The Exciting Universe Of Music Theory

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Scale 3117

Scale 3117, 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).


Cardinality6 (hexatonic)
Pitch Class Set{0,2,3,5,10,11}
Forte Number6-Z11
Rotational Symmetrynone
Reflection Axesnone
enantiomorph: 1671
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
prime: 183
Deep Scaleno
Interval Vector333231
Interval Spectrump3m2n3s3d3t
Distribution Spectra<1> = {1,2,5}
<2> = {2,3,6,7}
<3> = {4,5,7,8}
<4> = {5,6,9,10}
<5> = {7,10,11}
Spectra Variation3.667
Maximally Evenno
Maximal Area Setno
Interior Area1.866
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 TriadsA♯{10,2,5}110.5
Diminished Triads{11,2,5}110.5
Parsimonious Voice Leading Between Common Triads of Scale 3117. Created by Ian Ring ©2019 A# A# A#->b°

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 3117 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 1803
Scale 1803, Ian Ring Music Theory
3rd mode:
Scale 2949
Scale 2949, Ian Ring Music Theory
4th mode:
Scale 1761
Scale 1761, Ian Ring Music Theory
5th mode:
Scale 183
Scale 183, Ian Ring Music TheoryThis is the prime mode
6th mode:
Scale 2139
Scale 2139, Ian Ring Music Theory


The prime form of this scale is Scale 183

Scale 183Scale 183, Ian Ring Music Theory


The hexatonic modal family [3117, 1803, 2949, 1761, 183, 2139] (Forte: 6-Z11) is the complement of the hexatonic modal family [303, 753, 1929, 2199, 3147, 3621] (Forte: 6-Z40)


The inverse of a scale is a reflection using the root as its axis. The inverse of 3117 is 1671

Scale 1671Scale 1671, Ian Ring Music Theory


Only scales that are chiral will have an enantiomorph. Scale 3117 is chiral, and its enantiomorph is scale 1671

Scale 1671Scale 1671, Ian Ring Music Theory


T0 3117  T0I 1671
T1 2139  T1I 3342
T2 183  T2I 2589
T3 366  T3I 1083
T4 732  T4I 2166
T5 1464  T5I 237
T6 2928  T6I 474
T7 1761  T7I 948
T8 3522  T8I 1896
T9 2949  T9I 3792
T10 1803  T10I 3489
T11 3606  T11I 2883

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 3119Scale 3119, Ian Ring Music Theory
Scale 3113Scale 3113, Ian Ring Music Theory
Scale 3115Scale 3115, Ian Ring Music Theory
Scale 3109Scale 3109, Ian Ring Music Theory
Scale 3125Scale 3125, Ian Ring Music Theory
Scale 3133Scale 3133, Ian Ring Music Theory
Scale 3085Scale 3085, Ian Ring Music Theory
Scale 3101Scale 3101, Ian Ring Music Theory
Scale 3149Scale 3149: Phrycrimic, Ian Ring Music TheoryPhrycrimic
Scale 3181Scale 3181: Rolian, Ian Ring Music TheoryRolian
Scale 3245Scale 3245: Mela Varunapriya, Ian Ring Music TheoryMela Varunapriya
Scale 3373Scale 3373: Lodian, Ian Ring Music TheoryLodian
Scale 3629Scale 3629: Boptian, Ian Ring Music TheoryBoptian
Scale 2093Scale 2093, Ian Ring Music Theory
Scale 2605Scale 2605: Rylimic, Ian Ring Music TheoryRylimic
Scale 1069Scale 1069, 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.