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Scale 3953: "Thagyllic"

Scale 3953: Thagyllic, 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
Thagyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,4,5,6,8,9,10,11}
Forte Number8-5
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 479
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}241.86
F{5,9,0}331.43
Minor Triadsfm{5,8,0}321.29
am{9,0,4}231.57
Augmented TriadsC+{0,4,8}331.43
Diminished Triads{5,8,11}231.71
f♯°{6,9,0}142.14
Parsimonious Voice Leading Between Common Triads of Scale 3953. Created by Ian Ring ©2019 C+ C+ E E C+->E fm fm C+->fm am am C+->am E->f° f°->fm F F fm->F f#° f#° F->f#° F->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 Verticesfm
Peripheral VerticesE, f♯°

Modes

Modes are the rotational transformation of this scale. Scale 3953 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 503
Scale 503: Thoptyllic, Ian Ring Music TheoryThoptyllic
3rd mode:
Scale 2299
Scale 2299: Phraptyllic, Ian Ring Music TheoryPhraptyllic
4th mode:
Scale 3197
Scale 3197: Gylyllic, Ian Ring Music TheoryGylyllic
5th mode:
Scale 1823
Scale 1823: Phralyllic, Ian Ring Music TheoryPhralyllic
6th mode:
Scale 2959
Scale 2959: Dygyllic, Ian Ring Music TheoryDygyllic
7th mode:
Scale 3527
Scale 3527: Ronyllic, Ian Ring Music TheoryRonyllic
8th mode:
Scale 3811
Scale 3811: Epogyllic, Ian Ring Music TheoryEpogyllic

Prime

The prime form of this scale is Scale 479

Scale 479Scale 479: Kocryllic, Ian Ring Music TheoryKocryllic

Complement

The octatonic modal family [3953, 503, 2299, 3197, 1823, 2959, 3527, 3811] (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 3953 is 479

Scale 479Scale 479: Kocryllic, Ian Ring Music TheoryKocryllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3953 is chiral, and its enantiomorph is scale 479

Scale 479Scale 479: Kocryllic, Ian Ring Music TheoryKocryllic

Transformations:

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

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 3955Scale 3955: Pothygic, Ian Ring Music TheoryPothygic
Scale 3957Scale 3957: Porygic, Ian Ring Music TheoryPorygic
Scale 3961Scale 3961: Zathygic, Ian Ring Music TheoryZathygic
Scale 3937Scale 3937, Ian Ring Music Theory
Scale 3945Scale 3945: Lydyllic, Ian Ring Music TheoryLydyllic
Scale 3921Scale 3921: Pythian, Ian Ring Music TheoryPythian
Scale 3889Scale 3889: Parian, Ian Ring Music TheoryParian
Scale 4017Scale 4017: Dolyllic, Ian Ring Music TheoryDolyllic
Scale 4081Scale 4081: Manygic, Ian Ring Music TheoryManygic
Scale 3697Scale 3697: Ionarian, Ian Ring Music TheoryIonarian
Scale 3825Scale 3825: Pynyllic, Ian Ring Music TheoryPynyllic
Scale 3441Scale 3441: Thacrian, Ian Ring Music TheoryThacrian
Scale 2929Scale 2929: Aeolathian, Ian Ring Music TheoryAeolathian
Scale 1905Scale 1905: Katacrian, Ian Ring Music TheoryKatacrian

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.