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Scale 821: "Aeranimic"

Scale 821: Aeranimic, 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
Aeranimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,2,4,5,8,9}
Forte Number6-31
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1433
Hemitonia2 (dihemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections3
Modes5
Prime?no
prime: 691
Deep Scaleno
Interval Vector223431
Interval Spectrump3m4n3s2d2t
Distribution Spectra<1> = {1,2,3}
<2> = {3,4,5}
<3> = {5,6,7}
<4> = {7,8,9}
<5> = {9,10,11}
Spectra Variation1.667
Maximally Evenno
Maximal Area Setno
Interior Area2.366
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 TriadsF{5,9,0}321.17
Minor Triadsdm{2,5,9}231.5
fm{5,8,0}321.17
am{9,0,4}231.5
Augmented TriadsC+{0,4,8}231.5
Diminished Triads{2,5,8}231.5
Parsimonious Voice Leading Between Common Triads of Scale 821. Created by Ian Ring ©2019 C+ C+ fm fm C+->fm am am C+->am dm dm d°->dm d°->fm F F dm->F fm->F F->am

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 Verticesfm, F
Peripheral VerticesC+, d°, dm, am

Modes

Modes are the rotational transformation of this scale. Scale 821 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 1229
Scale 1229: Raga Simharava, Ian Ring Music TheoryRaga Simharava
3rd mode:
Scale 1331
Scale 1331: Raga Vasantabhairavi, Ian Ring Music TheoryRaga Vasantabhairavi
4th mode:
Scale 2713
Scale 2713: Porimic, Ian Ring Music TheoryPorimic
5th mode:
Scale 851
Scale 851: Raga Hejjajji, Ian Ring Music TheoryRaga Hejjajji
6th mode:
Scale 2473
Scale 2473: Raga Takka, Ian Ring Music TheoryRaga Takka

Prime

The prime form of this scale is Scale 691

Scale 691Scale 691: Raga Kalavati, Ian Ring Music TheoryRaga Kalavati

Complement

The hexatonic modal family [821, 1229, 1331, 2713, 851, 2473] (Forte: 6-31) is the complement of the hexatonic modal family [691, 811, 1433, 1637, 2393, 2453] (Forte: 6-31)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 821 is 1433

Scale 1433Scale 1433: Dynimic, Ian Ring Music TheoryDynimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 821 is chiral, and its enantiomorph is scale 1433

Scale 1433Scale 1433: Dynimic, Ian Ring Music TheoryDynimic

Transformations:

T0 821  T0I 1433
T1 1642  T1I 2866
T2 3284  T2I 1637
T3 2473  T3I 3274
T4 851  T4I 2453
T5 1702  T5I 811
T6 3404  T6I 1622
T7 2713  T7I 3244
T8 1331  T8I 2393
T9 2662  T9I 691
T10 1229  T10I 1382
T11 2458  T11I 2764

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 823Scale 823: Stodian, Ian Ring Music TheoryStodian
Scale 817Scale 817: Zothitonic, Ian Ring Music TheoryZothitonic
Scale 819Scale 819: Augmented Inverse, Ian Ring Music TheoryAugmented Inverse
Scale 825Scale 825: Thyptimic, Ian Ring Music TheoryThyptimic
Scale 829Scale 829: Lygian, Ian Ring Music TheoryLygian
Scale 805Scale 805: Rothitonic, Ian Ring Music TheoryRothitonic
Scale 813Scale 813: Larimic, Ian Ring Music TheoryLarimic
Scale 789Scale 789: Zogitonic, Ian Ring Music TheoryZogitonic
Scale 853Scale 853: Epothimic, Ian Ring Music TheoryEpothimic
Scale 885Scale 885: Sathian, Ian Ring Music TheorySathian
Scale 949Scale 949: Mela Mararanjani, Ian Ring Music TheoryMela Mararanjani
Scale 565Scale 565: Aeolyphritonic, Ian Ring Music TheoryAeolyphritonic
Scale 693Scale 693: Arezzo Major Diatonic Hexachord, Ian Ring Music TheoryArezzo Major Diatonic Hexachord
Scale 309Scale 309: Palitonic, Ian Ring Music TheoryPalitonic
Scale 1333Scale 1333: Lyptimic, Ian Ring Music TheoryLyptimic
Scale 1845Scale 1845: Lagian, Ian Ring Music TheoryLagian
Scale 2869Scale 2869: Major Augmented, Ian Ring Music TheoryMajor Augmented

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.