The Exciting Universe Of Music Theory

more than you ever wanted to know about...

Scale 39

Scale 39, 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).


Cardinality4 (tetratonic)
Pitch Class Set{0,1,2,5}
Forte Number4-4
Rotational Symmetrynone
Reflection Axesnone
enantiomorph: 3201
Hemitonia2 (dihemitonic)
Cohemitonia1 (uncohemitonic)
Deep Scaleno
Interval Vector211110
Interval Spectrumpmnsd2
Distribution Spectra<1> = {1,3,7}
<2> = {2,4,8,10}
<3> = {5,9,11}
Spectra Variation5
Maximally Evenno
Maximal Area Setno
Interior Area0.75
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 39 can be rotated to make 3 other scales. The 1st mode is itself.

2nd mode:
Scale 2067
Scale 2067, Ian Ring Music Theory
3rd mode:
Scale 3081
Scale 3081, Ian Ring Music Theory
4th mode:
Scale 897
Scale 897, Ian Ring Music Theory


This is the prime form of this scale.


The tetratonic modal family [39, 2067, 3081, 897] (Forte: 4-4) is the complement of the octatonic modal family [447, 2019, 2271, 3057, 3183, 3639, 3867, 3981] (Forte: 8-4)


The inverse of a scale is a reflection using the root as its axis. The inverse of 39 is 3201

Scale 3201Scale 3201, Ian Ring Music Theory


Only scales that are chiral will have an enantiomorph. Scale 39 is chiral, and its enantiomorph is scale 3201

Scale 3201Scale 3201, Ian Ring Music Theory


T0 39  T0I 3201
T1 78  T1I 2307
T2 156  T2I 519
T3 312  T3I 1038
T4 624  T4I 2076
T5 1248  T5I 57
T6 2496  T6I 114
T7 897  T7I 228
T8 1794  T8I 456
T9 3588  T9I 912
T10 3081  T10I 1824
T11 2067  T11I 3648

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 37Scale 37, Ian Ring Music Theory
Scale 35Scale 35, Ian Ring Music Theory
Scale 43Scale 43, Ian Ring Music Theory
Scale 47Scale 47, Ian Ring Music Theory
Scale 55Scale 55, Ian Ring Music Theory
Scale 7Scale 7, Ian Ring Music Theory
Scale 23Scale 23, Ian Ring Music Theory
Scale 71Scale 71, Ian Ring Music Theory
Scale 103Scale 103, Ian Ring Music Theory
Scale 167Scale 167, Ian Ring Music Theory
Scale 295Scale 295: Gyritonic, Ian Ring Music TheoryGyritonic
Scale 551Scale 551: Aeoloditonic, Ian Ring Music TheoryAeoloditonic
Scale 1063Scale 1063, Ian Ring Music Theory
Scale 2087Scale 2087, 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.