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Scale 3929: "Aeolothyllic"

Scale 3929: Aeolothyllic, 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
Aeolothyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,3,4,6,8,9,10,11}
Forte Number8-Z15
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 863
Hemitonia5 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections3
Modes7
Prime?no
prime: 863
Deep Scaleno
Interval Vector555553
Interval Spectrump5m5n5s5d5t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4}
<3> = {3,4,5,6}
<4> = {4,5,6,7,8}
<5> = {6,7,8,9}
<6> = {8,9,10}
<7> = {9,10,11}
Spectra Variation2.25
Maximally Evenno
Maximal Area Setno
Interior Area2.616
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 TriadsE{4,8,11}242.18
G♯{8,0,3}441.82
B{11,3,6}342
Minor Triadsd♯m{3,6,10}242.27
g♯m{8,11,3}341.91
am{9,0,4}342
Augmented TriadsC+{0,4,8}341.91
Diminished Triads{0,3,6}242.09
d♯°{3,6,9}242.36
f♯°{6,9,0}242.27
{9,0,3}242.09
Parsimonious Voice Leading Between Common Triads of Scale 3929. Created by Ian Ring ©2019 G# G# c°->G# B B c°->B C+ C+ E E C+->E C+->G# am am C+->am d#° d#° d#m d#m d#°->d#m f#° f#° d#°->f#° d#m->B g#m g#m E->g#m f#°->am g#m->G# g#m->B G#->a° a°->am

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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 3929 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 1003
Scale 1003: Ionyryllic, Ian Ring Music TheoryIonyryllic
3rd mode:
Scale 2549
Scale 2549: Rydyllic, Ian Ring Music TheoryRydyllic
4th mode:
Scale 1661
Scale 1661: Gonyllic, Ian Ring Music TheoryGonyllic
5th mode:
Scale 1439
Scale 1439: Rolyllic, Ian Ring Music TheoryRolyllic
6th mode:
Scale 2767
Scale 2767: Katydyllic, Ian Ring Music TheoryKatydyllic
7th mode:
Scale 3431
Scale 3431: Zyptyllic, Ian Ring Music TheoryZyptyllic
8th mode:
Scale 3763
Scale 3763: Modyllic, Ian Ring Music TheoryModyllic

Prime

The prime form of this scale is Scale 863

Scale 863Scale 863: Pyryllic, Ian Ring Music TheoryPyryllic

Complement

The octatonic modal family [3929, 1003, 2549, 1661, 1439, 2767, 3431, 3763] (Forte: 8-Z15) is the complement of the tetratonic modal family [83, 773, 1217, 2089] (Forte: 4-Z15)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3929 is 863

Scale 863Scale 863: Pyryllic, Ian Ring Music TheoryPyryllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3929 is chiral, and its enantiomorph is scale 863

Scale 863Scale 863: Pyryllic, Ian Ring Music TheoryPyryllic

Transformations:

T0 3929  T0I 863
T1 3763  T1I 1726
T2 3431  T2I 3452
T3 2767  T3I 2809
T4 1439  T4I 1523
T5 2878  T5I 3046
T6 1661  T6I 1997
T7 3322  T7I 3994
T8 2549  T8I 3893
T9 1003  T9I 3691
T10 2006  T10I 3287
T11 4012  T11I 2479

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 3931Scale 3931: Aerygic, Ian Ring Music TheoryAerygic
Scale 3933Scale 3933: Ionidygic, Ian Ring Music TheoryIonidygic
Scale 3921Scale 3921: Pythian, Ian Ring Music TheoryPythian
Scale 3925Scale 3925: Thyryllic, Ian Ring Music TheoryThyryllic
Scale 3913Scale 3913: Bonian, Ian Ring Music TheoryBonian
Scale 3945Scale 3945: Lydyllic, Ian Ring Music TheoryLydyllic
Scale 3961Scale 3961: Zathygic, Ian Ring Music TheoryZathygic
Scale 3865Scale 3865: Starian, Ian Ring Music TheoryStarian
Scale 3897Scale 3897: Kalyllic, Ian Ring Music TheoryKalyllic
Scale 3993Scale 3993: Ioniptyllic, Ian Ring Music TheoryIoniptyllic
Scale 4057Scale 4057: Phrygic, Ian Ring Music TheoryPhrygic
Scale 3673Scale 3673: Ranian, Ian Ring Music TheoryRanian
Scale 3801Scale 3801: Maptyllic, Ian Ring Music TheoryMaptyllic
Scale 3417Scale 3417: Golian, Ian Ring Music TheoryGolian
Scale 2905Scale 2905: Aeolian Flat 1, Ian Ring Music TheoryAeolian Flat 1
Scale 1881Scale 1881: Katorian, Ian Ring Music TheoryKatorian

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.