The Exciting Universe Of Music Theory

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Scale 3617

Scale 3617, 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{0,5,9,10,11}
Forte Number5-5
Rotational Symmetrynone
Reflection Axesnone
enantiomorph: 143
Hemitonia3 (trihemitonic)
Cohemitonia2 (dicohemitonic)
prime: 143
Deep Scaleno
Interval Vector321121
Interval Spectrump2mns2d3t
Distribution Spectra<1> = {1,4,5}
<2> = {2,5,6,9}
<3> = {3,6,7,10}
<4> = {7,8,11}
Spectra Variation4.4
Maximally Evenno
Maximal Area Setno
Interior Area1.433
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}000

Since there is only one common triad in this scale, there are no opportunities for parsimonious voice leading between triads.


Modes are the rotational transformation of this scale. Scale 3617 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 241
Scale 241, Ian Ring Music Theory
3rd mode:
Scale 271
Scale 271, Ian Ring Music Theory
4th mode:
Scale 2183
Scale 2183, Ian Ring Music Theory
5th mode:
Scale 3139
Scale 3139, Ian Ring Music Theory


The prime form of this scale is Scale 143

Scale 143Scale 143, Ian Ring Music Theory


The pentatonic modal family [3617, 241, 271, 2183, 3139] (Forte: 5-5) is the complement of the heptatonic modal family [239, 1927, 2167, 3011, 3131, 3553, 3613] (Forte: 7-5)


The inverse of a scale is a reflection using the root as its axis. The inverse of 3617 is 143

Scale 143Scale 143, Ian Ring Music Theory


Only scales that are chiral will have an enantiomorph. Scale 3617 is chiral, and its enantiomorph is scale 143

Scale 143Scale 143, Ian Ring Music Theory


T0 3617  T0I 143
T1 3139  T1I 286
T2 2183  T2I 572
T3 271  T3I 1144
T4 542  T4I 2288
T5 1084  T5I 481
T6 2168  T6I 962
T7 241  T7I 1924
T8 482  T8I 3848
T9 964  T9I 3601
T10 1928  T10I 3107
T11 3856  T11I 2119

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 3619Scale 3619: Thanimic, Ian Ring Music TheoryThanimic
Scale 3621Scale 3621: Gylimic, Ian Ring Music TheoryGylimic
Scale 3625Scale 3625: Podimic, Ian Ring Music TheoryPodimic
Scale 3633Scale 3633: Daptimic, Ian Ring Music TheoryDaptimic
Scale 3585Scale 3585, Ian Ring Music Theory
Scale 3601Scale 3601, Ian Ring Music Theory
Scale 3649Scale 3649, Ian Ring Music Theory
Scale 3681Scale 3681, Ian Ring Music Theory
Scale 3745Scale 3745, Ian Ring Music Theory
Scale 3873Scale 3873, Ian Ring Music Theory
Scale 3105Scale 3105, Ian Ring Music Theory
Scale 3361Scale 3361, Ian Ring Music Theory
Scale 2593Scale 2593, Ian Ring Music Theory
Scale 1569Scale 1569, 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.