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Scale 2837: "Aelothimic"

Scale 2837: Aelothimic, 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
Aelothimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,2,4,8,9,11}
Forte Number6-Z24
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1307
Hemitonia2 (dihemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections3
Modes5
Prime?no
prime: 347
Deep Scaleno
Interval Vector233331
Interval Spectrump3m3n3s3d2t
Distribution Spectra<1> = {1,2,4}
<2> = {3,4,5,6}
<3> = {4,5,7,8}
<4> = {6,7,8,9}
<5> = {8,10,11}
Spectra Variation2.667
Maximally Evenno
Maximal Area Setno
Interior Area2.232
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 TriadsE{4,8,11}221
Minor Triadsam{9,0,4}131.5
Augmented TriadsC+{0,4,8}221
Diminished Triadsg♯°{8,11,2}131.5
Parsimonious Voice Leading Between Common Triads of Scale 2837. Created by Ian Ring ©2019 C+ C+ E E C+->E am am C+->am g#° g#° E->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.

Diameter3
Radius2
Self-Centeredno
Central VerticesC+, E
Peripheral Verticesg♯°, am

Modes

Modes are the rotational transformation of this scale. Scale 2837 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 1733		Scale 1733: Raga Sarasvati, Ian Ring Music TheoryRaga Sarasvati
3rd mode:
Scale 1457		Scale 1457: Raga Kamalamanohari, Ian Ring Music TheoryRaga Kamalamanohari
4th mode:
Scale 347		Scale 347: Barimic, Ian Ring Music TheoryBarimicThis is the prime mode
5th mode:
Scale 2221		Scale 2221: Raga Sindhura Kafi, Ian Ring Music TheoryRaga Sindhura Kafi
6th mode:
Scale 1579		Scale 1579: Sagimic, Ian Ring Music TheorySagimic

Prime

The prime form of this scale is Scale 347

Scale 347Scale 347: Barimic, Ian Ring Music TheoryBarimic

Complement

The hexatonic modal family [2837, 1733, 1457, 347, 2221, 1579] (Forte: 6-Z24) is the complement of the hexatonic modal family [599, 697, 1481, 1829, 2347, 3221] (Forte: 6-Z46)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2837 is 1307

Scale 1307Scale 1307: Katorimic, Ian Ring Music TheoryKatorimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2837 is chiral, and its enantiomorph is scale 1307

Scale 1307Scale 1307: Katorimic, Ian Ring Music TheoryKatorimic

Transformations:

T0 2837  T0I 1307
T1 1579  T1I 2614
T2 3158  T2I 1133
T3 2221  T3I 2266
T4 347  T4I 437
T5 694  T5I 874
T6 1388  T6I 1748
T7 2776  T7I 3496
T8 1457  T8I 2897
T9 2914  T9I 1699
T10 1733  T10I 3398
T11 3466  T11I 2701

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 2839Scale 2839: Lyptian, Ian Ring Music TheoryLyptian
Scale 2833Scale 2833: Dolitonic, Ian Ring Music TheoryDolitonic
Scale 2835Scale 2835: Ionygimic, Ian Ring Music TheoryIonygimic
Scale 2841Scale 2841: Sothimic, Ian Ring Music TheorySothimic
Scale 2845Scale 2845: Baptian, Ian Ring Music TheoryBaptian
Scale 2821Scale 2821, Ian Ring Music Theory
Scale 2829Scale 2829, Ian Ring Music Theory
Scale 2853Scale 2853: Baptimic, Ian Ring Music TheoryBaptimic
Scale 2869Scale 2869: Major Augmented, Ian Ring Music TheoryMajor Augmented
Scale 2901Scale 2901: Lydian Augmented, Ian Ring Music TheoryLydian Augmented
Scale 2965Scale 2965: Darian, Ian Ring Music TheoryDarian
Scale 2581Scale 2581: Raga Neroshta, Ian Ring Music TheoryRaga Neroshta
Scale 2709Scale 2709: Raga Kumud, Ian Ring Music TheoryRaga Kumud
Scale 2325Scale 2325: Pynitonic, Ian Ring Music TheoryPynitonic
Scale 3349Scale 3349: Aeolocrimic, Ian Ring Music TheoryAeolocrimic
Scale 3861Scale 3861: Phroptian, Ian Ring Music TheoryPhroptian
Scale 789Scale 789: Zogitonic, Ian Ring Music TheoryZogitonic
Scale 1813Scale 1813: Katothimic, Ian Ring Music TheoryKatothimic

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.