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Scale 3211: "Epacrimic"

Scale 3211: Epacrimic, 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

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
Epacrimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,1,3,7,10,11}
Forte Number6-Z39
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2599
Hemitonia3 (trihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections4
Modes5
Prime?no
prime: 317
Deep Scaleno
Interval Vector333321
Interval Spectrump2m3n3s3d3t
Distribution Spectra<1> = {1,2,3,4}
<2> = {2,3,4,6,7}
<3> = {3,4,5,7,8,9}
<4> = {5,6,8,9,10}
<5> = {8,9,10,11}
Spectra Variation3.667
Maximally Evenno
Maximal Area Setno
Interior Area2.116
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicno

Modes

Modes are the rotational transformation of this scale. Scale 3211 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 3653
Scale 3653: Sathimic, Ian Ring Music TheorySathimic
3rd mode:
Scale 1937
Scale 1937: Galimic, Ian Ring Music TheoryGalimic
4th mode:
Scale 377
Scale 377: Kathimic, Ian Ring Music TheoryKathimic
5th mode:
Scale 559
Scale 559: Lylimic, Ian Ring Music TheoryLylimic
6th mode:
Scale 2327
Scale 2327: Epalimic, Ian Ring Music TheoryEpalimic

Prime

The prime form of this scale is Scale 317

Scale 317Scale 317: Korimic, Ian Ring Music TheoryKorimic

Complement

The hexatonic modal family [3211, 3653, 1937, 377, 559, 2327] (Forte: 6-Z39) is the complement of the hexatonic modal family [187, 1559, 1889, 2141, 2827, 3461] (Forte: 6-Z10)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3211 is 2599

Scale 2599Scale 2599: Malimic, Ian Ring Music TheoryMalimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3211 is chiral, and its enantiomorph is scale 2599

Scale 2599Scale 2599: Malimic, Ian Ring Music TheoryMalimic

Transformations:

T0 3211  T0I 2599
T1 2327  T1I 1103
T2 559  T2I 2206
T3 1118  T3I 317
T4 2236  T4I 634
T5 377  T5I 1268
T6 754  T6I 2536
T7 1508  T7I 977
T8 3016  T8I 1954
T9 1937  T9I 3908
T10 3874  T10I 3721
T11 3653  T11I 3347

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 3209Scale 3209: Aeraphitonic, Ian Ring Music TheoryAeraphitonic
Scale 3213Scale 3213: Eponimic, Ian Ring Music TheoryEponimic
Scale 3215Scale 3215: Katydian, Ian Ring Music TheoryKatydian
Scale 3203Scale 3203, Ian Ring Music Theory
Scale 3207Scale 3207, Ian Ring Music Theory
Scale 3219Scale 3219: Ionaphimic, Ian Ring Music TheoryIonaphimic
Scale 3227Scale 3227: Aeolocrian, Ian Ring Music TheoryAeolocrian
Scale 3243Scale 3243: Mela Rupavati, Ian Ring Music TheoryMela Rupavati
Scale 3275Scale 3275: Mela Divyamani, Ian Ring Music TheoryMela Divyamani
Scale 3083Scale 3083, Ian Ring Music Theory
Scale 3147Scale 3147: Ryrimic, Ian Ring Music TheoryRyrimic
Scale 3339Scale 3339, Ian Ring Music Theory
Scale 3467Scale 3467: Katonian, Ian Ring Music TheoryKatonian
Scale 3723Scale 3723: Myptian, Ian Ring Music TheoryMyptian
Scale 2187Scale 2187: Ionothitonic, Ian Ring Music TheoryIonothitonic
Scale 2699Scale 2699: Sythimic, Ian Ring Music TheorySythimic
Scale 1163Scale 1163: Raga Rukmangi, Ian Ring Music TheoryRaga Rukmangi

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. Some scale names used on this and other pages are ©2005 William Zeitler (http://allthescales.org). Peruse this Bibliography.