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Scale 3421: "Aerothyllic"

Scale 3421: Aerothyllic, 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.

Tonnetz Diagram

41161837294116105072918310504116183
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
Aerothyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,2,3,4,6,8,10,11}
Forte Number8-24
Rotational Symmetrynone
Reflection Axes1
Palindromicno
Chiralityno
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections4
Modes7
Prime?no
prime: 1399
Deep Scaleno
Interval Vector464743
Interval Spectrump4m7n4s6d4t3
Distribution Spectra<1> = {1,2}
<2> = {2,3,4}
<3> = {4,5,6}
<4> = {5,6,7}
<5> = {6,7,8}
<6> = {8,9,10}
<7> = {10,11}
Spectra Variation1.5
Maximally Evenno
Myhill Propertyno
Balancedno
Ridge Tones[2]
Coherenceno
Heliotonicno

Modes

Modes are the rotational transformation of this scale. Scale 3421 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 1879
Scale 1879: Mixoryllic, Ian Ring Music TheoryMixoryllic
3rd mode:
Scale 2987
Scale 2987: Neapolitan Major and Minor Mixed, Ian Ring Music TheoryNeapolitan Major and Minor Mixed
4th mode:
Scale 3541
Scale 3541: Racryllic, Ian Ring Music TheoryRacryllic
5th mode:
Scale 1909
Scale 1909: Epicryllic, Ian Ring Music TheoryEpicryllic
6th mode:
Scale 1501
Scale 1501: Stygyllic, Ian Ring Music TheoryStygyllic
7th mode:
Scale 1399
Scale 1399: Syryllic, Ian Ring Music TheorySyryllicThis is the prime mode
8th mode:
Scale 2747
Scale 2747: Stythyllic, Ian Ring Music TheoryStythyllic

Prime

The prime form of this scale is Scale 1399

Scale 1399Scale 1399: Syryllic, Ian Ring Music TheorySyryllic

Complement

The octatonic modal family [3421, 1879, 2987, 3541, 1909, 1501, 1399, 2747] (Forte: 8-24) is the complement of the tetratonic modal family [277, 337, 1093, 1297] (Forte: 4-24)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3421 is 1879

Scale 1879Scale 1879: Mixoryllic, Ian Ring Music TheoryMixoryllic

Transformations:

T0 3421  T0I 1879
T1 2747  T1I 3758
T2 1399  T2I 3421
T3 2798  T3I 2747
T4 1501  T4I 1399
T5 3002  T5I 2798
T6 1909  T6I 1501
T7 3818  T7I 3002
T8 3541  T8I 1909
T9 2987  T9I 3818
T10 1879  T10I 3541
T11 3758  T11I 2987

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 3423Scale 3423: Lothygic, Ian Ring Music TheoryLothygic
Scale 3417Scale 3417: Golian, Ian Ring Music TheoryGolian
Scale 3419Scale 3419: Magen Abot 1, Ian Ring Music TheoryMagen Abot 1
Scale 3413Scale 3413: Leading Whole-tone, Ian Ring Music TheoryLeading Whole-tone
Scale 3405Scale 3405: Stynian, Ian Ring Music TheoryStynian
Scale 3437Scale 3437, Ian Ring Music Theory
Scale 3453Scale 3453: Katarygic, Ian Ring Music TheoryKatarygic
Scale 3357Scale 3357: Phrodian, Ian Ring Music TheoryPhrodian
Scale 3389Scale 3389: Socryllic, Ian Ring Music TheorySocryllic
Scale 3485Scale 3485: Sabach, Ian Ring Music TheorySabach
Scale 3549Scale 3549: Messiaen Mode 3 Inverse, Ian Ring Music TheoryMessiaen Mode 3 Inverse
Scale 3165Scale 3165: Mylian, Ian Ring Music TheoryMylian
Scale 3293Scale 3293: Saryllic, Ian Ring Music TheorySaryllic
Scale 3677Scale 3677, Ian Ring Music Theory
Scale 3933Scale 3933: Ionidygic, Ian Ring Music TheoryIonidygic
Scale 2397Scale 2397: Stagian, Ian Ring Music TheoryStagian
Scale 2909Scale 2909: Mocryllic, Ian Ring Music TheoryMocryllic
Scale 1373Scale 1373: Storian, Ian Ring Music TheoryStorian

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, and MIDI playback by MIDI.js. Bibliography