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Scale 3869: "Bygyllic"

Scale 3869: Bygyllic, 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
Bygyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,2,3,4,8,9,10,11}
Forte Number8-5
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1823
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 TriadsE{4,8,11}231.57
G♯{8,0,3}321.29
Minor Triadsg♯m{8,11,3}331.43
am{9,0,4}241.86
Augmented TriadsC+{0,4,8}331.43
Diminished Triadsg♯°{8,11,2}142.14
{9,0,3}231.71
Parsimonious Voice Leading Between Common Triads of Scale 3869. Created by Ian Ring ©2019 C+ C+ E E C+->E G# G# C+->G# am am C+->am g#m g#m E->g#m g#° g#° g#°->g#m g#m->G# G#->a° a°->am

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 VerticesG♯
Peripheral Verticesg♯°, am

Modes

Modes are the rotational transformation of this scale. Scale 3869 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 1991
Scale 1991: Phryptyllic, Ian Ring Music TheoryPhryptyllic
3rd mode:
Scale 3043
Scale 3043: Ionayllic, Ian Ring Music TheoryIonayllic
4th mode:
Scale 3569
Scale 3569: Aeoladyllic, Ian Ring Music TheoryAeoladyllic
5th mode:
Scale 479
Scale 479: Kocryllic, Ian Ring Music TheoryKocryllicThis is the prime mode
6th mode:
Scale 2287
Scale 2287: Lodyllic, Ian Ring Music TheoryLodyllic
7th mode:
Scale 3191
Scale 3191: Bynyllic, Ian Ring Music TheoryBynyllic
8th mode:
Scale 3643
Scale 3643: Kydyllic, Ian Ring Music TheoryKydyllic

Prime

The prime form of this scale is Scale 479

Scale 479Scale 479: Kocryllic, Ian Ring Music TheoryKocryllic

Complement

The octatonic modal family [3869, 1991, 3043, 3569, 479, 2287, 3191, 3643] (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 3869 is 1823

Scale 1823Scale 1823: Phralyllic, Ian Ring Music TheoryPhralyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3869 is chiral, and its enantiomorph is scale 1823

Scale 1823Scale 1823: Phralyllic, Ian Ring Music TheoryPhralyllic

Transformations:

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

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 3871Scale 3871: Aerynygic, Ian Ring Music TheoryAerynygic
Scale 3865Scale 3865: Starian, Ian Ring Music TheoryStarian
Scale 3867Scale 3867: Storyllic, Ian Ring Music TheoryStoryllic
Scale 3861Scale 3861: Phroptian, Ian Ring Music TheoryPhroptian
Scale 3853Scale 3853, Ian Ring Music Theory
Scale 3885Scale 3885: Styryllic, Ian Ring Music TheoryStyryllic
Scale 3901Scale 3901: Bycrygic, Ian Ring Music TheoryBycrygic
Scale 3933Scale 3933: Ionidygic, Ian Ring Music TheoryIonidygic
Scale 3997Scale 3997: Dogygic, Ian Ring Music TheoryDogygic
Scale 3613Scale 3613, Ian Ring Music Theory
Scale 3741Scale 3741: Zydyllic, Ian Ring Music TheoryZydyllic
Scale 3357Scale 3357: Phrodian, Ian Ring Music TheoryPhrodian
Scale 2845Scale 2845: Baptian, Ian Ring Music TheoryBaptian
Scale 1821Scale 1821: Aeradian, Ian Ring Music TheoryAeradian

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.