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Scale 2117: "Raga Sumukam"

Scale 2117: Raga Sumukam, 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).

Common Names

Carnatic Raga
Raga Sumukam


Cardinality4 (tetratonic)
Pitch Class Set{0,2,6,11}
Forte Number4-Z29
Rotational Symmetrynone
Reflection Axesnone
enantiomorph: 1091
Hemitonia1 (unhemitonic)
Cohemitonia0 (ancohemitonic)
prime: 139
Deep Scaleno
Interval Vector111111
Interval Spectrumpmnsdt
Distribution Spectra<1> = {1,2,4,5}
<2> = {3,6,9}
<3> = {7,8,10,11}
Spectra Variation3.5
Maximally Evenno
Maximal Area Setno
Interior Area1.366
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
Minor Triadsbm{11,2,6}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 2117 can be rotated to make 3 other scales. The 1st mode is itself.

2nd mode:
Scale 1553
Scale 1553, Ian Ring Music Theory
3rd mode:
Scale 353
Scale 353, Ian Ring Music Theory
4th mode:
Scale 139
Scale 139, Ian Ring Music TheoryThis is the prime mode


The prime form of this scale is Scale 139

Scale 139Scale 139, Ian Ring Music Theory


The tetratonic modal family [2117, 1553, 353, 139] (Forte: 4-Z29) is the complement of the octatonic modal family [751, 1913, 1943, 2423, 3019, 3259, 3557, 3677] (Forte: 8-Z29)


The inverse of a scale is a reflection using the root as its axis. The inverse of 2117 is 1091

Scale 1091Scale 1091, Ian Ring Music Theory


Only scales that are chiral will have an enantiomorph. Scale 2117 is chiral, and its enantiomorph is scale 1091

Scale 1091Scale 1091, Ian Ring Music Theory


T0 2117  T0I 1091
T1 139  T1I 2182
T2 278  T2I 269
T3 556  T3I 538
T4 1112  T4I 1076
T5 2224  T5I 2152
T6 353  T6I 209
T7 706  T7I 418
T8 1412  T8I 836
T9 2824  T9I 1672
T10 1553  T10I 3344
T11 3106  T11I 2593

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 2119Scale 2119, Ian Ring Music Theory
Scale 2113Scale 2113, Ian Ring Music Theory
Scale 2115Scale 2115, Ian Ring Music Theory
Scale 2121Scale 2121, Ian Ring Music Theory
Scale 2125Scale 2125, Ian Ring Music Theory
Scale 2133Scale 2133: Raga Kumurdaki, Ian Ring Music TheoryRaga Kumurdaki
Scale 2149Scale 2149, Ian Ring Music Theory
Scale 2053Scale 2053, Ian Ring Music Theory
Scale 2085Scale 2085, Ian Ring Music Theory
Scale 2181Scale 2181, Ian Ring Music Theory
Scale 2245Scale 2245: Raga Vaijayanti, Ian Ring Music TheoryRaga Vaijayanti
Scale 2373Scale 2373: Dyptitonic, Ian Ring Music TheoryDyptitonic
Scale 2629Scale 2629: Raga Shubravarni, Ian Ring Music TheoryRaga Shubravarni
Scale 3141Scale 3141: Kanitonic, Ian Ring Music TheoryKanitonic
Scale 69Scale 69, Ian Ring Music Theory
Scale 1093Scale 1093: Lydic, Ian Ring Music TheoryLydic

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.