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Scale 921: "Bogimic"

Scale 921: Bogimic, 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
Bogimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,3,4,7,8,9}
Forte Number6-Z44
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 825
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes5
Prime?no
prime: 615
Deep Scaleno
Interval Vector313431
Interval Spectrump3m4n3sd3t
Distribution Spectra<1> = {1,3}
<2> = {2,4,6}
<3> = {5,7}
<4> = {6,8,10}
<5> = {9,11}
Spectra Variation2.333
Maximally Evenno
Maximal Area Setno
Interior Area2.25
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 TriadsC{0,4,7}231.5
G♯{8,0,3}321.17
Minor Triadscm{0,3,7}231.5
am{9,0,4}231.5
Augmented TriadsC+{0,4,8}321.17
Diminished Triads{9,0,3}231.5
Parsimonious Voice Leading Between Common Triads of Scale 921. Created by Ian Ring ©2019 cm cm C C cm->C G# G# cm->G# C+ C+ C->C+ C+->G# am am C+->am G#->a° a°->am

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 VerticesC+, G♯
Peripheral Verticescm, C, a°, am

Modes

Modes are the rotational transformation of this scale. Scale 921 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 627
Scale 627: Mogimic, Ian Ring Music TheoryMogimic
3rd mode:
Scale 2361
Scale 2361: Docrimic, Ian Ring Music TheoryDocrimic
4th mode:
Scale 807
Scale 807: Raga Suddha Mukhari, Ian Ring Music TheoryRaga Suddha Mukhari
5th mode:
Scale 2451
Scale 2451: Raga Bauli, Ian Ring Music TheoryRaga Bauli
6th mode:
Scale 3273
Scale 3273: Raga Jivantini, Ian Ring Music TheoryRaga Jivantini

Prime

The prime form of this scale is Scale 615

Scale 615Scale 615: Phrothimic, Ian Ring Music TheoryPhrothimic

Complement

The hexatonic modal family [921, 627, 2361, 807, 2451, 3273] (Forte: 6-Z44) is the complement of the hexatonic modal family [411, 867, 1587, 2253, 2481, 2841] (Forte: 6-Z19)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 921 is 825

Scale 825Scale 825: Thyptimic, Ian Ring Music TheoryThyptimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 921 is chiral, and its enantiomorph is scale 825

Scale 825Scale 825: Thyptimic, Ian Ring Music TheoryThyptimic

Transformations:

T0 921  T0I 825
T1 1842  T1I 1650
T2 3684  T2I 3300
T3 3273  T3I 2505
T4 2451  T4I 915
T5 807  T5I 1830
T6 1614  T6I 3660
T7 3228  T7I 3225
T8 2361  T8I 2355
T9 627  T9I 615
T10 1254  T10I 1230
T11 2508  T11I 2460

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 923Scale 923: Ultraphrygian, Ian Ring Music TheoryUltraphrygian
Scale 925Scale 925: Chromatic Hypodorian, Ian Ring Music TheoryChromatic Hypodorian
Scale 913Scale 913: Aeolyritonic, Ian Ring Music TheoryAeolyritonic
Scale 917Scale 917: Dygimic, Ian Ring Music TheoryDygimic
Scale 905Scale 905: Bylitonic, Ian Ring Music TheoryBylitonic
Scale 937Scale 937: Stothimic, Ian Ring Music TheoryStothimic
Scale 953Scale 953: Mela Yagapriya, Ian Ring Music TheoryMela Yagapriya
Scale 985Scale 985: Mela Sucaritra, Ian Ring Music TheoryMela Sucaritra
Scale 793Scale 793: Mocritonic, Ian Ring Music TheoryMocritonic
Scale 857Scale 857: Aeolydimic, Ian Ring Music TheoryAeolydimic
Scale 665Scale 665: Raga Mohanangi, Ian Ring Music TheoryRaga Mohanangi
Scale 409Scale 409: Laritonic, Ian Ring Music TheoryLaritonic
Scale 1433Scale 1433: Dynimic, Ian Ring Music TheoryDynimic
Scale 1945Scale 1945: Zarian, Ian Ring Music TheoryZarian
Scale 2969Scale 2969: Tholian, Ian Ring Music TheoryTholian

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.