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Scale 1639: "Aeolothian"

Scale 1639: Aeolothian, 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
Aeolothian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,2,5,6,9,10}
Forte Number7-21
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3277
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 TriadsD{2,6,9}331.7
F{5,9,0}242.1
F♯{6,10,1}331.7
A♯{10,2,5}341.9
Minor Triadsdm{2,5,9}331.7
f♯m{6,9,1}431.5
a♯m{10,1,5}331.7
Augmented TriadsC♯+{1,5,9}431.5
D+{2,6,10}341.9
Diminished Triadsf♯°{6,9,0}242.1
Parsimonious Voice Leading Between Common Triads of Scale 1639. Created by Ian Ring ©2019 C#+ C#+ dm dm C#+->dm F F C#+->F f#m f#m C#+->f#m a#m a#m C#+->a#m D D dm->D A# A# dm->A# D+ D+ D->D+ D->f#m F# F# D+->F# D+->A# f#° f#° F->f#° f#°->f#m f#m->F# F#->a#m a#m->A#

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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 VerticesC♯+, dm, D, f♯m, F♯, a♯m
Peripheral VerticesD+, F, f♯°, A♯

Modes

Modes are the rotational transformation of this scale. Scale 1639 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 2867
Scale 2867: Socrian, Ian Ring Music TheorySocrian
3rd mode:
Scale 3481
Scale 3481: Katathian, Ian Ring Music TheoryKatathian
4th mode:
Scale 947
Scale 947: Mela Gayakapriya, Ian Ring Music TheoryMela Gayakapriya
5th mode:
Scale 2521
Scale 2521: Mela Dhatuvardhani, Ian Ring Music TheoryMela Dhatuvardhani
6th mode:
Scale 827
Scale 827: Mixolocrian, Ian Ring Music TheoryMixolocrian
7th mode:
Scale 2461
Scale 2461: Sagian, Ian Ring Music TheorySagian

Prime

The prime form of this scale is Scale 823

Scale 823Scale 823: Stodian, Ian Ring Music TheoryStodian

Complement

The heptatonic modal family [1639, 2867, 3481, 947, 2521, 827, 2461] (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 1639 is 3277

Scale 3277Scale 3277: Mela Nitimati, Ian Ring Music TheoryMela Nitimati

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1639 is chiral, and its enantiomorph is scale 3277

Scale 3277Scale 3277: Mela Nitimati, Ian Ring Music TheoryMela Nitimati

Transformations:

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

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 1637Scale 1637: Syptimic, Ian Ring Music TheorySyptimic
Scale 1635Scale 1635: Sygimic, Ian Ring Music TheorySygimic
Scale 1643Scale 1643: Locrian Natural 6, Ian Ring Music TheoryLocrian Natural 6
Scale 1647Scale 1647: Polyllic, Ian Ring Music TheoryPolyllic
Scale 1655Scale 1655: Katygyllic, Ian Ring Music TheoryKatygyllic
Scale 1607Scale 1607: Epytimic, Ian Ring Music TheoryEpytimic
Scale 1623Scale 1623: Lothian, Ian Ring Music TheoryLothian
Scale 1575Scale 1575: Zycrimic, Ian Ring Music TheoryZycrimic
Scale 1703Scale 1703: Mela Vanaspati, Ian Ring Music TheoryMela Vanaspati
Scale 1767Scale 1767: Dyryllic, Ian Ring Music TheoryDyryllic
Scale 1895Scale 1895: Salyllic, Ian Ring Music TheorySalyllic
Scale 1127Scale 1127: Eparimic, Ian Ring Music TheoryEparimic
Scale 1383Scale 1383: Pynian, Ian Ring Music TheoryPynian
Scale 615Scale 615: Phrothimic, Ian Ring Music TheoryPhrothimic
Scale 2663Scale 2663: Lalian, Ian Ring Music TheoryLalian
Scale 3687Scale 3687: Zonyllic, Ian Ring Music TheoryZonyllic

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.