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Scale 3197: "Gylyllic"

Scale 3197: Gylyllic, 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
Gylyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,2,3,4,5,6,10,11}
Forte Number8-5
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1991
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 TriadsA♯{10,2,5}241.86
B{11,3,6}331.43
Minor Triadsd♯m{3,6,10}231.57
bm{11,2,6}321.29
Augmented TriadsD+{2,6,10}331.43
Diminished Triads{0,3,6}142.14
{11,2,5}231.71
Parsimonious Voice Leading Between Common Triads of Scale 3197. Created by Ian Ring ©2019 B B c°->B D+ D+ d#m d#m D+->d#m A# A# D+->A# bm bm D+->bm d#m->B A#->b° b°->bm bm->B

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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
Radius2
Self-Centeredno
Central Verticesbm
Peripheral Verticesc°, A♯

Modes

Modes are the rotational transformation of this scale. Scale 3197 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 1823
Scale 1823: Phralyllic, Ian Ring Music TheoryPhralyllic
3rd mode:
Scale 2959
Scale 2959: Dygyllic, Ian Ring Music TheoryDygyllic
4th mode:
Scale 3527
Scale 3527: Ronyllic, Ian Ring Music TheoryRonyllic
5th mode:
Scale 3811
Scale 3811: Epogyllic, Ian Ring Music TheoryEpogyllic
6th mode:
Scale 3953
Scale 3953: Thagyllic, Ian Ring Music TheoryThagyllic
7th mode:
Scale 503
Scale 503: Thoptyllic, Ian Ring Music TheoryThoptyllic
8th mode:
Scale 2299
Scale 2299: Phraptyllic, Ian Ring Music TheoryPhraptyllic

Prime

The prime form of this scale is Scale 479

Scale 479Scale 479: Kocryllic, Ian Ring Music TheoryKocryllic

Complement

The octatonic modal family [3197, 1823, 2959, 3527, 3811, 3953, 503, 2299] (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 3197 is 1991

Scale 1991Scale 1991: Phryptyllic, Ian Ring Music TheoryPhryptyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3197 is chiral, and its enantiomorph is scale 1991

Scale 1991Scale 1991: Phryptyllic, Ian Ring Music TheoryPhryptyllic

Transformations:

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

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 3199Scale 3199: Thaptygic, Ian Ring Music TheoryThaptygic
Scale 3193Scale 3193: Zathian, Ian Ring Music TheoryZathian
Scale 3195Scale 3195: Raryllic, Ian Ring Music TheoryRaryllic
Scale 3189Scale 3189: Aeolonian, Ian Ring Music TheoryAeolonian
Scale 3181Scale 3181: Rolian, Ian Ring Music TheoryRolian
Scale 3165Scale 3165: Mylian, Ian Ring Music TheoryMylian
Scale 3133Scale 3133, Ian Ring Music Theory
Scale 3261Scale 3261: Dodyllic, Ian Ring Music TheoryDodyllic
Scale 3325Scale 3325: Mixolygic, Ian Ring Music TheoryMixolygic
Scale 3453Scale 3453: Katarygic, Ian Ring Music TheoryKatarygic
Scale 3709Scale 3709: Katynygic, Ian Ring Music TheoryKatynygic
Scale 2173Scale 2173, Ian Ring Music Theory
Scale 2685Scale 2685: Ionoryllic, Ian Ring Music TheoryIonoryllic
Scale 1149Scale 1149: Bydian, Ian Ring Music TheoryBydian

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.