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Scale 2969: "Tholian"

Scale 2969: Tholian, 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
Tholian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,3,4,7,8,9,11}
Forte Number7-21
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 827
Hemitonia4 (multihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes6
Prime?no
prime: 823
Deep Scaleno
Interval Vector424641
Interval Spectrump4m6n4s2d4t
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4}
<3> = {4,5,6,7}
<4> = {5,6,7,8}
<5> = {8,9,10}
<6> = {9,10,11}
Spectra Variation2
Maximally Evenno
Maximal Area Setno
Interior Area2.433
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 TriadsC{0,4,7}331.7
E{4,8,11}331.7
G♯{8,0,3}431.5
Minor Triadscm{0,3,7}331.7
em{4,7,11}341.9
g♯m{8,11,3}331.7
am{9,0,4}242.1
Augmented TriadsC+{0,4,8}431.5
D♯+{3,7,11}341.9
Diminished Triads{9,0,3}242.1
Parsimonious Voice Leading Between Common Triads of Scale 2969. Created by Ian Ring ©2019 cm cm C C cm->C D#+ D#+ cm->D#+ G# G# cm->G# C+ C+ C->C+ em em C->em E E C+->E C+->G# am am C+->am D#+->em g#m g#m D#+->g#m em->E E->g#m g#m->G# G#->a° a°->am

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
Radius3
Self-Centeredno
Central Verticescm, C, C+, E, g♯m, G♯
Peripheral VerticesD♯+, em, a°, am

Modes

Modes are the rotational transformation of this scale. Scale 2969 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 883
Scale 883: Ralian, Ian Ring Music TheoryRalian
3rd mode:
Scale 2489
Scale 2489: Mela Gangeyabhusani, Ian Ring Music TheoryMela Gangeyabhusani
4th mode:
Scale 823
Scale 823: Stodian, Ian Ring Music TheoryStodianThis is the prime mode
5th mode:
Scale 2459
Scale 2459: Ionocrian, Ian Ring Music TheoryIonocrian
6th mode:
Scale 3277
Scale 3277: Mela Nitimati, Ian Ring Music TheoryMela Nitimati
7th mode:
Scale 1843
Scale 1843: Ionygian, Ian Ring Music TheoryIonygian

Prime

The prime form of this scale is Scale 823

Scale 823Scale 823: Stodian, Ian Ring Music TheoryStodian

Complement

The heptatonic modal family [2969, 883, 2489, 823, 2459, 3277, 1843] (Forte: 7-21) is the complement of the pentatonic modal family [307, 787, 817, 2201, 2441] (Forte: 5-21)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2969 is 827

Scale 827Scale 827: Mixolocrian, Ian Ring Music TheoryMixolocrian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2969 is chiral, and its enantiomorph is scale 827

Scale 827Scale 827: Mixolocrian, Ian Ring Music TheoryMixolocrian

Transformations:

T0 2969  T0I 827
T1 1843  T1I 1654
T2 3686  T2I 3308
T3 3277  T3I 2521
T4 2459  T4I 947
T5 823  T5I 1894
T6 1646  T6I 3788
T7 3292  T7I 3481
T8 2489  T8I 2867
T9 883  T9I 1639
T10 1766  T10I 3278
T11 3532  T11I 2461

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 2971Scale 2971: Aeolynyllic, Ian Ring Music TheoryAeolynyllic
Scale 2973Scale 2973: Panyllic, Ian Ring Music TheoryPanyllic
Scale 2961Scale 2961: Bygimic, Ian Ring Music TheoryBygimic
Scale 2965Scale 2965: Darian, Ian Ring Music TheoryDarian
Scale 2953Scale 2953: Ionylimic, Ian Ring Music TheoryIonylimic
Scale 2985Scale 2985: Epacrian, Ian Ring Music TheoryEpacrian
Scale 3001Scale 3001: Lonyllic, Ian Ring Music TheoryLonyllic
Scale 3033Scale 3033: Doptyllic, Ian Ring Music TheoryDoptyllic
Scale 2841Scale 2841: Sothimic, Ian Ring Music TheorySothimic
Scale 2905Scale 2905: Aeolian Flat 1, Ian Ring Music TheoryAeolian Flat 1
Scale 2713Scale 2713: Porimic, Ian Ring Music TheoryPorimic
Scale 2457Scale 2457: Major Augmented, Ian Ring Music TheoryMajor Augmented
Scale 3481Scale 3481: Katathian, Ian Ring Music TheoryKatathian
Scale 3993Scale 3993: Ioniptyllic, Ian Ring Music TheoryIoniptyllic
Scale 921Scale 921: Bogimic, Ian Ring Music TheoryBogimic
Scale 1945Scale 1945: Zarian, Ian Ring Music TheoryZarian

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.