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Scale 2633: "Bartók Beta Chord"

Scale 2633: Bartók Beta Chord, 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

Named After Composers
Bartók Beta Chord
Zeitler
Mixitonic

Analysis

Cardinality5 (pentatonic)
Pitch Class Set{0,3,6,9,11}
Forte Number5-31
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 587
Hemitonia1 (unhemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections4
Modes4
Prime?no
prime: 587
Deep Scaleno
Interval Vector114112
Interval Spectrumpmn4sdt2
Distribution Spectra<1> = {1,2,3}
<2> = {3,4,5,6}
<3> = {6,7,8,9}
<4> = {9,10,11}
Spectra Variation2
Maximally Evenno
Maximal Area Setno
Interior Area2.183
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyProper
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 TriadsB{11,3,6}221.2
Diminished Triads{0,3,6}221.2
d♯°{3,6,9}221.2
f♯°{6,9,0}221.2
{9,0,3}221.2
Parsimonious Voice Leading Between Common Triads of Scale 2633. Created by Ian Ring ©2019 c°->a° B B c°->B d#° d#° f#° f#° d#°->f#° d#°->B f#°->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
Radius2
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 2633 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 841
Scale 841: Phrothitonic, Ian Ring Music TheoryPhrothitonic
3rd mode:
Scale 617
Scale 617: Katycritonic, Ian Ring Music TheoryKatycritonic
4th mode:
Scale 589
Scale 589: Ionalitonic, Ian Ring Music TheoryIonalitonic
5th mode:
Scale 1171
Scale 1171: Raga Manaranjani I, Ian Ring Music TheoryRaga Manaranjani I

Prime

The prime form of this scale is Scale 587

Scale 587Scale 587: Pathitonic, Ian Ring Music TheoryPathitonic

Complement

The pentatonic modal family [2633, 841, 617, 589, 1171] (Forte: 5-31) is the complement of the heptatonic modal family [731, 1627, 1739, 1753, 2413, 2861, 2917] (Forte: 7-31)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2633 is 587

Scale 587Scale 587: Pathitonic, Ian Ring Music TheoryPathitonic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2633 is chiral, and its enantiomorph is scale 587

Scale 587Scale 587: Pathitonic, Ian Ring Music TheoryPathitonic

Transformations:

T0 2633  T0I 587
T1 1171  T1I 1174
T2 2342  T2I 2348
T3 589  T3I 601
T4 1178  T4I 1202
T5 2356  T5I 2404
T6 617  T6I 713
T7 1234  T7I 1426
T8 2468  T8I 2852
T9 841  T9I 1609
T10 1682  T10I 3218
T11 3364  T11I 2341

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 2635Scale 2635: Gocrimic, Ian Ring Music TheoryGocrimic
Scale 2637Scale 2637: Raga Ranjani, Ian Ring Music TheoryRaga Ranjani
Scale 2625Scale 2625, Ian Ring Music Theory
Scale 2629Scale 2629: Raga Shubravarni, Ian Ring Music TheoryRaga Shubravarni
Scale 2641Scale 2641: Raga Hindol, Ian Ring Music TheoryRaga Hindol
Scale 2649Scale 2649: Aeolythimic, Ian Ring Music TheoryAeolythimic
Scale 2665Scale 2665: Aeradimic, Ian Ring Music TheoryAeradimic
Scale 2569Scale 2569, Ian Ring Music Theory
Scale 2601Scale 2601: Raga Chandrakauns, Ian Ring Music TheoryRaga Chandrakauns
Scale 2697Scale 2697: Katagitonic, Ian Ring Music TheoryKatagitonic
Scale 2761Scale 2761: Dagimic, Ian Ring Music TheoryDagimic
Scale 2889Scale 2889: Thoptimic, Ian Ring Music TheoryThoptimic
Scale 2121Scale 2121, Ian Ring Music Theory
Scale 2377Scale 2377: Bartók Gamma Chord, Ian Ring Music TheoryBartók Gamma Chord
Scale 3145Scale 3145: Stolitonic, Ian Ring Music TheoryStolitonic
Scale 3657Scale 3657: Epynimic, Ian Ring Music TheoryEpynimic
Scale 585Scale 585: Diminished Seventh, Ian Ring Music TheoryDiminished Seventh
Scale 1609Scale 1609: Thyritonic, Ian Ring Music TheoryThyritonic

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.