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Scale 3191: "Bynyllic"

Scale 3191: Bynyllic, 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
Bynyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,2,4,5,6,10,11}
Forte Number8-5
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3527
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♯{6,10,1}231.57
A♯{10,2,5}321.29
Minor Triadsa♯m{10,1,5}331.43
bm{11,2,6}241.86
Augmented TriadsD+{2,6,10}331.43
Diminished Triadsa♯°{10,1,4}142.14
{11,2,5}231.71
Parsimonious Voice Leading Between Common Triads of Scale 3191. Created by Ian Ring ©2019 D+ D+ F# F# D+->F# A# A# D+->A# bm bm D+->bm a#m a#m F#->a#m a#° a#° a#°->a#m a#m->A# A#->b° b°->bm

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 VerticesA♯
Peripheral Verticesa♯°, bm

Modes

Modes are the rotational transformation of this scale. Scale 3191 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3643
Scale 3643: Kydyllic, Ian Ring Music TheoryKydyllic
3rd mode:
Scale 3869
Scale 3869: Bygyllic, Ian Ring Music TheoryBygyllic
4th mode:
Scale 1991
Scale 1991: Phryptyllic, Ian Ring Music TheoryPhryptyllic
5th mode:
Scale 3043
Scale 3043: Ionayllic, Ian Ring Music TheoryIonayllic
6th mode:
Scale 3569
Scale 3569: Aeoladyllic, Ian Ring Music TheoryAeoladyllic
7th mode:
Scale 479
Scale 479: Kocryllic, Ian Ring Music TheoryKocryllicThis is the prime mode
8th mode:
Scale 2287
Scale 2287: Lodyllic, Ian Ring Music TheoryLodyllic

Prime

The prime form of this scale is Scale 479

Scale 479Scale 479: Kocryllic, Ian Ring Music TheoryKocryllic

Complement

The octatonic modal family [3191, 3643, 3869, 1991, 3043, 3569, 479, 2287] (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 3191 is 3527

Scale 3527Scale 3527: Ronyllic, Ian Ring Music TheoryRonyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3191 is chiral, and its enantiomorph is scale 3527

Scale 3527Scale 3527: Ronyllic, Ian Ring Music TheoryRonyllic

Transformations:

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

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 3189Scale 3189: Aeolonian, Ian Ring Music TheoryAeolonian
Scale 3187Scale 3187: Koptian, Ian Ring Music TheoryKoptian
Scale 3195Scale 3195: Raryllic, Ian Ring Music TheoryRaryllic
Scale 3199Scale 3199: Thaptygic, Ian Ring Music TheoryThaptygic
Scale 3175Scale 3175: Eponian, Ian Ring Music TheoryEponian
Scale 3183Scale 3183: Mixonyllic, Ian Ring Music TheoryMixonyllic
Scale 3159Scale 3159: Stocrian, Ian Ring Music TheoryStocrian
Scale 3127Scale 3127, Ian Ring Music Theory
Scale 3255Scale 3255: Daryllic, Ian Ring Music TheoryDaryllic
Scale 3319Scale 3319: Tholygic, Ian Ring Music TheoryTholygic
Scale 3447Scale 3447: Kynygic, Ian Ring Music TheoryKynygic
Scale 3703Scale 3703: Katalygic, Ian Ring Music TheoryKatalygic
Scale 2167Scale 2167, Ian Ring Music Theory
Scale 2679Scale 2679: Rathyllic, Ian Ring Music TheoryRathyllic
Scale 1143Scale 1143: Styrian, Ian Ring Music TheoryStyrian

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.