raga Hamsa Vinodini, Ian Ring Music TheoryRaga Hamsa Vinodini
Scale 1077Scale 1077, 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.