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Scale 2959: "Dygyllic"

Scale 2959: Dygyllic, 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
Dygyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,2,3,7,8,9,11}
Forte Number8-5
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3643
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 TriadsG{7,11,2}241.86
G♯{8,0,3}331.43
Minor Triadscm{0,3,7}231.57
g♯m{8,11,3}321.29
Augmented TriadsD♯+{3,7,11}331.43
Diminished Triadsg♯°{8,11,2}231.71
{9,0,3}142.14
Parsimonious Voice Leading Between Common Triads of Scale 2959. Created by Ian Ring ©2019 cm cm D#+ D#+ cm->D#+ G# G# cm->G# Parsimonious Voice Leading Between Common Triads of Scale 2959. Created by Ian Ring ©2019 G D#+->G g#m g#m D#+->g#m g#° g#° G->g#° g#°->g#m g#m->G# G#->a°

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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 Verticesg♯m
Peripheral VerticesG, a°

Modes

Modes are the rotational transformation of this scale. Scale 2959 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3527
Scale 3527: Ronyllic, Ian Ring Music TheoryRonyllic
3rd mode:
Scale 3811
Scale 3811: Epogyllic, Ian Ring Music TheoryEpogyllic
4th mode:
Scale 3953
Scale 3953: Thagyllic, Ian Ring Music TheoryThagyllic
5th mode:
Scale 503
Scale 503: Thoptyllic, Ian Ring Music TheoryThoptyllic
6th mode:
Scale 2299
Scale 2299: Phraptyllic, Ian Ring Music TheoryPhraptyllic
7th mode:
Scale 3197
Scale 3197: Gylyllic, Ian Ring Music TheoryGylyllic
8th mode:
Scale 1823
Scale 1823: Phralyllic, Ian Ring Music TheoryPhralyllic

Prime

The prime form of this scale is Scale 479

Scale 479Scale 479: Kocryllic, Ian Ring Music TheoryKocryllic

Complement

The octatonic modal family [2959, 3527, 3811, 3953, 503, 2299, 3197, 1823] (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 2959 is 3643

Scale 3643Scale 3643: Kydyllic, Ian Ring Music TheoryKydyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2959 is chiral, and its enantiomorph is scale 3643

Scale 3643Scale 3643: Kydyllic, Ian Ring Music TheoryKydyllic

Transformations:

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

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 2957Scale 2957: Thygian, Ian Ring Music TheoryThygian
Scale 2955Scale 2955: Thorian, Ian Ring Music TheoryThorian
Scale 2951Scale 2951, Ian Ring Music Theory
Scale 2967Scale 2967: Madyllic, Ian Ring Music TheoryMadyllic
Scale 2975Scale 2975: Aeroptygic, Ian Ring Music TheoryAeroptygic
Scale 2991Scale 2991: Zanygic, Ian Ring Music TheoryZanygic
Scale 3023Scale 3023: Mothygic, Ian Ring Music TheoryMothygic
Scale 2831Scale 2831, Ian Ring Music Theory
Scale 2895Scale 2895: Aeoryllic, Ian Ring Music TheoryAeoryllic
Scale 2703Scale 2703: Galian, Ian Ring Music TheoryGalian
Scale 2447Scale 2447: Thagian, Ian Ring Music TheoryThagian
Scale 3471Scale 3471: Gyryllic, Ian Ring Music TheoryGyryllic
Scale 3983Scale 3983: Thyptygic, Ian Ring Music TheoryThyptygic
Scale 911Scale 911: Radian, Ian Ring Music TheoryRadian
Scale 1935Scale 1935: Mycryllic, Ian Ring Music TheoryMycryllic

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.