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Scale 317: "Korimic"

Scale 317: Korimic, 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

41161837294116105072918310504116183
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
Korimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,2,3,4,5,8}
Forte Number6-Z39
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1937
Hemitonia3 (trihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections4
Modes5
Prime?yes
Deep Scaleno
Interval Vector333321
Interval Spectrump2m3n3s3d3t
Distribution Spectra<1> = {1,2,3,4}
<2> = {2,3,4,6,7}
<3> = {3,4,5,7,8,9}
<4> = {5,6,8,9,10}
<5> = {8,9,10,11}
Spectra Variation3.667
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 TriadsG♯{8,0,3}131.5
Minor Triadsfm{5,8,0}221
Augmented TriadsC+{0,4,8}221
Diminished Triads{2,5,8}131.5
Parsimonious Voice Leading Between Common Triads of Scale 317. Created by Ian Ring ©2019 C+ C+ fm fm C+->fm G# G# C+->G# d°->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.

Diameter3
Radius2
Self-Centeredno
Central VerticesC+, fm
Peripheral Verticesd°, G♯

Modes

Modes are the rotational transformation of this scale. Scale 317 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 1103
Scale 1103: Lynimic, Ian Ring Music TheoryLynimic
3rd mode:
Scale 2599
Scale 2599: Malimic, Ian Ring Music TheoryMalimic
4th mode:
Scale 3347
Scale 3347: Synimic, Ian Ring Music TheorySynimic
5th mode:
Scale 3721
Scale 3721: Phragimic, Ian Ring Music TheoryPhragimic
6th mode:
Scale 977
Scale 977: Kocrimic, Ian Ring Music TheoryKocrimic

Prime

This is the prime form of this scale.

Complement

The hexatonic modal family [317, 1103, 2599, 3347, 3721, 977] (Forte: 6-Z39) is the complement of the hexatonic modal family [187, 1559, 1889, 2141, 2827, 3461] (Forte: 6-Z10)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 317 is 1937

Scale 1937Scale 1937: Galimic, Ian Ring Music TheoryGalimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 317 is chiral, and its enantiomorph is scale 1937

Scale 1937Scale 1937: Galimic, Ian Ring Music TheoryGalimic

Transformations:

T0 317  T0I 1937
T1 634  T1I 3874
T2 1268  T2I 3653
T3 2536  T3I 3211
T4 977  T4I 2327
T5 1954  T5I 559
T6 3908  T6I 1118
T7 3721  T7I 2236
T8 3347  T8I 377
T9 2599  T9I 754
T10 1103  T10I 1508
T11 2206  T11I 3016

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 319Scale 319: Epodian, Ian Ring Music TheoryEpodian
Scale 313Scale 313: Goritonic, Ian Ring Music TheoryGoritonic
Scale 315Scale 315: Stodimic, Ian Ring Music TheoryStodimic
Scale 309Scale 309: Palitonic, Ian Ring Music TheoryPalitonic
Scale 301Scale 301: Raga Audav Tukhari, Ian Ring Music TheoryRaga Audav Tukhari
Scale 285Scale 285: Zaritonic, Ian Ring Music TheoryZaritonic
Scale 349Scale 349: Borimic, Ian Ring Music TheoryBorimic
Scale 381Scale 381: Kogian, Ian Ring Music TheoryKogian
Scale 445Scale 445: Gocrian, Ian Ring Music TheoryGocrian
Scale 61Scale 61, Ian Ring Music Theory
Scale 189Scale 189, Ian Ring Music Theory
Scale 573Scale 573: Saptimic, Ian Ring Music TheorySaptimic
Scale 829Scale 829: Lygian, Ian Ring Music TheoryLygian
Scale 1341Scale 1341: Madian, Ian Ring Music TheoryMadian
Scale 2365Scale 2365: Sythian, Ian Ring Music TheorySythian

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.