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Scale 3685: "Kodian"

Scale 3685: Kodian, 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
Kodian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,2,5,6,9,10,11}
Forte Number7-Z18
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1231
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections3
Modes6
Prime?no
prime: 755
Deep Scaleno
Interval Vector434442
Interval Spectrump4m4n4s3d4t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {3,4,5,6,7}
<4> = {5,6,7,8,9}
<5> = {7,8,9,10}
<6> = {9,10,11}
Spectra Variation2.571
Maximally Evenno
Maximal Area Setno
Interior Area2.433
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicyes

Harmonic Chords

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 TriadsD{2,6,9}331.5
F{5,9,0}242
A♯{10,2,5}331.5
Minor Triadsdm{2,5,9}331.5
bm{11,2,6}242
Augmented TriadsD+{2,6,10}331.5
Diminished Triadsf♯°{6,9,0}242
{11,2,5}242
Parsimonious Voice Leading Between Common Triads of Scale 3685. Created by Ian Ring ©2019 dm dm D D dm->D F F dm->F A# A# dm->A# D+ D+ D->D+ f#° f#° D->f#° D+->A# bm bm D+->bm F->f#° A#->b° b°->bm

view full size

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.

Diameter4
Radius3
Self-Centeredno
Central Verticesdm, D, D+, A♯
Peripheral VerticesF, f♯°, b°, bm

Modes

Modes are the rotational transformation of this scale. Scale 3685 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 1945
Scale 1945: Zarian, Ian Ring Music TheoryZarian
3rd mode:
Scale 755
Scale 755: Phrythian, Ian Ring Music TheoryPhrythianThis is the prime mode
4th mode:
Scale 2425
Scale 2425: Rorian, Ian Ring Music TheoryRorian
5th mode:
Scale 815
Scale 815: Bolian, Ian Ring Music TheoryBolian
6th mode:
Scale 2455
Scale 2455: Bothian, Ian Ring Music TheoryBothian
7th mode:
Scale 3275
Scale 3275: Mela Divyamani, Ian Ring Music TheoryMela Divyamani

Prime

The prime form of this scale is Scale 755

Scale 755Scale 755: Phrythian, Ian Ring Music TheoryPhrythian

Complement

The heptatonic modal family [3685, 1945, 755, 2425, 815, 2455, 3275] (Forte: 7-Z18) is the complement of the pentatonic modal family [179, 779, 1633, 2137, 2437] (Forte: 5-Z18)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3685 is 1231

Scale 1231Scale 1231: Logian, Ian Ring Music TheoryLogian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3685 is chiral, and its enantiomorph is scale 1231

Scale 1231Scale 1231: Logian, Ian Ring Music TheoryLogian

Transformations:

T0 3685  T0I 1231
T1 3275  T1I 2462
T2 2455  T2I 829
T3 815  T3I 1658
T4 1630  T4I 3316
T5 3260  T5I 2537
T6 2425  T6I 979
T7 755  T7I 1958
T8 1510  T8I 3916
T9 3020  T9I 3737
T10 1945  T10I 3379
T11 3890  T11I 2663

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 3687Scale 3687: Zonyllic, Ian Ring Music TheoryZonyllic
Scale 3681Scale 3681, Ian Ring Music Theory
Scale 3683Scale 3683: Dycrian, Ian Ring Music TheoryDycrian
Scale 3689Scale 3689: Katocrian, Ian Ring Music TheoryKatocrian
Scale 3693Scale 3693: Stadyllic, Ian Ring Music TheoryStadyllic
Scale 3701Scale 3701: Bagyllic, Ian Ring Music TheoryBagyllic
Scale 3653Scale 3653: Sathimic, Ian Ring Music TheorySathimic
Scale 3669Scale 3669: Mothian, Ian Ring Music TheoryMothian
Scale 3621Scale 3621: Gylimic, Ian Ring Music TheoryGylimic
Scale 3749Scale 3749: Raga Sorati, Ian Ring Music TheoryRaga Sorati
Scale 3813Scale 3813: Aeologyllic, Ian Ring Music TheoryAeologyllic
Scale 3941Scale 3941: Stathyllic, Ian Ring Music TheoryStathyllic
Scale 3173Scale 3173: Zarimic, Ian Ring Music TheoryZarimic
Scale 3429Scale 3429: Marian, Ian Ring Music TheoryMarian
Scale 2661Scale 2661: Stydimic, Ian Ring Music TheoryStydimic
Scale 1637Scale 1637: Syptimic, Ian Ring Music TheorySyptimic

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.