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Scale 2361: "Docrimic"

Scale 2361: Docrimic, 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

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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

Zeitler
Docrimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,3,4,5,8,11}
Forte Number6-Z44
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 915
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes5
Prime?no
prime: 615
Deep Scaleno
Interval Vector313431
Interval Spectrump3m4n3sd3t
Distribution Spectra<1> = {1,3}
<2> = {2,4,6}
<3> = {5,7}
<4> = {6,8,10}
<5> = {9,11}
Spectra Variation2.333
Maximally Evenno
Maximal Area Setno
Interior Area2.25
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicno

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 TriadsE{4,8,11}321.17
G♯{8,0,3}231.5
Minor Triadsfm{5,8,0}231.5
g♯m{8,11,3}231.5
Augmented TriadsC+{0,4,8}321.17
Diminished Triads{5,8,11}231.5
Parsimonious Voice Leading Between Common Triads of Scale 2361. Created by Ian Ring ©2019 C+ C+ E E C+->E fm fm C+->fm G# G# C+->G# E->f° g#m g#m E->g#m f°->fm g#m->G#

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.

Diameter3
Radius2
Self-Centeredno
Central VerticesC+, E
Peripheral Verticesf°, fm, g♯m, G♯

Modes

Modes are the rotational transformation of this scale. Scale 2361 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 807
Scale 807: Raga Suddha Mukhari, Ian Ring Music TheoryRaga Suddha Mukhari
3rd mode:
Scale 2451
Scale 2451: Raga Bauli, Ian Ring Music TheoryRaga Bauli
4th mode:
Scale 3273
Scale 3273: Raga Jivantini, Ian Ring Music TheoryRaga Jivantini
5th mode:
Scale 921
Scale 921: Bogimic, Ian Ring Music TheoryBogimic
6th mode:
Scale 627
Scale 627: Mogimic, Ian Ring Music TheoryMogimic

Prime

The prime form of this scale is Scale 615

Scale 615Scale 615: Phrothimic, Ian Ring Music TheoryPhrothimic

Complement

The hexatonic modal family [2361, 807, 2451, 3273, 921, 627] (Forte: 6-Z44) is the complement of the hexatonic modal family [411, 867, 1587, 2253, 2481, 2841] (Forte: 6-Z19)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2361 is 915

Scale 915Scale 915: Raga Kalagada, Ian Ring Music TheoryRaga Kalagada

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2361 is chiral, and its enantiomorph is scale 915

Scale 915Scale 915: Raga Kalagada, Ian Ring Music TheoryRaga Kalagada

Transformations:

T0 2361  T0I 915
T1 627  T1I 1830
T2 1254  T2I 3660
T3 2508  T3I 3225
T4 921  T4I 2355
T5 1842  T5I 615
T6 3684  T6I 1230
T7 3273  T7I 2460
T8 2451  T8I 825
T9 807  T9I 1650
T10 1614  T10I 3300
T11 3228  T11I 2505

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 2363Scale 2363: Kataptian, Ian Ring Music TheoryKataptian
Scale 2365Scale 2365: Sythian, Ian Ring Music TheorySythian
Scale 2353Scale 2353: Raga Girija, Ian Ring Music TheoryRaga Girija
Scale 2357Scale 2357: Raga Sarasanana, Ian Ring Music TheoryRaga Sarasanana
Scale 2345Scale 2345: Raga Chandrakauns, Ian Ring Music TheoryRaga Chandrakauns
Scale 2329Scale 2329: Styditonic, Ian Ring Music TheoryStyditonic
Scale 2393Scale 2393: Zathimic, Ian Ring Music TheoryZathimic
Scale 2425Scale 2425: Rorian, Ian Ring Music TheoryRorian
Scale 2489Scale 2489: Mela Gangeyabhusani, Ian Ring Music TheoryMela Gangeyabhusani
Scale 2105Scale 2105, Ian Ring Music Theory
Scale 2233Scale 2233: Donimic, Ian Ring Music TheoryDonimic
Scale 2617Scale 2617: Pylimic, Ian Ring Music TheoryPylimic
Scale 2873Scale 2873: Ionian Augmented Sharp 2, Ian Ring Music TheoryIonian Augmented Sharp 2
Scale 3385Scale 3385: Chromatic Phrygian, Ian Ring Music TheoryChromatic Phrygian
Scale 313Scale 313: Goritonic, Ian Ring Music TheoryGoritonic
Scale 1337Scale 1337: Epogimic, Ian Ring Music TheoryEpogimic

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 (http://allthescales.org) 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.