The Exciting Universe Of Music Theory

more than you ever wanted to know about...

Scale 3937

Scale 3937, 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).


Cardinality7 (heptatonic)
Pitch Class Set{0,5,6,8,9,10,11}
Forte Number7-4
Rotational Symmetrynone
Reflection Axesnone
enantiomorph: 223
Hemitonia5 (multihemitonic)
Cohemitonia3 (tricohemitonic)
prime: 223
Deep Scaleno
Interval Vector544332
Interval Spectrump3m3n4s4d5t2
Distribution Spectra<1> = {1,2,5}
<2> = {2,3,6}
<3> = {3,4,7,8}
<4> = {4,5,8,9}
<5> = {6,9,10}
<6> = {7,10,11}
Spectra Variation3.714
Maximally Evenno
Maximal Area Setno
Interior Area1.933
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 TriadsF{5,9,0}221
Minor Triadsfm{5,8,0}221
Diminished Triads{5,8,11}131.5
Parsimonious Voice Leading Between Common Triads of Scale 3937. Created by Ian Ring ©2019 fm fm f°->fm F F fm->F f#° f#° F->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.

Central Verticesfm, F
Peripheral Verticesf°, f♯°


Modes are the rotational transformation of this scale. Scale 3937 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 251
Scale 251, Ian Ring Music Theory
3rd mode:
Scale 2173
Scale 2173, Ian Ring Music Theory
4th mode:
Scale 1567
Scale 1567, Ian Ring Music Theory
5th mode:
Scale 2831
Scale 2831, Ian Ring Music Theory
6th mode:
Scale 3463
Scale 3463, Ian Ring Music Theory
7th mode:
Scale 3779
Scale 3779, Ian Ring Music Theory


The prime form of this scale is Scale 223

Scale 223Scale 223, Ian Ring Music Theory


The heptatonic modal family [3937, 251, 2173, 1567, 2831, 3463, 3779] (Forte: 7-4) is the complement of the pentatonic modal family [79, 961, 2087, 3091, 3593] (Forte: 5-4)


The inverse of a scale is a reflection using the root as its axis. The inverse of 3937 is 223

Scale 223Scale 223, Ian Ring Music Theory


Only scales that are chiral will have an enantiomorph. Scale 3937 is chiral, and its enantiomorph is scale 223

Scale 223Scale 223, Ian Ring Music Theory


T0 3937  T0I 223
T1 3779  T1I 446
T2 3463  T2I 892
T3 2831  T3I 1784
T4 1567  T4I 3568
T5 3134  T5I 3041
T6 2173  T6I 1987
T7 251  T7I 3974
T8 502  T8I 3853
T9 1004  T9I 3611
T10 2008  T10I 3127
T11 4016  T11I 2159

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 3939Scale 3939: Dogyllic, Ian Ring Music TheoryDogyllic
Scale 3941Scale 3941: Stathyllic, Ian Ring Music TheoryStathyllic
Scale 3945Scale 3945: Lydyllic, Ian Ring Music TheoryLydyllic
Scale 3953Scale 3953: Thagyllic, Ian Ring Music TheoryThagyllic
Scale 3905Scale 3905, Ian Ring Music Theory
Scale 3921Scale 3921: Pythian, Ian Ring Music TheoryPythian
Scale 3873Scale 3873, Ian Ring Music Theory
Scale 4001Scale 4001, Ian Ring Music Theory
Scale 4065Scale 4065, Ian Ring Music Theory
Scale 3681Scale 3681, Ian Ring Music Theory
Scale 3809Scale 3809, Ian Ring Music Theory
Scale 3425Scale 3425, Ian Ring Music Theory
Scale 2913Scale 2913, Ian Ring Music Theory
Scale 1889Scale 1889, 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.