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Scale 3563: "Ionoptygic"

Scale 3563: Ionoptygic, 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
Ionoptygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,1,3,5,6,7,8,10,11}
Forte Number9-9
Rotational Symmetrynone
Reflection Axes3
Palindromicno
Chiralityno
Hemitonia6 (multihemitonic)
Cohemitonia4 (multicohemitonic)
Imperfections1
Modes8
Prime?no
prime: 1519
Deep Scaleno
Interval Vector676683
Interval Spectrump8m6n6s7d6t3
Distribution Spectra<1> = {1,2}
<2> = {2,3,4}
<3> = {3,4,5}
<4> = {5,6}
<5> = {6,7}
<6> = {7,8,9}
<7> = {8,9,10}
<8> = {10,11}
Spectra Variation1.333
Maximally Evenno
Maximal Area Setyes
Interior Area2.799
Myhill Propertyno
Balancedno
Ridge Tones[6]
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♯{1,5,8}242.57
D♯{3,7,10}342.21
F♯{6,10,1}342.43
G♯{8,0,3}342.29
B{11,3,6}342.21
Minor Triadscm{0,3,7}342.21
d♯m{3,6,10}342.29
fm{5,8,0}342.43
g♯m{8,11,3}342.21
a♯m{10,1,5}242.57
Augmented TriadsD♯+{3,7,11}442
Diminished Triads{0,3,6}242.57
{5,8,11}242.57
{7,10,1}242.57
Parsimonious Voice Leading Between Common Triads of Scale 3563. Created by Ian Ring ©2019 cm cm c°->cm B B c°->B D#+ D#+ cm->D#+ G# G# cm->G# C# C# fm fm C#->fm a#m a#m C#->a#m d#m d#m D# D# d#m->D# F# F# d#m->F# d#m->B D#->D#+ D#->g° g#m g#m D#+->g#m D#+->B f°->fm f°->g#m fm->G# F#->g° F#->a#m g#m->G#

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
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 3563 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 3829
Scale 3829: Taishikicho, Ian Ring Music TheoryTaishikicho
3rd mode:
Scale 1981
Scale 1981: Houseini, Ian Ring Music TheoryHouseini
4th mode:
Scale 1519
Scale 1519: Locrian/Aeolian Mixed, Ian Ring Music TheoryLocrian/Aeolian MixedThis is the prime mode
5th mode:
Scale 2807
Scale 2807: Zylygic, Ian Ring Music TheoryZylygic
6th mode:
Scale 3451
Scale 3451: Garygic, Ian Ring Music TheoryGarygic
7th mode:
Scale 3773
Scale 3773: Raga Malgunji, Ian Ring Music TheoryRaga Malgunji
8th mode:
Scale 1967
Scale 1967: Diatonic Dorian Mixed, Ian Ring Music TheoryDiatonic Dorian Mixed
9th mode:
Scale 3031
Scale 3031: Epithygic, Ian Ring Music TheoryEpithygic

Prime

The prime form of this scale is Scale 1519

Scale 1519Scale 1519: Locrian/Aeolian Mixed, Ian Ring Music TheoryLocrian/Aeolian Mixed

Complement

The nonatonic modal family [3563, 3829, 1981, 1519, 2807, 3451, 3773, 1967, 3031] (Forte: 9-9) is the complement of the tritonic modal family [133, 161, 1057] (Forte: 3-9)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3563 is 2807

Scale 2807Scale 2807: Zylygic, Ian Ring Music TheoryZylygic

Transformations:

T0 3563  T0I 2807
T1 3031  T1I 1519
T2 1967  T2I 3038
T3 3934  T3I 1981
T4 3773  T4I 3962
T5 3451  T5I 3829
T6 2807  T6I 3563
T7 1519  T7I 3031
T8 3038  T8I 1967
T9 1981  T9I 3934
T10 3962  T10I 3773
T11 3829  T11I 3451

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 3561Scale 3561: Pothyllic, Ian Ring Music TheoryPothyllic
Scale 3565Scale 3565: Aeolorygic, Ian Ring Music TheoryAeolorygic
Scale 3567Scale 3567: Epityllian, Ian Ring Music TheoryEpityllian
Scale 3555Scale 3555: Pylyllic, Ian Ring Music TheoryPylyllic
Scale 3559Scale 3559: Thophygic, Ian Ring Music TheoryThophygic
Scale 3571Scale 3571: Dyrygic, Ian Ring Music TheoryDyrygic
Scale 3579Scale 3579: Zyphyllian, Ian Ring Music TheoryZyphyllian
Scale 3531Scale 3531: Neveseri, Ian Ring Music TheoryNeveseri
Scale 3547Scale 3547: Sadygic, Ian Ring Music TheorySadygic
Scale 3499Scale 3499: Hamel, Ian Ring Music TheoryHamel
Scale 3435Scale 3435: Prokofiev, Ian Ring Music TheoryProkofiev
Scale 3307Scale 3307: Boptyllic, Ian Ring Music TheoryBoptyllic
Scale 3819Scale 3819: Aeolanygic, Ian Ring Music TheoryAeolanygic
Scale 4075Scale 4075: Katyllian, Ian Ring Music TheoryKatyllian
Scale 2539Scale 2539: Half-Diminished Bebop, Ian Ring Music TheoryHalf-Diminished Bebop
Scale 3051Scale 3051: Stalygic, Ian Ring Music TheoryStalygic
Scale 1515Scale 1515: Phrygian/Locrian Mixed, Ian Ring Music TheoryPhrygian/Locrian Mixed

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.