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Scale 503: "Thoptyllic"

Scale 503: Thoptyllic, 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
Thoptyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,2,4,5,6,7,8}
Forte Number8-5
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3569
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 TriadsC{0,4,7}241.86
C♯{1,5,8}331.43
Minor Triadsc♯m{1,4,8}321.29
fm{5,8,0}231.57
Augmented TriadsC+{0,4,8}331.43
Diminished Triadsc♯°{1,4,7}231.71
{2,5,8}142.14
Parsimonious Voice Leading Between Common Triads of Scale 503. Created by Ian Ring ©2019 C C C+ C+ C->C+ c#° c#° C->c#° c#m c#m C+->c#m fm fm C+->fm c#°->c#m C# C# c#m->C# C#->d° C#->fm

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 Verticesc♯m
Peripheral VerticesC, d°

Modes

Modes are the rotational transformation of this scale. Scale 503 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 2299
Scale 2299: Phraptyllic, Ian Ring Music TheoryPhraptyllic
3rd mode:
Scale 3197
Scale 3197: Gylyllic, Ian Ring Music TheoryGylyllic
4th mode:
Scale 1823
Scale 1823: Phralyllic, Ian Ring Music TheoryPhralyllic
5th mode:
Scale 2959
Scale 2959: Dygyllic, Ian Ring Music TheoryDygyllic
6th mode:
Scale 3527
Scale 3527: Ronyllic, Ian Ring Music TheoryRonyllic
7th mode:
Scale 3811
Scale 3811: Epogyllic, Ian Ring Music TheoryEpogyllic
8th mode:
Scale 3953
Scale 3953: Thagyllic, Ian Ring Music TheoryThagyllic

Prime

The prime form of this scale is Scale 479

Scale 479Scale 479: Kocryllic, Ian Ring Music TheoryKocryllic

Complement

The octatonic modal family [503, 2299, 3197, 1823, 2959, 3527, 3811, 3953] (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 503 is 3569

Scale 3569Scale 3569: Aeoladyllic, Ian Ring Music TheoryAeoladyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 503 is chiral, and its enantiomorph is scale 3569

Scale 3569Scale 3569: Aeoladyllic, Ian Ring Music TheoryAeoladyllic

Transformations:

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

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 501Scale 501: Katylian, Ian Ring Music TheoryKatylian
Scale 499Scale 499: Ionaptian, Ian Ring Music TheoryIonaptian
Scale 507Scale 507: Moryllic, Ian Ring Music TheoryMoryllic
Scale 511Scale 511: Polygic, Ian Ring Music TheoryPolygic
Scale 487Scale 487: Dynian, Ian Ring Music TheoryDynian
Scale 495Scale 495: Bocryllic, Ian Ring Music TheoryBocryllic
Scale 471Scale 471: Dodian, Ian Ring Music TheoryDodian
Scale 439Scale 439: Bythian, Ian Ring Music TheoryBythian
Scale 375Scale 375: Sodian, Ian Ring Music TheorySodian
Scale 247Scale 247, Ian Ring Music Theory
Scale 759Scale 759: Katalyllic, Ian Ring Music TheoryKatalyllic
Scale 1015Scale 1015: Ionodygic, Ian Ring Music TheoryIonodygic
Scale 1527Scale 1527: Aeolyrigic, Ian Ring Music TheoryAeolyrigic
Scale 2551Scale 2551: Thocrygic, Ian Ring Music TheoryThocrygic

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.