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Scale 333: "Bogitonic"

Scale 333: Bogitonic, 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
Bogitonic

Analysis

Cardinality5 (pentatonic)
Pitch Class Set{0,2,3,6,8}
Forte Number5-28
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1617
Hemitonia1 (unhemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections4
Modes4
Prime?yes
Deep Scaleno
Interval Vector122212
Interval Spectrumpm2n2s2dt2
Distribution Spectra<1> = {1,2,3,4}
<2> = {3,4,5,6}
<3> = {6,7,8,9}
<4> = {8,9,10,11}
Spectra Variation2.4
Maximally Evenno
Maximal Area Setno
Interior Area2.049
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}110.5
Diminished Triads{0,3,6}110.5
Parsimonious Voice Leading Between Common Triads of Scale 333. Created by Ian Ring ©2019 G# G# c°->G#

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.

Diameter1
Radius1
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 333 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 1107
Scale 1107: Mogitonic, Ian Ring Music TheoryMogitonic
3rd mode:
Scale 2601
Scale 2601: Raga Chandrakauns, Ian Ring Music TheoryRaga Chandrakauns
4th mode:
Scale 837
Scale 837: Epaditonic, Ian Ring Music TheoryEpaditonic
5th mode:
Scale 1233
Scale 1233: Ionoditonic, Ian Ring Music TheoryIonoditonic

Prime

This is the prime form of this scale.

Complement

The pentatonic modal family [333, 1107, 2601, 837, 1233] (Forte: 5-28) is the complement of the heptatonic modal family [747, 1431, 1629, 1881, 2421, 2763, 3429] (Forte: 7-28)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 333 is 1617

Scale 1617Scale 1617: Phronitonic, Ian Ring Music TheoryPhronitonic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 333 is chiral, and its enantiomorph is scale 1617

Scale 1617Scale 1617: Phronitonic, Ian Ring Music TheoryPhronitonic

Transformations:

T0 333  T0I 1617
T1 666  T1I 3234
T2 1332  T2I 2373
T3 2664  T3I 651
T4 1233  T4I 1302
T5 2466  T5I 2604
T6 837  T6I 1113
T7 1674  T7I 2226
T8 3348  T8I 357
T9 2601  T9I 714
T10 1107  T10I 1428
T11 2214  T11I 2856

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 335Scale 335: Zanimic, Ian Ring Music TheoryZanimic
Scale 329Scale 329: Mynic 2, Ian Ring Music TheoryMynic 2
Scale 331Scale 331: Raga Chhaya Todi, Ian Ring Music TheoryRaga Chhaya Todi
Scale 325Scale 325: Messiaen Truncated Mode 6, Ian Ring Music TheoryMessiaen Truncated Mode 6
Scale 341Scale 341: Bothitonic, Ian Ring Music TheoryBothitonic
Scale 349Scale 349: Borimic, Ian Ring Music TheoryBorimic
Scale 365Scale 365: Marimic, Ian Ring Music TheoryMarimic
Scale 269Scale 269, Ian Ring Music Theory
Scale 301Scale 301: Raga Audav Tukhari, Ian Ring Music TheoryRaga Audav Tukhari
Scale 397Scale 397: Aeolian Pentatonic, Ian Ring Music TheoryAeolian Pentatonic
Scale 461Scale 461: Raga Syamalam, Ian Ring Music TheoryRaga Syamalam
Scale 77Scale 77, Ian Ring Music Theory
Scale 205Scale 205, Ian Ring Music Theory
Scale 589Scale 589: Ionalitonic, Ian Ring Music TheoryIonalitonic
Scale 845Scale 845: Raga Neelangi, Ian Ring Music TheoryRaga Neelangi
Scale 1357Scale 1357: Takemitsu Linea Mode 2, Ian Ring Music TheoryTakemitsu Linea Mode 2
Scale 2381Scale 2381: Takemitsu Linea Mode 1, Ian Ring Music TheoryTakemitsu Linea Mode 1

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.