The Exciting Universe Of Music Theory

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Scale 3713

Scale 3713, 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{0,7,9,10,11}
Forte Number5-2
Rotational Symmetrynone
Reflection Axesnone
enantiomorph: 47
Hemitonia3 (trihemitonic)
Cohemitonia2 (dicohemitonic)
prime: 47
Deep Scaleno
Interval Vector332110
Interval Spectrumpmn2s3d3
Distribution Spectra<1> = {1,2,7}
<2> = {2,3,8,9}
<3> = {3,4,9,10}
<4> = {5,10,11}
Spectra Variation5.2
Maximally Evenno
Myhill Propertyno
Ridge Tonesnone


Modes are the rotational transformation of this scale. Scale 3713 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 61
Scale 61, Ian Ring Music Theory
3rd mode:
Scale 1039
Scale 1039, Ian Ring Music Theory
4th mode:
Scale 2567
Scale 2567, Ian Ring Music Theory
5th mode:
Scale 3331
Scale 3331, Ian Ring Music Theory


The prime form of this scale is Scale 47

Scale 47Scale 47, Ian Ring Music Theory


The pentatonic modal family [3713, 61, 1039, 2567, 3331] (Forte: 5-2) is the complement of the heptatonic modal family [191, 2017, 2143, 3119, 3607, 3851, 3973] (Forte: 7-2)


The inverse of a scale is a reflection using the root as its axis. The inverse of 3713 is 47

Scale 47Scale 47, Ian Ring Music Theory


Only scales that are chiral will have an enantiomorph. Scale 3713 is chiral, and its enantiomorph is scale 47

Scale 47Scale 47, Ian Ring Music Theory


T0 3713  T0I 47
T1 3331  T1I 94
T2 2567  T2I 188
T3 1039  T3I 376
T4 2078  T4I 752
T5 61  T5I 1504
T6 122  T6I 3008
T7 244  T7I 1921
T8 488  T8I 3842
T9 976  T9I 3589
T10 1952  T10I 3083
T11 3904  T11I 2071

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 3715Scale 3715, Ian Ring Music Theory
Scale 3717Scale 3717, Ian Ring Music Theory
Scale 3721Scale 3721: Phragimic, Ian Ring Music TheoryPhragimic
Scale 3729Scale 3729: Starimic, Ian Ring Music TheoryStarimic
Scale 3745Scale 3745, Ian Ring Music Theory
Scale 3777Scale 3777, Ian Ring Music Theory
Scale 3585Scale 3585, Ian Ring Music Theory
Scale 3649Scale 3649, Ian Ring Music Theory
Scale 3841Scale 3841, Ian Ring Music Theory
Scale 3969Scale 3969, Ian Ring Music Theory
Scale 3201Scale 3201, Ian Ring Music Theory
Scale 3457Scale 3457, Ian Ring Music Theory
Scale 2689Scale 2689, Ian Ring Music Theory
Scale 1665Scale 1665, 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, and MIDI playback by MIDI.js. Some scale names used on this and other pages are ©2005 William Zeitler ( Peruse this Bibliography.