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Scale 907: "Tholimic"

Scale 907: Tholimic, 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
Tholimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,1,3,7,8,9}
Forte Number6-Z43
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2617
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes5
Prime?no
prime: 359
Deep Scaleno
Interval Vector322332
Interval Spectrump3m3n2s2d3t2
Distribution Spectra<1> = {1,2,3,4}
<2> = {2,3,4,5,6}
<3> = {5,6,7}
<4> = {6,7,8,9,10}
<5> = {8,9,10,11}
Spectra Variation2.667
Maximally Evenno
Maximal Area Setno
Interior Area2.116
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 TriadsG♯{8,0,3}210.67
Minor Triadscm{0,3,7}121
Diminished Triads{9,0,3}121
Parsimonious Voice Leading Between Common Triads of Scale 907. Created by Ian Ring ©2019 cm cm G# G# cm->G# G#->a°

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.

Diameter2
Radius1
Self-Centeredno
Central VerticesG♯
Peripheral Verticescm, a°

Modes

Modes are the rotational transformation of this scale. Scale 907 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 2501
Scale 2501: Ralimic, Ian Ring Music TheoryRalimic
3rd mode:
Scale 1649
Scale 1649: Bolimic, Ian Ring Music TheoryBolimic
4th mode:
Scale 359
Scale 359: Bothimic, Ian Ring Music TheoryBothimicThis is the prime mode
5th mode:
Scale 2227
Scale 2227: Raga Gaula, Ian Ring Music TheoryRaga Gaula
6th mode:
Scale 3161
Scale 3161: Kodimic, Ian Ring Music TheoryKodimic

Prime

The prime form of this scale is Scale 359

Scale 359Scale 359: Bothimic, Ian Ring Music TheoryBothimic

Complement

The hexatonic modal family [907, 2501, 1649, 359, 2227, 3161] (Forte: 6-Z43) is the complement of the hexatonic modal family [407, 739, 1817, 2251, 2417, 3173] (Forte: 6-Z17)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 907 is 2617

Scale 2617Scale 2617: Pylimic, Ian Ring Music TheoryPylimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 907 is chiral, and its enantiomorph is scale 2617

Scale 2617Scale 2617: Pylimic, Ian Ring Music TheoryPylimic

Transformations:

T0 907  T0I 2617
T1 1814  T1I 1139
T2 3628  T2I 2278
T3 3161  T3I 461
T4 2227  T4I 922
T5 359  T5I 1844
T6 718  T6I 3688
T7 1436  T7I 3281
T8 2872  T8I 2467
T9 1649  T9I 839
T10 3298  T10I 1678
T11 2501  T11I 3356

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 905Scale 905: Bylitonic, Ian Ring Music TheoryBylitonic
Scale 909Scale 909: Katarimic, Ian Ring Music TheoryKatarimic
Scale 911Scale 911: Radian, Ian Ring Music TheoryRadian
Scale 899Scale 899, Ian Ring Music Theory
Scale 903Scale 903, Ian Ring Music Theory
Scale 915Scale 915: Raga Kalagada, Ian Ring Music TheoryRaga Kalagada
Scale 923Scale 923: Ultraphrygian, Ian Ring Music TheoryUltraphrygian
Scale 939Scale 939: Mela Senavati, Ian Ring Music TheoryMela Senavati
Scale 971Scale 971: Mela Gavambodhi, Ian Ring Music TheoryMela Gavambodhi
Scale 779Scale 779, Ian Ring Music Theory
Scale 843Scale 843: Molimic, Ian Ring Music TheoryMolimic
Scale 651Scale 651: Golitonic, Ian Ring Music TheoryGolitonic
Scale 395Scale 395: Phrygian Pentatonic, Ian Ring Music TheoryPhrygian Pentatonic
Scale 1419Scale 1419: Raga Kashyapi, Ian Ring Music TheoryRaga Kashyapi
Scale 1931Scale 1931: Stogian, Ian Ring Music TheoryStogian
Scale 2955Scale 2955: Thorian, Ian Ring Music TheoryThorian

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.