The Exciting Universe Of Music Theory

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Scale 3121

Scale 3121, 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).


Cardinality5 (pentatonic)
Pitch Class Set{0,4,5,10,11}
Forte Number5-7
Rotational Symmetrynone
Reflection Axesnone
enantiomorph: 391
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
prime: 199
Deep Scaleno
Interval Vector310132
Interval Spectrump3msd3t2
Distribution Spectra<1> = {1,4,5}
<2> = {2,5,6}
<3> = {6,7,10}
<4> = {7,8,11}
Spectra Variation3.2
Maximally Evenno
Myhill Propertyno
Ridge Tonesnone


Modes are the rotational transformation of this scale. Scale 3121 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 451
Scale 451: Raga Saugandhini, Ian Ring Music TheoryRaga Saugandhini
3rd mode:
Scale 2273
Scale 2273, Ian Ring Music Theory
4th mode:
Scale 199
Scale 199: Raga Nabhomani, Ian Ring Music TheoryRaga NabhomaniThis is the prime mode
5th mode:
Scale 2147
Scale 2147, Ian Ring Music Theory


The prime form of this scale is Scale 199

Scale 199Scale 199: Raga Nabhomani, Ian Ring Music TheoryRaga Nabhomani


The pentatonic modal family [3121, 451, 2273, 199, 2147] (Forte: 5-7) is the complement of the heptatonic modal family [463, 967, 2279, 2531, 3187, 3313, 3641] (Forte: 7-7)


The inverse of a scale is a reflection using the root as its axis. The inverse of 3121 is 391

Scale 391Scale 391, Ian Ring Music Theory


Only scales that are chiral will have an enantiomorph. Scale 3121 is chiral, and its enantiomorph is scale 391

Scale 391Scale 391, Ian Ring Music Theory


T0 3121  T0I 391
T1 2147  T1I 782
T2 199  T2I 1564
T3 398  T3I 3128
T4 796  T4I 2161
T5 1592  T5I 227
T6 3184  T6I 454
T7 2273  T7I 908
T8 451  T8I 1816
T9 902  T9I 3632
T10 1804  T10I 3169
T11 3608  T11I 2243

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 3123Scale 3123, Ian Ring Music Theory
Scale 3125Scale 3125, Ian Ring Music Theory
Scale 3129Scale 3129, Ian Ring Music Theory
Scale 3105Scale 3105, Ian Ring Music Theory
Scale 3113Scale 3113, Ian Ring Music Theory
Scale 3089Scale 3089, Ian Ring Music Theory
Scale 3153Scale 3153: Zathitonic, Ian Ring Music TheoryZathitonic
Scale 3185Scale 3185: Messiaen Mode 5 Inverse, Ian Ring Music TheoryMessiaen Mode 5 Inverse
Scale 3249Scale 3249: Raga Tilang, Ian Ring Music TheoryRaga Tilang
Scale 3377Scale 3377: Phralimic, Ian Ring Music TheoryPhralimic
Scale 3633Scale 3633: Daptimic, Ian Ring Music TheoryDaptimic
Scale 2097Scale 2097, Ian Ring Music Theory
Scale 2609Scale 2609: Raga Bhinna Shadja, Ian Ring Music TheoryRaga Bhinna Shadja
Scale 1073Scale 1073, 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, and MIDI playback by MIDI.js. Some scale names used on this and other pages are ©2005 William Zeitler ( Peruse this Bibliography.