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Scale 951: "Thogyllic"

Scale 951: Thogyllic, 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

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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
Thogyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,2,4,5,7,8,9}
Forte Number8-20
Rotational Symmetrynone
Reflection Axes4.5
Palindromicno
Chiralityno
Hemitonia5 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections2
Modes7
Prime?yes
Deep Scaleno
Interval Vector545662
Interval Spectrump6m6n5s4d5t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4}
<3> = {4,5}
<4> = {5,6,7}
<5> = {7,8}
<6> = {8,9,10}
<7> = {9,10,11}
Spectra Variation1.5
Maximally Evenno
Maximal Area Setno
Interior Area2.616
Myhill Propertyno
Balancedno
Ridge Tones[9]
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}252.5
C♯{1,5,8}431.67
F{5,9,0}342
A{9,1,4}331.83
Minor Triadsc♯m{1,4,8}431.67
dm{2,5,9}252.5
fm{5,8,0}331.83
am{9,0,4}342
Augmented TriadsC+{0,4,8}441.83
C♯+{1,5,9}441.83
Diminished Triadsc♯°{1,4,7}242.33
{2,5,8}242.33
Parsimonious Voice Leading Between Common Triads of Scale 951. 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 am am C+->am c#°->c#m C# C# c#m->C# A A c#m->A C#+ C#+ C#->C#+ C#->d° C#->fm dm dm C#+->dm F F C#+->F C#+->A d°->dm fm->F F->am am->A

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.

Diameter5
Radius3
Self-Centeredno
Central Verticesc♯m, C♯, fm, A
Peripheral VerticesC, dm

Modes

Modes are the rotational transformation of this scale. Scale 951 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 2523
Scale 2523: Mirage Scale, Ian Ring Music TheoryMirage Scale
3rd mode:
Scale 3309
Scale 3309: Bycryllic, Ian Ring Music TheoryBycryllic
4th mode:
Scale 1851
Scale 1851: Zacryllic, Ian Ring Music TheoryZacryllic
5th mode:
Scale 2973
Scale 2973: Panyllic, Ian Ring Music TheoryPanyllic
6th mode:
Scale 1767
Scale 1767: Dyryllic, Ian Ring Music TheoryDyryllic
7th mode:
Scale 2931
Scale 2931: Zathyllic, Ian Ring Music TheoryZathyllic
8th mode:
Scale 3513
Scale 3513: Dydyllic, Ian Ring Music TheoryDydyllic

Prime

This is the prime form of this scale.

Complement

The octatonic modal family [951, 2523, 3309, 1851, 2973, 1767, 2931, 3513] (Forte: 8-20) is the complement of the tetratonic modal family [291, 393, 561, 2193] (Forte: 4-20)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 951 is 3513

Scale 3513Scale 3513: Dydyllic, Ian Ring Music TheoryDydyllic

Transformations:

T0 951  T0I 3513
T1 1902  T1I 2931
T2 3804  T2I 1767
T3 3513  T3I 3534
T4 2931  T4I 2973
T5 1767  T5I 1851
T6 3534  T6I 3702
T7 2973  T7I 3309
T8 1851  T8I 2523
T9 3702  T9I 951
T10 3309  T10I 1902
T11 2523  T11I 3804

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 949Scale 949: Mela Mararanjani, Ian Ring Music TheoryMela Mararanjani
Scale 947Scale 947: Mela Gayakapriya, Ian Ring Music TheoryMela Gayakapriya
Scale 955Scale 955: Ionogyllic, Ian Ring Music TheoryIonogyllic
Scale 959Scale 959: Katylygic, Ian Ring Music TheoryKatylygic
Scale 935Scale 935: Chromatic Dorian, Ian Ring Music TheoryChromatic Dorian
Scale 943Scale 943: Aerygyllic, Ian Ring Music TheoryAerygyllic
Scale 919Scale 919: Chromatic Phrygian Inverse, Ian Ring Music TheoryChromatic Phrygian Inverse
Scale 983Scale 983: Thocryllic, Ian Ring Music TheoryThocryllic
Scale 1015Scale 1015: Ionodygic, Ian Ring Music TheoryIonodygic
Scale 823Scale 823: Stodian, Ian Ring Music TheoryStodian
Scale 887Scale 887: Sathyllic, Ian Ring Music TheorySathyllic
Scale 695Scale 695: Sarian, Ian Ring Music TheorySarian
Scale 439Scale 439: Bythian, Ian Ring Music TheoryBythian
Scale 1463Scale 1463, Ian Ring Music Theory
Scale 1975Scale 1975: Ionocrygic, Ian Ring Music TheoryIonocrygic
Scale 2999Scale 2999: Chromatic and Permuted Diatonic Dorian Mixed, Ian Ring Music TheoryChromatic and Permuted Diatonic Dorian Mixed

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. Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography.