The Exciting Universe Of Music Theory

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Scale 3613

Scale 3613, 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{0,2,3,4,9,10,11}
Forte Number7-5
Rotational Symmetrynone
Reflection Axesnone
enantiomorph: 1807
Hemitonia5 (multihemitonic)
Cohemitonia3 (tricohemitonic)
prime: 239
Deep Scaleno
Interval Vector543342
Interval Spectrump4m3n3s4d5t2
Distribution Spectra<1> = {1,2,5}
<2> = {2,3,6}
<3> = {3,4,7}
<4> = {5,8,9}
<5> = {6,9,10}
<6> = {7,10,11}
Spectra Variation3.429
Maximally Evenno
Maximal Area Setno
Interior Area1.933
Myhill Propertyno
Ridge Tonesnone

Harmonic Chords

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
Minor Triadsam{9,0,4}110.5
Diminished Triads{9,0,3}110.5
Parsimonious Voice Leading Between Common Triads of Scale 3613. Created by Ian Ring ©2019 am am a°->am

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 3613 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 1927
Scale 1927, Ian Ring Music Theory
3rd mode:
Scale 3011
Scale 3011, Ian Ring Music Theory
4th mode:
Scale 3553
Scale 3553, Ian Ring Music Theory
5th mode:
Scale 239
Scale 239, Ian Ring Music TheoryThis is the prime mode
6th mode:
Scale 2167
Scale 2167, Ian Ring Music Theory
7th mode:
Scale 3131
Scale 3131, Ian Ring Music Theory


The prime form of this scale is Scale 239

Scale 239Scale 239, Ian Ring Music Theory


The heptatonic modal family [3613, 1927, 3011, 3553, 239, 2167, 3131] (Forte: 7-5) is the complement of the pentatonic modal family [143, 481, 2119, 3107, 3601] (Forte: 5-5)


The inverse of a scale is a reflection using the root as its axis. The inverse of 3613 is 1807

Scale 1807Scale 1807, Ian Ring Music Theory


Only scales that are chiral will have an enantiomorph. Scale 3613 is chiral, and its enantiomorph is scale 1807

Scale 1807Scale 1807, Ian Ring Music Theory


T0 3613  T0I 1807
T1 3131  T1I 3614
T2 2167  T2I 3133
T3 239  T3I 2171
T4 478  T4I 247
T5 956  T5I 494
T6 1912  T6I 988
T7 3824  T7I 1976
T8 3553  T8I 3952
T9 3011  T9I 3809
T10 1927  T10I 3523
T11 3854  T11I 2951

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 3615Scale 3615, Ian Ring Music Theory
Scale 3609Scale 3609, Ian Ring Music Theory
Scale 3611Scale 3611, Ian Ring Music Theory
Scale 3605Scale 3605, Ian Ring Music Theory
Scale 3597Scale 3597, Ian Ring Music Theory
Scale 3629Scale 3629: Boptian, Ian Ring Music TheoryBoptian
Scale 3645Scale 3645: Zycryllic, Ian Ring Music TheoryZycryllic
Scale 3677Scale 3677, Ian Ring Music Theory
Scale 3741Scale 3741: Zydyllic, Ian Ring Music TheoryZydyllic
Scale 3869Scale 3869: Bygyllic, Ian Ring Music TheoryBygyllic
Scale 3101Scale 3101, Ian Ring Music Theory
Scale 3357Scale 3357: Phrodian, Ian Ring Music TheoryPhrodian
Scale 2589Scale 2589, Ian Ring Music Theory
Scale 1565Scale 1565, 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.