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Scale 423: "Sogimic"

Scale 423: Sogimic, 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
Sogimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,1,2,5,7,8}
Forte Number6-18
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3249
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections2
Modes5
Prime?yes
Deep Scaleno
Interval Vector322242
Interval Spectrump4m2n2s2d3t2
Distribution Spectra<1> = {1,2,3,4}
<2> = {2,3,4,5}
<3> = {5,6,7}
<4> = {7,8,9,10}
<5> = {8,9,10,11}
Spectra Variation2.333
Maximally Evenno
Maximal Area Setno
Interior Area2.116
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 TriadsC♯{1,5,8}210.67
Minor Triadsfm{5,8,0}121
Diminished Triads{2,5,8}121
Parsimonious Voice Leading Between Common Triads of Scale 423. Created by Ian Ring ©2019 C# C# C#->d° fm fm C#->fm

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.

Diameter2
Radius1
Self-Centeredno
Central VerticesC♯
Peripheral Verticesd°, fm

Modes

Modes are the rotational transformation of this scale. Scale 423 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 2259
Scale 2259: Raga Mandari, Ian Ring Music TheoryRaga Mandari
3rd mode:
Scale 3177
Scale 3177: Rothimic, Ian Ring Music TheoryRothimic
4th mode:
Scale 909
Scale 909: Katarimic, Ian Ring Music TheoryKatarimic
5th mode:
Scale 1251
Scale 1251: Sylimic, Ian Ring Music TheorySylimic
6th mode:
Scale 2673
Scale 2673: Mythimic, Ian Ring Music TheoryMythimic

Prime

This is the prime form of this scale.

Complement

The hexatonic modal family [423, 2259, 3177, 909, 1251, 2673] (Forte: 6-18) is the complement of the hexatonic modal family [423, 909, 1251, 2259, 2673, 3177] (Forte: 6-18)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 423 is 3249

Scale 3249Scale 3249: Raga Tilang, Ian Ring Music TheoryRaga Tilang

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 423 is chiral, and its enantiomorph is scale 3249

Scale 3249Scale 3249: Raga Tilang, Ian Ring Music TheoryRaga Tilang

Transformations:

T0 423  T0I 3249
T1 846  T1I 2403
T2 1692  T2I 711
T3 3384  T3I 1422
T4 2673  T4I 2844
T5 1251  T5I 1593
T6 2502  T6I 3186
T7 909  T7I 2277
T8 1818  T8I 459
T9 3636  T9I 918
T10 3177  T10I 1836
T11 2259  T11I 3672

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 421Scale 421: Han-kumoi, Ian Ring Music TheoryHan-kumoi
Scale 419Scale 419: Hon-kumoi-joshi, Ian Ring Music TheoryHon-kumoi-joshi
Scale 427Scale 427: Raga Suddha Simantini, Ian Ring Music TheoryRaga Suddha Simantini
Scale 431Scale 431: Epyrian, Ian Ring Music TheoryEpyrian
Scale 439Scale 439: Bythian, Ian Ring Music TheoryBythian
Scale 391Scale 391, Ian Ring Music Theory
Scale 407Scale 407: Zylimic, Ian Ring Music TheoryZylimic
Scale 455Scale 455: Messiaen Mode 5, Ian Ring Music TheoryMessiaen Mode 5
Scale 487Scale 487: Dynian, Ian Ring Music TheoryDynian
Scale 295Scale 295: Gyritonic, Ian Ring Music TheoryGyritonic
Scale 359Scale 359: Bothimic, Ian Ring Music TheoryBothimic
Scale 167Scale 167, Ian Ring Music Theory
Scale 679Scale 679: Lanimic, Ian Ring Music TheoryLanimic
Scale 935Scale 935: Chromatic Dorian, Ian Ring Music TheoryChromatic Dorian
Scale 1447Scale 1447: Mela Ratnangi, Ian Ring Music TheoryMela Ratnangi
Scale 2471Scale 2471: Mela Ganamurti, Ian Ring Music TheoryMela Ganamurti

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.