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Scale 977: "Kocrimic"

Scale 977: Kocrimic, 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
Kocrimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,4,6,7,8,9}
Forte Number6-Z39
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 377
Hemitonia3 (trihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections4
Modes5
Prime?no
prime: 317
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 TriadsC{0,4,7}131.5
Minor Triadsam{9,0,4}221
Augmented TriadsC+{0,4,8}221
Diminished Triadsf♯°{6,9,0}131.5
Parsimonious Voice Leading Between Common Triads of Scale 977. Created by Ian Ring ©2019 C C C+ C+ C->C+ am am C+->am f#° f#° f#°->am

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+, am
Peripheral VerticesC, f♯°

Modes

Modes are the rotational transformation of this scale. Scale 977 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 317
Scale 317: Korimic, Ian Ring Music TheoryKorimicThis is the prime mode
3rd mode:
Scale 1103
Scale 1103: Lynimic, Ian Ring Music TheoryLynimic
4th mode:
Scale 2599
Scale 2599: Malimic, Ian Ring Music TheoryMalimic
5th mode:
Scale 3347
Scale 3347: Synimic, Ian Ring Music TheorySynimic
6th mode:
Scale 3721
Scale 3721: Phragimic, Ian Ring Music TheoryPhragimic

Prime

The prime form of this scale is Scale 317

Scale 317Scale 317: Korimic, Ian Ring Music TheoryKorimic

Complement

The hexatonic modal family [977, 317, 1103, 2599, 3347, 3721] (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 977 is 377

Scale 377Scale 377: Kathimic, Ian Ring Music TheoryKathimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 977 is chiral, and its enantiomorph is scale 377

Scale 377Scale 377: Kathimic, Ian Ring Music TheoryKathimic

Transformations:

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

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 979Scale 979: Mela Dhavalambari, Ian Ring Music TheoryMela Dhavalambari
Scale 981Scale 981: Mela Kantamani, Ian Ring Music TheoryMela Kantamani
Scale 985Scale 985: Mela Sucaritra, Ian Ring Music TheoryMela Sucaritra
Scale 961Scale 961, Ian Ring Music Theory
Scale 969Scale 969: Ionogimic, Ian Ring Music TheoryIonogimic
Scale 993Scale 993, Ian Ring Music Theory
Scale 1009Scale 1009: Katyptian, Ian Ring Music TheoryKatyptian
Scale 913Scale 913: Aeolyritonic, Ian Ring Music TheoryAeolyritonic
Scale 945Scale 945: Raga Saravati, Ian Ring Music TheoryRaga Saravati
Scale 849Scale 849: Aerynitonic, Ian Ring Music TheoryAerynitonic
Scale 721Scale 721: Raga Dhavalashri, Ian Ring Music TheoryRaga Dhavalashri
Scale 465Scale 465: Zoditonic, Ian Ring Music TheoryZoditonic
Scale 1489Scale 1489: Raga Jyoti, Ian Ring Music TheoryRaga Jyoti
Scale 2001Scale 2001: Gydian, Ian Ring Music TheoryGydian
Scale 3025Scale 3025: Epycrian, Ian Ring Music TheoryEpycrian

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.