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Scale 3643: "Kydyllic"

Scale 3643: Kydyllic, 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
Kydyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,3,4,5,9,10,11}
Forte Number8-5
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2959
Hemitonia6 (multihemitonic)
Cohemitonia4 (multicohemitonic)
Imperfections3
Modes7
Prime?no
prime: 479
Deep Scaleno
Interval Vector654553
Interval Spectrump5m5n4s5d6t3
Distribution Spectra<1> = {1,2,4}
<2> = {2,3,5}
<3> = {3,4,6}
<4> = {4,5,7,8}
<5> = {6,8,9}
<6> = {7,9,10}
<7> = {8,10,11}
Spectra Variation2.75
Maximally Evenno
Maximal Area Setno
Interior Area2.366
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 TriadsF{5,9,0}231.57
A{9,1,4}321.29
Minor Triadsam{9,0,4}331.43
a♯m{10,1,5}241.86
Augmented TriadsC♯+{1,5,9}331.43
Diminished Triads{9,0,3}142.14
a♯°{10,1,4}231.71
Parsimonious Voice Leading Between Common Triads of Scale 3643. Created by Ian Ring ©2019 C#+ C#+ F F C#+->F A A C#+->A a#m a#m C#+->a#m am am F->am a°->am am->A a#° a#° A->a#° a#°->a#m

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
Radius2
Self-Centeredno
Central VerticesA
Peripheral Verticesa°, a♯m

Modes

Modes are the rotational transformation of this scale. Scale 3643 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3869
Scale 3869: Bygyllic, Ian Ring Music TheoryBygyllic
3rd mode:
Scale 1991
Scale 1991: Phryptyllic, Ian Ring Music TheoryPhryptyllic
4th mode:
Scale 3043
Scale 3043: Ionayllic, Ian Ring Music TheoryIonayllic
5th mode:
Scale 3569
Scale 3569: Aeoladyllic, Ian Ring Music TheoryAeoladyllic
6th mode:
Scale 479
Scale 479: Kocryllic, Ian Ring Music TheoryKocryllicThis is the prime mode
7th mode:
Scale 2287
Scale 2287: Lodyllic, Ian Ring Music TheoryLodyllic
8th mode:
Scale 3191
Scale 3191: Bynyllic, Ian Ring Music TheoryBynyllic

Prime

The prime form of this scale is Scale 479

Scale 479Scale 479: Kocryllic, Ian Ring Music TheoryKocryllic

Complement

The octatonic modal family [3643, 3869, 1991, 3043, 3569, 479, 2287, 3191] (Forte: 8-5) is the complement of the tetratonic modal family [71, 449, 2083, 3089] (Forte: 4-5)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3643 is 2959

Scale 2959Scale 2959: Dygyllic, Ian Ring Music TheoryDygyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3643 is chiral, and its enantiomorph is scale 2959

Scale 2959Scale 2959: Dygyllic, Ian Ring Music TheoryDygyllic

Transformations:

T0 3643  T0I 2959
T1 3191  T1I 1823
T2 2287  T2I 3646
T3 479  T3I 3197
T4 958  T4I 2299
T5 1916  T5I 503
T6 3832  T6I 1006
T7 3569  T7I 2012
T8 3043  T8I 4024
T9 1991  T9I 3953
T10 3982  T10I 3811
T11 3869  T11I 3527

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 3641Scale 3641: Thocrian, Ian Ring Music TheoryThocrian
Scale 3645Scale 3645: Zycryllic, Ian Ring Music TheoryZycryllic
Scale 3647Scale 3647: Eporygic, Ian Ring Music TheoryEporygic
Scale 3635Scale 3635: Katygian, Ian Ring Music TheoryKatygian
Scale 3639Scale 3639: Paptyllic, Ian Ring Music TheoryPaptyllic
Scale 3627Scale 3627: Kalian, Ian Ring Music TheoryKalian
Scale 3611Scale 3611, Ian Ring Music Theory
Scale 3675Scale 3675: Monyllic, Ian Ring Music TheoryMonyllic
Scale 3707Scale 3707: Rynygic, Ian Ring Music TheoryRynygic
Scale 3771Scale 3771: Stophygic, Ian Ring Music TheoryStophygic
Scale 3899Scale 3899: Katorygic, Ian Ring Music TheoryKatorygic
Scale 3131Scale 3131, Ian Ring Music Theory
Scale 3387Scale 3387: Aeryptyllic, Ian Ring Music TheoryAeryptyllic
Scale 2619Scale 2619: Ionyrian, Ian Ring Music TheoryIonyrian
Scale 1595Scale 1595: Dacrian, Ian Ring Music TheoryDacrian

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.