The Exciting Universe Of Music Theory

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Scale 3333

Scale 3333, 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{0,2,8,10,11}
Forte Number5-8
Rotational Symmetrynone
Reflection Axes5
Hemitonia2 (dihemitonic)
Cohemitonia1 (uncohemitonic)
prime: 93
Deep Scaleno
Interval Vector232201
Interval Spectrumm2n2s3d2t
Distribution Spectra<1> = {1,2,6}
<2> = {2,3,8}
<3> = {4,9,10}
<4> = {6,10,11}
Spectra Variation4.4
Maximally Evenno
Maximal Area Setno
Interior Area1.366
Myhill Propertyno
Ridge Tones[10]

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
Diminished Triadsg♯°{8,11,2}000

Since there is only one common triad in this scale, there are no opportunities for parsimonious voice leading between triads.


Modes are the rotational transformation of this scale. Scale 3333 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 1857
Scale 1857, Ian Ring Music Theory
3rd mode:
Scale 93
Scale 93, Ian Ring Music TheoryThis is the prime mode
4th mode:
Scale 1047
Scale 1047, Ian Ring Music Theory
5th mode:
Scale 2571
Scale 2571, Ian Ring Music Theory


The prime form of this scale is Scale 93

Scale 93Scale 93, Ian Ring Music Theory


The pentatonic modal family [3333, 1857, 93, 1047, 2571] (Forte: 5-8) is the complement of the heptatonic modal family [381, 1119, 2001, 2607, 3351, 3723, 3909] (Forte: 7-8)


The inverse of a scale is a reflection using the root as its axis. The inverse of 3333 is 1047

Scale 1047Scale 1047, Ian Ring Music Theory


T0 3333  T0I 1047
T1 2571  T1I 2094
T2 1047  T2I 93
T3 2094  T3I 186
T4 93  T4I 372
T5 186  T5I 744
T6 372  T6I 1488
T7 744  T7I 2976
T8 1488  T8I 1857
T9 2976  T9I 3714
T10 1857  T10I 3333
T11 3714  T11I 2571

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 3335Scale 3335, Ian Ring Music Theory
Scale 3329Scale 3329, Ian Ring Music Theory
Scale 3331Scale 3331, Ian Ring Music Theory
Scale 3337Scale 3337, Ian Ring Music Theory
Scale 3341Scale 3341, Ian Ring Music Theory
Scale 3349Scale 3349: Aeolocrimic, Ian Ring Music TheoryAeolocrimic
Scale 3365Scale 3365: Katolimic, Ian Ring Music TheoryKatolimic
Scale 3397Scale 3397: Sydimic, Ian Ring Music TheorySydimic
Scale 3461Scale 3461, Ian Ring Music Theory
Scale 3077Scale 3077, Ian Ring Music Theory
Scale 3205Scale 3205, Ian Ring Music Theory
Scale 3589Scale 3589, Ian Ring Music Theory
Scale 3845Scale 3845, Ian Ring Music Theory
Scale 2309Scale 2309, Ian Ring Music Theory
Scale 2821Scale 2821, Ian Ring Music Theory
Scale 1285Scale 1285, 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.