The Exciting Universe Of Music Theory

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Scale 3361

Scale 3361, 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{0,5,8,10,11}
Forte Number5-Z36
Rotational Symmetrynone
Reflection Axesnone
enantiomorph: 151
Hemitonia2 (dihemitonic)
Cohemitonia1 (uncohemitonic)
prime: 151
Deep Scaleno
Interval Vector222121
Interval Spectrump2mn2s2d2t
Distribution Spectra<1> = {1,2,3,5}
<2> = {2,3,5,6,8}
<3> = {4,6,7,9,10}
<4> = {7,9,10,11}
Spectra Variation4
Maximally Evenno
Maximal Area Setno
Interior Area1.683
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
Minor Triadsfm{5,8,0}110.5
Diminished Triads{5,8,11}110.5
Parsimonious Voice Leading Between Common Triads of Scale 3361. Created by Ian Ring ©2019 fm fm f°->fm

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 3361 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 233
Scale 233, Ian Ring Music Theory
3rd mode:
Scale 541
Scale 541, Ian Ring Music Theory
4th mode:
Scale 1159
Scale 1159, Ian Ring Music Theory
5th mode:
Scale 2627
Scale 2627, Ian Ring Music Theory


The prime form of this scale is Scale 151

Scale 151Scale 151, Ian Ring Music Theory


The pentatonic modal family [3361, 233, 541, 1159, 2627] (Forte: 5-Z36) is the complement of the heptatonic modal family [367, 1777, 1931, 2231, 3013, 3163, 3629] (Forte: 7-Z36)


The inverse of a scale is a reflection using the root as its axis. The inverse of 3361 is 151

Scale 151Scale 151, Ian Ring Music Theory


Only scales that are chiral will have an enantiomorph. Scale 3361 is chiral, and its enantiomorph is scale 151

Scale 151Scale 151, Ian Ring Music Theory


T0 3361  T0I 151
T1 2627  T1I 302
T2 1159  T2I 604
T3 2318  T3I 1208
T4 541  T4I 2416
T5 1082  T5I 737
T6 2164  T6I 1474
T7 233  T7I 2948
T8 466  T8I 1801
T9 932  T9I 3602
T10 1864  T10I 3109
T11 3728  T11I 2123

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 3363Scale 3363: Rogimic, Ian Ring Music TheoryRogimic
Scale 3365Scale 3365: Katolimic, Ian Ring Music TheoryKatolimic
Scale 3369Scale 3369: Mixolimic, Ian Ring Music TheoryMixolimic
Scale 3377Scale 3377: Phralimic, Ian Ring Music TheoryPhralimic
Scale 3329Scale 3329, Ian Ring Music Theory
Scale 3345Scale 3345: Zylitonic, Ian Ring Music TheoryZylitonic
Scale 3393Scale 3393, Ian Ring Music Theory
Scale 3425Scale 3425, Ian Ring Music Theory
Scale 3489Scale 3489, Ian Ring Music Theory
Scale 3105Scale 3105, Ian Ring Music Theory
Scale 3233Scale 3233, Ian Ring Music Theory
Scale 3617Scale 3617, Ian Ring Music Theory
Scale 3873Scale 3873, Ian Ring Music Theory
Scale 2337Scale 2337, Ian Ring Music Theory
Scale 2849Scale 2849, Ian Ring Music Theory
Scale 1313Scale 1313, 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.