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Scale 3811: "Epogyllic"

Scale 3811: Epogyllic, 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
Epogyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,5,6,7,9,10,11}
Forte Number8-5
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2287
Hemitonia6 (multihemitonic)
Cohemitonia4 (multicohemitonic)
Imperfections3
Modes7
Prime?no
prime: 479
Deep Scaleno
Interval Vector654553
Interval Spectrump5m5n4s5d6t3
Distribution Spectra<1> = {1,2,4}
<2> = {2,3,5}
<3> = {3,4,6}
<4> = {4,5,7,8}
<5> = {6,8,9}
<6> = {7,9,10}
<7> = {8,10,11}
Spectra Variation2.75
Maximally Evenno
Maximal Area Setno
Interior Area2.366
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 TriadsF{5,9,0}241.86
F♯{6,10,1}331.43
Minor Triadsf♯m{6,9,1}321.29
a♯m{10,1,5}231.57
Augmented TriadsC♯+{1,5,9}331.43
Diminished Triadsf♯°{6,9,0}231.71
{7,10,1}142.14
Parsimonious Voice Leading Between Common Triads of Scale 3811. Created by Ian Ring ©2019 C#+ C#+ F F C#+->F f#m f#m C#+->f#m a#m a#m C#+->a#m f#° f#° F->f#° f#°->f#m F# F# f#m->F# F#->g° F#->a#m

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
Radius2
Self-Centeredno
Central Verticesf♯m
Peripheral VerticesF, g°

Modes

Modes are the rotational transformation of this scale. Scale 3811 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3953
Scale 3953: Thagyllic, Ian Ring Music TheoryThagyllic
3rd mode:
Scale 503
Scale 503: Thoptyllic, Ian Ring Music TheoryThoptyllic
4th mode:
Scale 2299
Scale 2299: Phraptyllic, Ian Ring Music TheoryPhraptyllic
5th mode:
Scale 3197
Scale 3197: Gylyllic, Ian Ring Music TheoryGylyllic
6th mode:
Scale 1823
Scale 1823: Phralyllic, Ian Ring Music TheoryPhralyllic
7th mode:
Scale 2959
Scale 2959: Dygyllic, Ian Ring Music TheoryDygyllic
8th mode:
Scale 3527
Scale 3527: Ronyllic, Ian Ring Music TheoryRonyllic

Prime

The prime form of this scale is Scale 479

Scale 479Scale 479: Kocryllic, Ian Ring Music TheoryKocryllic

Complement

The octatonic modal family [3811, 3953, 503, 2299, 3197, 1823, 2959, 3527] (Forte: 8-5) is the complement of the tetratonic modal family [71, 449, 2083, 3089] (Forte: 4-5)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3811 is 2287

Scale 2287Scale 2287: Lodyllic, Ian Ring Music TheoryLodyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3811 is chiral, and its enantiomorph is scale 2287

Scale 2287Scale 2287: Lodyllic, Ian Ring Music TheoryLodyllic

Transformations:

T0 3811  T0I 2287
T1 3527  T1I 479
T2 2959  T2I 958
T3 1823  T3I 1916
T4 3646  T4I 3832
T5 3197  T5I 3569
T6 2299  T6I 3043
T7 503  T7I 1991
T8 1006  T8I 3982
T9 2012  T9I 3869
T10 4024  T10I 3643
T11 3953  T11I 3191

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 3809Scale 3809, Ian Ring Music Theory
Scale 3813Scale 3813: Aeologyllic, Ian Ring Music TheoryAeologyllic
Scale 3815Scale 3815: Galygic, Ian Ring Music TheoryGalygic
Scale 3819Scale 3819: Aeolanygic, Ian Ring Music TheoryAeolanygic
Scale 3827Scale 3827: Bodygic, Ian Ring Music TheoryBodygic
Scale 3779Scale 3779, Ian Ring Music Theory
Scale 3795Scale 3795: Epothyllic, Ian Ring Music TheoryEpothyllic
Scale 3747Scale 3747: Myrian, Ian Ring Music TheoryMyrian
Scale 3683Scale 3683: Dycrian, Ian Ring Music TheoryDycrian
Scale 3939Scale 3939: Dogyllic, Ian Ring Music TheoryDogyllic
Scale 4067Scale 4067: Aeolarygic, Ian Ring Music TheoryAeolarygic
Scale 3299Scale 3299: Syptian, Ian Ring Music TheorySyptian
Scale 3555Scale 3555: Pylyllic, Ian Ring Music TheoryPylyllic
Scale 2787Scale 2787: Zyrian, Ian Ring Music TheoryZyrian
Scale 1763Scale 1763: Katalian, Ian Ring Music TheoryKatalian

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.