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Scale 687: "Aeolythian"

Scale 687: Aeolythian, 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
Aeolythian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,2,3,5,7,9}
Forte Number7-24
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3753
Hemitonia3 (trihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections3
Modes6
Prime?yes
Deep Scaleno
Interval Vector353442
Interval Spectrump4m4n3s5d3t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {3,4,5,6,7}
<4> = {5,6,7,8,9}
<5> = {7,8,9,10}
<6> = {9,10,11}
Spectra Variation2.571
Maximally Evenno
Maximal Area Setno
Interior Area2.549
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 TriadsF{5,9,0}221.2
Minor Triadscm{0,3,7}142
dm{2,5,9}142
Augmented TriadsC♯+{1,5,9}231.4
Diminished Triads{9,0,3}231.4
Parsimonious Voice Leading Between Common Triads of Scale 687. Created by Ian Ring ©2019 cm cm cm->a° C#+ C#+ dm dm C#+->dm F F C#+->F F->a°

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.

Diameter4
Radius2
Self-Centeredno
Central VerticesF
Peripheral Verticescm, dm

Modes

Modes are the rotational transformation of this scale. Scale 687 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 2391
Scale 2391: Molian, Ian Ring Music TheoryMolian
3rd mode:
Scale 3243
Scale 3243: Mela Rupavati, Ian Ring Music TheoryMela Rupavati
4th mode:
Scale 3669
Scale 3669: Mothian, Ian Ring Music TheoryMothian
5th mode:
Scale 1941
Scale 1941: Aeranian, Ian Ring Music TheoryAeranian
6th mode:
Scale 1509
Scale 1509: Ragian, Ian Ring Music TheoryRagian
7th mode:
Scale 1401
Scale 1401: Pagian, Ian Ring Music TheoryPagian

Prime

This is the prime form of this scale.

Complement

The heptatonic modal family [687, 2391, 3243, 3669, 1941, 1509, 1401] (Forte: 7-24) is the complement of the pentatonic modal family [171, 1377, 1413, 1557, 2133] (Forte: 5-24)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 687 is 3753

Scale 3753Scale 3753: Phraptian, Ian Ring Music TheoryPhraptian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 687 is chiral, and its enantiomorph is scale 3753

Scale 3753Scale 3753: Phraptian, Ian Ring Music TheoryPhraptian

Transformations:

T0 687  T0I 3753
T1 1374  T1I 3411
T2 2748  T2I 2727
T3 1401  T3I 1359
T4 2802  T4I 2718
T5 1509  T5I 1341
T6 3018  T6I 2682
T7 1941  T7I 1269
T8 3882  T8I 2538
T9 3669  T9I 981
T10 3243  T10I 1962
T11 2391  T11I 3924

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 685Scale 685: Raga Suddha Bangala, Ian Ring Music TheoryRaga Suddha Bangala
Scale 683Scale 683: Stogimic, Ian Ring Music TheoryStogimic
Scale 679Scale 679: Lanimic, Ian Ring Music TheoryLanimic
Scale 695Scale 695: Sarian, Ian Ring Music TheorySarian
Scale 703Scale 703: Aerocryllic, Ian Ring Music TheoryAerocryllic
Scale 655Scale 655: Kataptimic, Ian Ring Music TheoryKataptimic
Scale 671Scale 671: Stycrian, Ian Ring Music TheoryStycrian
Scale 719Scale 719: Kanian, Ian Ring Music TheoryKanian
Scale 751Scale 751, Ian Ring Music Theory
Scale 559Scale 559: Lylimic, Ian Ring Music TheoryLylimic
Scale 623Scale 623: Sycrian, Ian Ring Music TheorySycrian
Scale 815Scale 815: Bolian, Ian Ring Music TheoryBolian
Scale 943Scale 943: Aerygyllic, Ian Ring Music TheoryAerygyllic
Scale 175Scale 175, Ian Ring Music Theory
Scale 431Scale 431: Epyrian, Ian Ring Music TheoryEpyrian
Scale 1199Scale 1199: Magian, Ian Ring Music TheoryMagian
Scale 1711Scale 1711: Adonai Malakh, Ian Ring Music TheoryAdonai Malakh
Scale 2735Scale 2735: Gynyllic, Ian Ring Music TheoryGynyllic

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. Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography.