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Scale 3663: "Sonyllic"

Scale 3663: Sonyllic, 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
Sonyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,2,3,6,9,10,11}
Forte Number8-3
Rotational Symmetrynone
Reflection Axes0
Palindromicyes
Chiralityno
Hemitonia6 (multihemitonic)
Cohemitonia5 (multicohemitonic)
Imperfections4
Modes7
Prime?no
prime: 639
Deep Scaleno
Interval Vector656542
Interval Spectrump4m5n6s5d6t2
Distribution Spectra<1> = {1,3}
<2> = {2,4,6}
<3> = {3,5,7}
<4> = {4,6,8}
<5> = {5,7,9}
<6> = {6,8,10}
<7> = {9,11}
Spectra Variation3
Maximally Evenno
Maximal Area Setno
Interior Area2.5
Myhill Propertyno
Balancedno
Ridge Tones[0]
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 TriadsD{2,6,9}341.91
F♯{6,10,1}242.09
B{11,3,6}342
Minor Triadsd♯m{3,6,10}341.91
f♯m{6,9,1}342
bm{11,2,6}242.09
Augmented TriadsD+{2,6,10}441.82
Diminished Triads{0,3,6}242.27
d♯°{3,6,9}242.18
f♯°{6,9,0}242.27
{9,0,3}242.36
Parsimonious Voice Leading Between Common Triads of Scale 3663. Created by Ian Ring ©2019 c°->a° B B c°->B D D D+ D+ D->D+ d#° d#° D->d#° f#m f#m D->f#m d#m d#m D+->d#m F# F# D+->F# bm bm D+->bm d#°->d#m d#m->B f#° f#° f#°->f#m f#°->a° f#m->F# bm->B

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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
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 3663 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3879
Scale 3879: Pathyllic, Ian Ring Music TheoryPathyllic
3rd mode:
Scale 3987
Scale 3987: Loryllic, Ian Ring Music TheoryLoryllic
4th mode:
Scale 4041
Scale 4041: Zaryllic, Ian Ring Music TheoryZaryllic
5th mode:
Scale 1017
Scale 1017: Dythyllic, Ian Ring Music TheoryDythyllic
6th mode:
Scale 639
Scale 639: Ionaryllic, Ian Ring Music TheoryIonaryllicThis is the prime mode
7th mode:
Scale 2367
Scale 2367: Laryllic, Ian Ring Music TheoryLaryllic
8th mode:
Scale 3231
Scale 3231: Kataptyllic, Ian Ring Music TheoryKataptyllic

Prime

The prime form of this scale is Scale 639

Scale 639Scale 639: Ionaryllic, Ian Ring Music TheoryIonaryllic

Complement

The octatonic modal family [3663, 3879, 3987, 4041, 1017, 639, 2367, 3231] (Forte: 8-3) is the complement of the tetratonic modal family [27, 1539, 2061, 2817] (Forte: 4-3)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3663 is itself, because it is a palindromic scale!

Scale 3663Scale 3663: Sonyllic, Ian Ring Music TheorySonyllic

Transformations:

T0 3663  T0I 3663
T1 3231  T1I 3231
T2 2367  T2I 2367
T3 639  T3I 639
T4 1278  T4I 1278
T5 2556  T5I 2556
T6 1017  T6I 1017
T7 2034  T7I 2034
T8 4068  T8I 4068
T9 4041  T9I 4041
T10 3987  T10I 3987
T11 3879  T11I 3879

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 3661Scale 3661: Mixodorian, Ian Ring Music TheoryMixodorian
Scale 3659Scale 3659: Polian, Ian Ring Music TheoryPolian
Scale 3655Scale 3655: Mathian, Ian Ring Music TheoryMathian
Scale 3671Scale 3671: Aeonyllic, Ian Ring Music TheoryAeonyllic
Scale 3679Scale 3679: Rycrygic, Ian Ring Music TheoryRycrygic
Scale 3695Scale 3695: Kodygic, Ian Ring Music TheoryKodygic
Scale 3599Scale 3599, Ian Ring Music Theory
Scale 3631Scale 3631: Gydyllic, Ian Ring Music TheoryGydyllic
Scale 3727Scale 3727: Tholyllic, Ian Ring Music TheoryTholyllic
Scale 3791Scale 3791: Stodygic, Ian Ring Music TheoryStodygic
Scale 3919Scale 3919: Lynygic, Ian Ring Music TheoryLynygic
Scale 3151Scale 3151: Pacrian, Ian Ring Music TheoryPacrian
Scale 3407Scale 3407: Katocryllic, Ian Ring Music TheoryKatocryllic
Scale 2639Scale 2639: Dothian, Ian Ring Music TheoryDothian
Scale 1615Scale 1615: Sydian, Ian Ring Music TheorySydian

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.