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Scale 2957: "Thygian"

Scale 2957: Thygian, 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
Thygian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,2,3,7,8,9,11}
Forte Number7-Z38
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1595
Hemitonia4 (multihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes6
Prime?no
prime: 439
Deep Scaleno
Interval Vector434442
Interval Spectrump4m4n4s3d4t2
Distribution Spectra<1> = {1,2,4}
<2> = {2,3,5}
<3> = {4,5,6,7}
<4> = {5,6,7,8}
<5> = {7,9,10}
<6> = {8,10,11}
Spectra Variation2.571
Maximally Evenno
Maximal Area Setno
Interior Area2.299
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicyes

Harmonic Chords

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 2957. Created by Ian Ring ©2019 cm cm D#+ D#+ cm->D#+ G# G# cm->G# Parsimonious Voice Leading Between Common Triads of Scale 2957. 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 2957 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 1763
Scale 1763: Katalian, Ian Ring Music TheoryKatalian
3rd mode:
Scale 2929
Scale 2929: Aeolathian, Ian Ring Music TheoryAeolathian
4th mode:
Scale 439
Scale 439: Bythian, Ian Ring Music TheoryBythianThis is the prime mode
5th mode:
Scale 2267
Scale 2267: Padian, Ian Ring Music TheoryPadian
6th mode:
Scale 3181
Scale 3181: Rolian, Ian Ring Music TheoryRolian
7th mode:
Scale 1819
Scale 1819: Pydian, Ian Ring Music TheoryPydian

Prime

The prime form of this scale is Scale 439

Scale 439Scale 439: Bythian, Ian Ring Music TheoryBythian

Complement

The heptatonic modal family [2957, 1763, 2929, 439, 2267, 3181, 1819] (Forte: 7-Z38) is the complement of the pentatonic modal family [295, 625, 905, 2195, 3145] (Forte: 5-Z38)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2957 is 1595

Scale 1595Scale 1595: Dacrian, Ian Ring Music TheoryDacrian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2957 is chiral, and its enantiomorph is scale 1595

Scale 1595Scale 1595: Dacrian, Ian Ring Music TheoryDacrian

Transformations:

T0 2957  T0I 1595
T1 1819  T1I 3190
T2 3638  T2I 2285
T3 3181  T3I 475
T4 2267  T4I 950
T5 439  T5I 1900
T6 878  T6I 3800
T7 1756  T7I 3505
T8 3512  T8I 2915
T9 2929  T9I 1735
T10 1763  T10I 3470
T11 3526  T11I 2845

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 2959Scale 2959: Dygyllic, Ian Ring Music TheoryDygyllic
Scale 2953Scale 2953: Ionylimic, Ian Ring Music TheoryIonylimic
Scale 2955Scale 2955: Thorian, Ian Ring Music TheoryThorian
Scale 2949Scale 2949, Ian Ring Music Theory
Scale 2965Scale 2965: Darian, Ian Ring Music TheoryDarian
Scale 2973Scale 2973: Panyllic, Ian Ring Music TheoryPanyllic
Scale 2989Scale 2989: Bebop Minor, Ian Ring Music TheoryBebop Minor
Scale 3021Scale 3021: Stodyllic, Ian Ring Music TheoryStodyllic
Scale 2829Scale 2829, Ian Ring Music Theory
Scale 2893Scale 2893: Lylian, Ian Ring Music TheoryLylian
Scale 2701Scale 2701: Hawaiian, Ian Ring Music TheoryHawaiian
Scale 2445Scale 2445: Zadimic, Ian Ring Music TheoryZadimic
Scale 3469Scale 3469: Monian, Ian Ring Music TheoryMonian
Scale 3981Scale 3981: Phrycryllic, Ian Ring Music TheoryPhrycryllic
Scale 909Scale 909: Katarimic, Ian Ring Music TheoryKatarimic
Scale 1933Scale 1933: Mocrian, Ian Ring Music TheoryMocrian

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.