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Scale 3963: "Aeoryllian"

Scale 3963: Aeoryllian, 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
Aeoryllian

Analysis

Cardinality10 (decatonic)
Pitch Class Set{0,1,3,4,5,6,8,9,10,11}
Forte Number10-5
Rotational Symmetrynone
Reflection Axes4.5
Palindromicno
Chiralityno
Hemitonia8 (multihemitonic)
Cohemitonia6 (multicohemitonic)
Imperfections1
Modes9
Prime?no
prime: 1983
Deep Scaleno
Interval Vector888894
Interval Spectrump9m8n8s8d8t4
Distribution Spectra<1> = {1,2}
<2> = {2,3}
<3> = {3,4}
<4> = {4,5}
<5> = {5,6,7}
<6> = {7,8}
<7> = {8,9}
<8> = {9,10}
<9> = {10,11}
Spectra Variation1
Maximally Evenno
Maximal Area Setyes
Interior Area2.866
Myhill Propertyno
Balancedno
Ridge Tones[9]
ProprietyProper
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}352.59
E{4,8,11}352.77
F{5,9,0}452.41
F♯{6,10,1}352.86
G♯{8,0,3}452.68
A{9,1,4}452.5
B{11,3,6}352.95
Minor Triadsc♯m{1,4,8}352.59
d♯m{3,6,10}352.95
fm{5,8,0}452.5
f♯m{6,9,1}452.68
g♯m{8,11,3}352.86
am{9,0,4}452.41
a♯m{10,1,5}352.77
Augmented TriadsC+{0,4,8}552.41
C♯+{1,5,9}552.41
Diminished Triads{0,3,6}253.05
d♯°{3,6,9}253.05
{5,8,11}253.05
f♯°{6,9,0}252.86
{9,0,3}252.86
a♯°{10,1,4}253.05
Parsimonious Voice Leading Between Common Triads of Scale 3963. Created by Ian Ring ©2019 G# G# c°->G# B B c°->B C+ C+ c#m c#m C+->c#m E E C+->E fm fm C+->fm C+->G# am am C+->am C# C# c#m->C# A A c#m->A C#+ C#+ C#->C#+ C#->fm F F C#+->F f#m f#m C#+->f#m C#+->A a#m a#m C#+->a#m d#° d#° d#m d#m d#°->d#m d#°->f#m F# F# d#m->F# d#m->B E->f° g#m g#m E->g#m f°->fm fm->F f#° f#° F->f#° F->am f#°->f#m f#m->F# F#->a#m g#m->G# g#m->B G#->a° a°->am am->A a#° a#° A->a#° a#°->a#m

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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.

Diameter5
Radius5
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 3963 can be rotated to make 9 other scales. The 1st mode is itself.

2nd mode:
Scale 4029
Scale 4029: Major/Minor Mixed, Ian Ring Music TheoryMajor/Minor Mixed
3rd mode:
Scale 2031
Scale 2031: Gadyllian, Ian Ring Music TheoryGadyllian
4th mode:
Scale 3063
Scale 3063: Solyllian, Ian Ring Music TheorySolyllian
5th mode:
Scale 3579
Scale 3579: Zyphyllian, Ian Ring Music TheoryZyphyllian
6th mode:
Scale 3837
Scale 3837: Minor Pentatonic With Leading Tones, Ian Ring Music TheoryMinor Pentatonic With Leading Tones
7th mode:
Scale 1983
Scale 1983: Soryllian, Ian Ring Music TheorySoryllianThis is the prime mode
8th mode:
Scale 3039
Scale 3039: Godyllian, Ian Ring Music TheoryGodyllian
9th mode:
Scale 3567
Scale 3567: Epityllian, Ian Ring Music TheoryEpityllian
10th mode:
Scale 3831
Scale 3831: Ionyllian, Ian Ring Music TheoryIonyllian

Prime

The prime form of this scale is Scale 1983

Scale 1983Scale 1983: Soryllian, Ian Ring Music TheorySoryllian

Complement

The decatonic modal family [3963, 4029, 2031, 3063, 3579, 3837, 1983, 3039, 3567, 3831] (Forte: 10-5) is the complement of the modal family [33, 129] (Forte: 2-5)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3963 is 3039

Scale 3039Scale 3039: Godyllian, Ian Ring Music TheoryGodyllian

Transformations:

T0 3963  T0I 3039
T1 3831  T1I 1983
T2 3567  T2I 3966
T3 3039  T3I 3837
T4 1983  T4I 3579
T5 3966  T5I 3063
T6 3837  T6I 2031
T7 3579  T7I 4062
T8 3063  T8I 4029
T9 2031  T9I 3963
T10 4062  T10I 3831
T11 4029  T11I 3567

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 3961Scale 3961: Zathygic, Ian Ring Music TheoryZathygic
Scale 3965Scale 3965: Messiaen Mode 7 Inverse, Ian Ring Music TheoryMessiaen Mode 7 Inverse
Scale 3967Scale 3967: Soratic, Ian Ring Music TheorySoratic
Scale 3955Scale 3955: Pothygic, Ian Ring Music TheoryPothygic
Scale 3959Scale 3959: Katagyllian, Ian Ring Music TheoryKatagyllian
Scale 3947Scale 3947: Ryptygic, Ian Ring Music TheoryRyptygic
Scale 3931Scale 3931: Aerygic, Ian Ring Music TheoryAerygic
Scale 3899Scale 3899: Katorygic, Ian Ring Music TheoryKatorygic
Scale 4027Scale 4027: Ragyllian, Ian Ring Music TheoryRagyllian
Scale 4091Scale 4091: Thydatic, Ian Ring Music TheoryThydatic
Scale 3707Scale 3707: Rynygic, Ian Ring Music TheoryRynygic
Scale 3835Scale 3835: Katodyllian, Ian Ring Music TheoryKatodyllian
Scale 3451Scale 3451: Garygic, Ian Ring Music TheoryGarygic
Scale 2939Scale 2939: Goptygic, Ian Ring Music TheoryGoptygic
Scale 1915Scale 1915: Thydygic, Ian Ring Music TheoryThydygic

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.