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Scale 3813: "Aeologyllic"

Scale 3813: Aeologyllic, 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
Aeologyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,2,5,6,7,9,10,11}
Forte Number8-14
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1263
Hemitonia5 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections2
Modes7
Prime?no
prime: 759
Deep Scaleno
Interval Vector555562
Interval Spectrump6m5n5s5d5t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {3,4,5,6}
<4> = {5,7}
<5> = {6,7,8,9}
<6> = {7,8,9,10}
<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 TriadsD{2,6,9}331.7
F{5,9,0}252.5
G{7,11,2}252.5
A♯{10,2,5}331.7
Minor Triadsdm{2,5,9}341.9
gm{7,10,2}242.1
bm{11,2,6}341.9
Augmented TriadsD+{2,6,10}431.5
Diminished Triadsf♯°{6,9,0}242.3
{11,2,5}242.1
Parsimonious Voice Leading Between Common Triads of Scale 3813. Created by Ian Ring ©2019 dm dm D D dm->D F F dm->F A# A# dm->A# D+ D+ D->D+ f#° f#° D->f#° gm gm D+->gm D+->A# bm bm D+->bm F->f#° Parsimonious Voice Leading Between Common Triads of Scale 3813. Created by Ian Ring ©2019 G gm->G G->bm A#->b° b°->bm

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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
Radius3
Self-Centeredno
Central VerticesD, D+, A♯
Peripheral VerticesF, G

Modes

Modes are the rotational transformation of this scale. Scale 3813 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 1977
Scale 1977: Dagyllic, Ian Ring Music TheoryDagyllic
3rd mode:
Scale 759
Scale 759: Katalyllic, Ian Ring Music TheoryKatalyllicThis is the prime mode
4th mode:
Scale 2427
Scale 2427: Katoryllic, Ian Ring Music TheoryKatoryllic
5th mode:
Scale 3261
Scale 3261: Dodyllic, Ian Ring Music TheoryDodyllic
6th mode:
Scale 1839
Scale 1839: Zogyllic, Ian Ring Music TheoryZogyllic
7th mode:
Scale 2967
Scale 2967: Madyllic, Ian Ring Music TheoryMadyllic
8th mode:
Scale 3531
Scale 3531: Neveseri, Ian Ring Music TheoryNeveseri

Prime

The prime form of this scale is Scale 759

Scale 759Scale 759: Katalyllic, Ian Ring Music TheoryKatalyllic

Complement

The octatonic modal family [3813, 1977, 759, 2427, 3261, 1839, 2967, 3531] (Forte: 8-14) is the complement of the tetratonic modal family [141, 417, 1059, 2577] (Forte: 4-14)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3813 is 1263

Scale 1263Scale 1263: Stynyllic, Ian Ring Music TheoryStynyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3813 is chiral, and its enantiomorph is scale 1263

Scale 1263Scale 1263: Stynyllic, Ian Ring Music TheoryStynyllic

Transformations:

T0 3813  T0I 1263
T1 3531  T1I 2526
T2 2967  T2I 957
T3 1839  T3I 1914
T4 3678  T4I 3828
T5 3261  T5I 3561
T6 2427  T6I 3027
T7 759  T7I 1959
T8 1518  T8I 3918
T9 3036  T9I 3741
T10 1977  T10I 3387
T11 3954  T11I 2679

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 3815Scale 3815: Galygic, Ian Ring Music TheoryGalygic
Scale 3809Scale 3809, Ian Ring Music Theory
Scale 3811Scale 3811: Epogyllic, Ian Ring Music TheoryEpogyllic
Scale 3817Scale 3817: Zoryllic, Ian Ring Music TheoryZoryllic
Scale 3821Scale 3821: Epyrygic, Ian Ring Music TheoryEpyrygic
Scale 3829Scale 3829: Taishikicho, Ian Ring Music TheoryTaishikicho
Scale 3781Scale 3781: Gyphian, Ian Ring Music TheoryGyphian
Scale 3797Scale 3797: Rocryllic, Ian Ring Music TheoryRocryllic
Scale 3749Scale 3749: Raga Sorati, Ian Ring Music TheoryRaga Sorati
Scale 3685Scale 3685: Kodian, Ian Ring Music TheoryKodian
Scale 3941Scale 3941: Stathyllic, Ian Ring Music TheoryStathyllic
Scale 4069Scale 4069: Starygic, Ian Ring Music TheoryStarygic
Scale 3301Scale 3301: Chromatic Mixolydian Inverse, Ian Ring Music TheoryChromatic Mixolydian Inverse
Scale 3557Scale 3557, Ian Ring Music Theory
Scale 2789Scale 2789: Zolian, Ian Ring Music TheoryZolian
Scale 1765Scale 1765: Lonian, Ian Ring Music TheoryLonian

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.