The Exciting Universe Of Music Theory

more than you ever wanted to know about...

Scale 3233

Scale 3233, 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{0,5,7,10,11}
Forte Number5-14
Rotational Symmetrynone
Reflection Axesnone
enantiomorph: 167
Hemitonia2 (dihemitonic)
Cohemitonia1 (uncohemitonic)
prime: 167
Deep Scaleno
Interval Vector221131
Interval Spectrump3mns2d2t
Distribution Spectra<1> = {1,2,3,5}
<2> = {2,4,5,6,7}
<3> = {5,6,7,8,10}
<4> = {7,9,10,11}
Spectra Variation3.6
Maximally Evenno
Maximal Area Setno
Interior Area1.683
Myhill Propertyno
Ridge Tonesnone

Common Triads

There are no common triads (major, minor, augmented and diminished) that can be formed using notes in this scale.


Modes are the rotational transformation of this scale. Scale 3233 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 229
Scale 229, Ian Ring Music Theory
3rd mode:
Scale 1081
Scale 1081, Ian Ring Music Theory
4th mode:
Scale 647
Scale 647, Ian Ring Music Theory
5th mode:
Scale 2371
Scale 2371, Ian Ring Music Theory


The prime form of this scale is Scale 167

Scale 167Scale 167, Ian Ring Music Theory


The pentatonic modal family [3233, 229, 1081, 647, 2371] (Forte: 5-14) is the complement of the heptatonic modal family [431, 1507, 1933, 2263, 2801, 3179, 3637] (Forte: 7-14)


The inverse of a scale is a reflection using the root as its axis. The inverse of 3233 is 167

Scale 167Scale 167, Ian Ring Music Theory


Only scales that are chiral will have an enantiomorph. Scale 3233 is chiral, and its enantiomorph is scale 167

Scale 167Scale 167, Ian Ring Music Theory


T0 3233  T0I 167
T1 2371  T1I 334
T2 647  T2I 668
T3 1294  T3I 1336
T4 2588  T4I 2672
T5 1081  T5I 1249
T6 2162  T6I 2498
T7 229  T7I 901
T8 458  T8I 1802
T9 916  T9I 3604
T10 1832  T10I 3113
T11 3664  T11I 2131

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 3235Scale 3235: Pothimic, Ian Ring Music TheoryPothimic
Scale 3237Scale 3237: Raga Brindabani Sarang, Ian Ring Music TheoryRaga Brindabani Sarang
Scale 3241Scale 3241: Dalimic, Ian Ring Music TheoryDalimic
Scale 3249Scale 3249: Raga Tilang, Ian Ring Music TheoryRaga Tilang
Scale 3201Scale 3201, Ian Ring Music Theory
Scale 3217Scale 3217: Molitonic, Ian Ring Music TheoryMolitonic
Scale 3265Scale 3265, Ian Ring Music Theory
Scale 3297Scale 3297, Ian Ring Music Theory
Scale 3105Scale 3105, Ian Ring Music Theory
Scale 3169Scale 3169, Ian Ring Music Theory
Scale 3361Scale 3361, Ian Ring Music Theory
Scale 3489Scale 3489, Ian Ring Music Theory
Scale 3745Scale 3745, Ian Ring Music Theory
Scale 2209Scale 2209, Ian Ring Music Theory
Scale 2721Scale 2721: Raga Puruhutika, Ian Ring Music TheoryRaga Puruhutika
Scale 1185Scale 1185: Genus Primum Inverse, Ian Ring Music TheoryGenus Primum Inverse

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. Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography.