The Exciting Universe Of Music Theory

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Scale 3337

Scale 3337, 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{0,3,8,10,11}
Forte Number5-11
Rotational Symmetrynone
Reflection Axesnone
enantiomorph: 535
Hemitonia2 (dihemitonic)
Cohemitonia1 (uncohemitonic)
prime: 157
Deep Scaleno
Interval Vector222220
Interval Spectrump2m2n2s2d2
Distribution Spectra<1> = {1,2,3,5}
<2> = {2,3,4,7,8}
<3> = {4,5,8,9,10}
<4> = {7,9,10,11}
Spectra Variation4
Maximally Evenno
Myhill Propertyno
Ridge Tonesnone


Modes are the rotational transformation of this scale. Scale 3337 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 929
Scale 929, Ian Ring Music Theory
3rd mode:
Scale 157
Scale 157, Ian Ring Music TheoryThis is the prime mode
4th mode:
Scale 1063
Scale 1063, Ian Ring Music Theory
5th mode:
Scale 2579
Scale 2579, Ian Ring Music Theory


The prime form of this scale is Scale 157

Scale 157Scale 157, Ian Ring Music Theory


The pentatonic modal family [3337, 929, 157, 1063, 2579] (Forte: 5-11) is the complement of the heptatonic modal family [379, 1583, 1969, 2237, 2839, 3467, 3781] (Forte: 7-11)


The inverse of a scale is a reflection using the root as its axis. The inverse of 3337 is 535

Scale 535Scale 535, Ian Ring Music Theory


Only scales that are chiral will have an enantiomorph. Scale 3337 is chiral, and its enantiomorph is scale 535

Scale 535Scale 535, Ian Ring Music Theory


T0 3337  T0I 535
T1 2579  T1I 1070
T2 1063  T2I 2140
T3 2126  T3I 185
T4 157  T4I 370
T5 314  T5I 740
T6 628  T6I 1480
T7 1256  T7I 2960
T8 2512  T8I 1825
T9 929  T9I 3650
T10 1858  T10I 3205
T11 3716  T11I 2315

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 3339Scale 3339, Ian Ring Music Theory
Scale 3341Scale 3341, Ian Ring Music Theory
Scale 3329Scale 3329, Ian Ring Music Theory
Scale 3333Scale 3333, Ian Ring Music Theory
Scale 3345Scale 3345: Zylitonic, Ian Ring Music TheoryZylitonic
Scale 3353Scale 3353: Phraptimic, Ian Ring Music TheoryPhraptimic
Scale 3369Scale 3369: Mixolimic, Ian Ring Music TheoryMixolimic
Scale 3401Scale 3401: Palimic, Ian Ring Music TheoryPalimic
Scale 3465Scale 3465: Katathimic, Ian Ring Music TheoryKatathimic
Scale 3081Scale 3081, Ian Ring Music Theory
Scale 3209Scale 3209: Aeraphitonic, Ian Ring Music TheoryAeraphitonic
Scale 3593Scale 3593, Ian Ring Music Theory
Scale 3849Scale 3849, Ian Ring Music Theory
Scale 2313Scale 2313, Ian Ring Music Theory
Scale 2825Scale 2825, Ian Ring Music Theory
Scale 1289Scale 1289, 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.