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Scale 2639: "Dothian"

Scale 2639: Dothian, 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
Dothian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,2,3,6,9,11}
Forte Number7-10
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3659
Hemitonia4 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections4
Modes6
Prime?no
prime: 607
Deep Scaleno
Interval Vector445332
Interval Spectrump3m3n5s4d4t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5,6}
<3> = {3,4,5,6,7,8}
<4> = {4,5,6,7,8,9}
<5> = {6,7,8,9,10}
<6> = {9,10,11}
Spectra Variation3.143
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 TriadsD{2,6,9}331.63
B{11,3,6}331.63
Minor Triadsf♯m{6,9,1}231.75
bm{11,2,6}231.75
Diminished Triads{0,3,6}231.75
d♯°{3,6,9}231.75
f♯°{6,9,0}231.88
{9,0,3}231.88
Parsimonious Voice Leading Between Common Triads of Scale 2639. Created by Ian Ring ©2019 c°->a° B B c°->B D D d#° d#° D->d#° f#m f#m D->f#m bm bm D->bm d#°->B f#° f#° f#°->f#m f#°->a° bm->B

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.

Diameter3
Radius3
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 2639 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 3367
Scale 3367: Moptian, Ian Ring Music TheoryMoptian
3rd mode:
Scale 3731
Scale 3731: Aeryrian, Ian Ring Music TheoryAeryrian
4th mode:
Scale 3913
Scale 3913: Bonian, Ian Ring Music TheoryBonian
5th mode:
Scale 1001
Scale 1001: Badian, Ian Ring Music TheoryBadian
6th mode:
Scale 637
Scale 637: Debussy's Heptatonic, Ian Ring Music TheoryDebussy's Heptatonic
7th mode:
Scale 1183
Scale 1183: Sadian, Ian Ring Music TheorySadian

Prime

The prime form of this scale is Scale 607

Scale 607Scale 607: Kadian, Ian Ring Music TheoryKadian

Complement

The heptatonic modal family [2639, 3367, 3731, 3913, 1001, 637, 1183] (Forte: 7-10) is the complement of the pentatonic modal family [91, 1547, 1729, 2093, 2821] (Forte: 5-10)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2639 is 3659

Scale 3659Scale 3659: Polian, Ian Ring Music TheoryPolian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2639 is chiral, and its enantiomorph is scale 3659

Scale 3659Scale 3659: Polian, Ian Ring Music TheoryPolian

Transformations:

T0 2639  T0I 3659
T1 1183  T1I 3223
T2 2366  T2I 2351
T3 637  T3I 607
T4 1274  T4I 1214
T5 2548  T5I 2428
T6 1001  T6I 761
T7 2002  T7I 1522
T8 4004  T8I 3044
T9 3913  T9I 1993
T10 3731  T10I 3986
T11 3367  T11I 3877

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 2637Scale 2637: Raga Ranjani, Ian Ring Music TheoryRaga Ranjani
Scale 2635Scale 2635: Gocrimic, Ian Ring Music TheoryGocrimic
Scale 2631Scale 2631: Macrimic, Ian Ring Music TheoryMacrimic
Scale 2647Scale 2647: Dadian, Ian Ring Music TheoryDadian
Scale 2655Scale 2655, Ian Ring Music Theory
Scale 2671Scale 2671: Aerolyllic, Ian Ring Music TheoryAerolyllic
Scale 2575Scale 2575, Ian Ring Music Theory
Scale 2607Scale 2607: Aerolian, Ian Ring Music TheoryAerolian
Scale 2703Scale 2703: Galian, Ian Ring Music TheoryGalian
Scale 2767Scale 2767: Katydyllic, Ian Ring Music TheoryKatydyllic
Scale 2895Scale 2895: Aeoryllic, Ian Ring Music TheoryAeoryllic
Scale 2127Scale 2127, Ian Ring Music Theory
Scale 2383Scale 2383: Katorian, Ian Ring Music TheoryKatorian
Scale 3151Scale 3151: Pacrian, Ian Ring Music TheoryPacrian
Scale 3663Scale 3663: Sonyllic, Ian Ring Music TheorySonyllic
Scale 591Scale 591: Gaptimic, Ian Ring Music TheoryGaptimic
Scale 1615Scale 1615: Sydian, Ian Ring Music TheorySydian

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.