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Scale 3161: "Kodimic"

Scale 3161: Kodimic, 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
Kodimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,3,4,6,10,11}
Forte Number6-Z43
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 839
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes5
Prime?no
prime: 359
Deep Scaleno
Interval Vector322332
Interval Spectrump3m3n2s2d3t2
Distribution Spectra<1> = {1,2,3,4}
<2> = {2,3,4,5,6}
<3> = {5,6,7}
<4> = {6,7,8,9,10}
<5> = {8,9,10,11}
Spectra Variation2.667
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 TriadsB{11,3,6}210.67
Minor Triadsd♯m{3,6,10}121
Diminished Triads{0,3,6}121
Parsimonious Voice Leading Between Common Triads of Scale 3161. Created by Ian Ring ©2019 B B c°->B d#m d#m d#m->B

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 VerticesB
Peripheral Verticesc°, d♯m

Modes

Modes are the rotational transformation of this scale. Scale 3161 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 907
Scale 907: Tholimic, Ian Ring Music TheoryTholimic
3rd mode:
Scale 2501
Scale 2501: Ralimic, Ian Ring Music TheoryRalimic
4th mode:
Scale 1649
Scale 1649: Bolimic, Ian Ring Music TheoryBolimic
5th mode:
Scale 359
Scale 359: Bothimic, Ian Ring Music TheoryBothimicThis is the prime mode
6th mode:
Scale 2227
Scale 2227: Raga Gaula, Ian Ring Music TheoryRaga Gaula

Prime

The prime form of this scale is Scale 359

Scale 359Scale 359: Bothimic, Ian Ring Music TheoryBothimic

Complement

The hexatonic modal family [3161, 907, 2501, 1649, 359, 2227] (Forte: 6-Z43) is the complement of the hexatonic modal family [407, 739, 1817, 2251, 2417, 3173] (Forte: 6-Z17)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3161 is 839

Scale 839Scale 839: Ionathimic, Ian Ring Music TheoryIonathimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3161 is chiral, and its enantiomorph is scale 839

Scale 839Scale 839: Ionathimic, Ian Ring Music TheoryIonathimic

Transformations:

T0 3161  T0I 839
T1 2227  T1I 1678
T2 359  T2I 3356
T3 718  T3I 2617
T4 1436  T4I 1139
T5 2872  T5I 2278
T6 1649  T6I 461
T7 3298  T7I 922
T8 2501  T8I 1844
T9 907  T9I 3688
T10 1814  T10I 3281
T11 3628  T11I 2467

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 3163Scale 3163: Rogian, Ian Ring Music TheoryRogian
Scale 3165Scale 3165: Mylian, Ian Ring Music TheoryMylian
Scale 3153Scale 3153: Zathitonic, Ian Ring Music TheoryZathitonic
Scale 3157Scale 3157: Zyptimic, Ian Ring Music TheoryZyptimic
Scale 3145Scale 3145: Stolitonic, Ian Ring Music TheoryStolitonic
Scale 3177Scale 3177: Rothimic, Ian Ring Music TheoryRothimic
Scale 3193Scale 3193: Zathian, Ian Ring Music TheoryZathian
Scale 3097Scale 3097, Ian Ring Music Theory
Scale 3129Scale 3129, Ian Ring Music Theory
Scale 3225Scale 3225: Ionalimic, Ian Ring Music TheoryIonalimic
Scale 3289Scale 3289: Lydian Sharp 2 Sharp 6, Ian Ring Music TheoryLydian Sharp 2 Sharp 6
Scale 3417Scale 3417: Golian, Ian Ring Music TheoryGolian
Scale 3673Scale 3673: Ranian, Ian Ring Music TheoryRanian
Scale 2137Scale 2137, Ian Ring Music Theory
Scale 2649Scale 2649: Aeolythimic, Ian Ring Music TheoryAeolythimic
Scale 1113Scale 1113: Locrian Pentatonic 2, Ian Ring Music TheoryLocrian Pentatonic 2

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. Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography.