The Exciting Universe Of Music Theory

more than you ever wanted to know about...

Scale 837: "Epaditonic"

Scale 837: Epaditonic, 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).

Common Names



Cardinality5 (pentatonic)
Pitch Class Set{0,2,6,8,9}
Forte Number5-28
Rotational Symmetrynone
Reflection Axesnone
enantiomorph: 1113
Hemitonia1 (unhemitonic)
Cohemitonia0 (ancohemitonic)
prime: 333
Deep Scaleno
Interval Vector122212
Interval Spectrumpm2n2s2dt2
Distribution Spectra<1> = {1,2,3,4}
<2> = {3,4,5,6}
<3> = {6,7,8,9}
<4> = {8,9,10,11}
Spectra Variation2.4
Maximally Evenno
Maximal Area Setno
Interior Area2.049
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
Major TriadsD{2,6,9}110.5
Diminished Triadsf♯°{6,9,0}110.5
Parsimonious Voice Leading Between Common Triads of Scale 837. Created by Ian Ring ©2019 D D f#° f#° D->f#°

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

2nd mode:
Scale 1233
Scale 1233: Ionoditonic, Ian Ring Music TheoryIonoditonic
3rd mode:
Scale 333
Scale 333: Bogitonic, Ian Ring Music TheoryBogitonicThis is the prime mode
4th mode:
Scale 1107
Scale 1107: Mogitonic, Ian Ring Music TheoryMogitonic
5th mode:
Scale 2601
Scale 2601: Raga Chandrakauns, Ian Ring Music TheoryRaga Chandrakauns


The prime form of this scale is Scale 333

Scale 333Scale 333: Bogitonic, Ian Ring Music TheoryBogitonic


The pentatonic modal family [837, 1233, 333, 1107, 2601] (Forte: 5-28) is the complement of the heptatonic modal family [747, 1431, 1629, 1881, 2421, 2763, 3429] (Forte: 7-28)


The inverse of a scale is a reflection using the root as its axis. The inverse of 837 is 1113

Scale 1113Scale 1113: Locrian Pentatonic 2, Ian Ring Music TheoryLocrian Pentatonic 2


Only scales that are chiral will have an enantiomorph. Scale 837 is chiral, and its enantiomorph is scale 1113

Scale 1113Scale 1113: Locrian Pentatonic 2, Ian Ring Music TheoryLocrian Pentatonic 2


T0 837  T0I 1113
T1 1674  T1I 2226
T2 3348  T2I 357
T3 2601  T3I 714
T4 1107  T4I 1428
T5 2214  T5I 2856
T6 333  T6I 1617
T7 666  T7I 3234
T8 1332  T8I 2373
T9 2664  T9I 651
T10 1233  T10I 1302
T11 2466  T11I 2604

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 839Scale 839: Ionathimic, Ian Ring Music TheoryIonathimic
Scale 833Scale 833, Ian Ring Music Theory
Scale 835Scale 835, Ian Ring Music Theory
Scale 841Scale 841: Phrothitonic, Ian Ring Music TheoryPhrothitonic
Scale 845Scale 845: Raga Neelangi, Ian Ring Music TheoryRaga Neelangi
Scale 853Scale 853: Epothimic, Ian Ring Music TheoryEpothimic
Scale 869Scale 869: Kothimic, Ian Ring Music TheoryKothimic
Scale 773Scale 773, Ian Ring Music Theory
Scale 805Scale 805: Rothitonic, Ian Ring Music TheoryRothitonic
Scale 901Scale 901, Ian Ring Music Theory
Scale 965Scale 965: Ionothimic, Ian Ring Music TheoryIonothimic
Scale 581Scale 581: Eporic, Ian Ring Music TheoryEporic
Scale 709Scale 709: Raga Shri Kalyan, Ian Ring Music TheoryRaga Shri Kalyan
Scale 325Scale 325: Messiaen Truncated Mode 6, Ian Ring Music TheoryMessiaen Truncated Mode 6
Scale 1349Scale 1349: Tholitonic, Ian Ring Music TheoryTholitonic
Scale 1861Scale 1861: Phrygimic, Ian Ring Music TheoryPhrygimic
Scale 2885Scale 2885: Byrimic, Ian Ring Music TheoryByrimic

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.