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Scale 2955: "Thorian"

Scale 2955: Thorian, 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
Thorian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,3,7,8,9,11}
Forte Number7-13
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2619
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections4
Modes6
Prime?no
prime: 375
Deep Scaleno
Interval Vector443532
Interval Spectrump3m5n3s4d4t2
Distribution Spectra<1> = {1,2,4}
<2> = {2,3,5,6}
<3> = {4,6,7}
<4> = {5,6,8}
<5> = {6,7,9,10}
<6> = {8,10,11}
Spectra Variation2.857
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♯{8,0,3}321
Minor Triadscm{0,3,7}221.2
g♯m{8,11,3}221.2
Augmented TriadsD♯+{3,7,11}231.4
Diminished Triads{9,0,3}131.6
Parsimonious Voice Leading Between Common Triads of Scale 2955. Created by Ian Ring ©2019 cm cm D#+ D#+ cm->D#+ G# G# cm->G# g#m g#m D#+->g#m g#m->G# G#->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.

Diameter3
Radius2
Self-Centeredno
Central Verticescm, g♯m, G♯
Peripheral VerticesD♯+, a°

Modes

Modes are the rotational transformation of this scale. Scale 2955 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 3525
Scale 3525: Zocrian, Ian Ring Music TheoryZocrian
3rd mode:
Scale 1905
Scale 1905: Katacrian, Ian Ring Music TheoryKatacrian
4th mode:
Scale 375
Scale 375: Sodian, Ian Ring Music TheorySodianThis is the prime mode
5th mode:
Scale 2235
Scale 2235: Bathian, Ian Ring Music TheoryBathian
6th mode:
Scale 3165
Scale 3165: Mylian, Ian Ring Music TheoryMylian
7th mode:
Scale 1815
Scale 1815: Godian, Ian Ring Music TheoryGodian

Prime

The prime form of this scale is Scale 375

Scale 375Scale 375: Sodian, Ian Ring Music TheorySodian

Complement

The heptatonic modal family [2955, 3525, 1905, 375, 2235, 3165, 1815] (Forte: 7-13) is the complement of the pentatonic modal family [279, 369, 1809, 2187, 3141] (Forte: 5-13)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2955 is 2619

Scale 2619Scale 2619: Ionyrian, Ian Ring Music TheoryIonyrian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2955 is chiral, and its enantiomorph is scale 2619

Scale 2619Scale 2619: Ionyrian, Ian Ring Music TheoryIonyrian

Transformations:

T0 2955  T0I 2619
T1 1815  T1I 1143
T2 3630  T2I 2286
T3 3165  T3I 477
T4 2235  T4I 954
T5 375  T5I 1908
T6 750  T6I 3816
T7 1500  T7I 3537
T8 3000  T8I 2979
T9 1905  T9I 1863
T10 3810  T10I 3726
T11 3525  T11I 3357

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 2953Scale 2953: Ionylimic, Ian Ring Music TheoryIonylimic
Scale 2957Scale 2957: Thygian, Ian Ring Music TheoryThygian
Scale 2959Scale 2959: Dygyllic, Ian Ring Music TheoryDygyllic
Scale 2947Scale 2947, Ian Ring Music Theory
Scale 2951Scale 2951, Ian Ring Music Theory
Scale 2963Scale 2963: Bygian, Ian Ring Music TheoryBygian
Scale 2971Scale 2971: Aeolynyllic, Ian Ring Music TheoryAeolynyllic
Scale 2987Scale 2987: Neapolitan Major and Minor Mixed, Ian Ring Music TheoryNeapolitan Major and Minor Mixed
Scale 3019Scale 3019, Ian Ring Music Theory
Scale 2827Scale 2827, Ian Ring Music Theory
Scale 2891Scale 2891: Phrogian, Ian Ring Music TheoryPhrogian
Scale 2699Scale 2699: Sythimic, Ian Ring Music TheorySythimic
Scale 2443Scale 2443: Panimic, Ian Ring Music TheoryPanimic
Scale 3467Scale 3467: Katonian, Ian Ring Music TheoryKatonian
Scale 3979Scale 3979: Dynyllic, Ian Ring Music TheoryDynyllic
Scale 907Scale 907: Tholimic, Ian Ring Music TheoryTholimic
Scale 1931Scale 1931: Stogian, Ian Ring Music TheoryStogian

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.