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Scale 367: "Aerodian"

Scale 367: Aerodian, 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
Aerodian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,2,3,5,6,8}
Forte Number7-Z36
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3793
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections3
Modes6
Prime?yes
Deep Scaleno
Interval Vector444342
Interval Spectrump4m3n4s4d4t2
Distribution Spectra<1> = {1,2,4}
<2> = {2,3,5,6}
<3> = {3,4,5,6,7}
<4> = {5,6,7,8,9}
<5> = {6,7,9,10}
<6> = {8,10,11}
Spectra Variation3.143
Maximally Evenno
Maximal Area Setno
Interior Area2.299
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 TriadsC♯{1,5,8}231.4
G♯{8,0,3}231.4
Minor Triadsfm{5,8,0}221.2
Diminished Triads{0,3,6}142
{2,5,8}142
Parsimonious Voice Leading Between Common Triads of Scale 367. Created by Ian Ring ©2019 G# G# c°->G# C# C# C#->d° fm fm C#->fm fm->G#

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 Verticesfm
Peripheral Verticesc°, d°

Modes

Modes are the rotational transformation of this scale. Scale 367 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 2231
Scale 2231: Macrian, Ian Ring Music TheoryMacrian
3rd mode:
Scale 3163
Scale 3163: Rogian, Ian Ring Music TheoryRogian
4th mode:
Scale 3629
Scale 3629: Boptian, Ian Ring Music TheoryBoptian
5th mode:
Scale 1931
Scale 1931: Stogian, Ian Ring Music TheoryStogian
6th mode:
Scale 3013
Scale 3013: Thynian, Ian Ring Music TheoryThynian
7th mode:
Scale 1777
Scale 1777: Saptian, Ian Ring Music TheorySaptian

Prime

This is the prime form of this scale.

Complement

The heptatonic modal family [367, 2231, 3163, 3629, 1931, 3013, 1777] (Forte: 7-Z36) is the complement of the pentatonic modal family [151, 737, 1801, 2123, 3109] (Forte: 5-Z36)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 367 is 3793

Scale 3793Scale 3793: Aeopian, Ian Ring Music TheoryAeopian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 367 is chiral, and its enantiomorph is scale 3793

Scale 3793Scale 3793: Aeopian, Ian Ring Music TheoryAeopian

Transformations:

T0 367  T0I 3793
T1 734  T1I 3491
T2 1468  T2I 2887
T3 2936  T3I 1679
T4 1777  T4I 3358
T5 3554  T5I 2621
T6 3013  T6I 1147
T7 1931  T7I 2294
T8 3862  T8I 493
T9 3629  T9I 986
T10 3163  T10I 1972
T11 2231  T11I 3944

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 365Scale 365: Marimic, Ian Ring Music TheoryMarimic
Scale 363Scale 363: Soptimic, Ian Ring Music TheorySoptimic
Scale 359Scale 359: Bothimic, Ian Ring Music TheoryBothimic
Scale 375Scale 375: Sodian, Ian Ring Music TheorySodian
Scale 383Scale 383: Logyllic, Ian Ring Music TheoryLogyllic
Scale 335Scale 335: Zanimic, Ian Ring Music TheoryZanimic
Scale 351Scale 351: Epanian, Ian Ring Music TheoryEpanian
Scale 303Scale 303: Golimic, Ian Ring Music TheoryGolimic
Scale 431Scale 431: Epyrian, Ian Ring Music TheoryEpyrian
Scale 495Scale 495: Bocryllic, Ian Ring Music TheoryBocryllic
Scale 111Scale 111, Ian Ring Music Theory
Scale 239Scale 239, Ian Ring Music Theory
Scale 623Scale 623: Sycrian, Ian Ring Music TheorySycrian
Scale 879Scale 879: Aeranyllic, Ian Ring Music TheoryAeranyllic
Scale 1391Scale 1391: Aeradyllic, Ian Ring Music TheoryAeradyllic
Scale 2415Scale 2415: Lothyllic, Ian Ring Music TheoryLothyllic

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.