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Scale 867: "Phrocrimic"

Scale 867: Phrocrimic, Ian Ring Music Theory

Bracelet Diagram

Tonnetz Diagram


Common Names



Cardinality6 (hexatonic)
Pitch Class Set{0,1,5,6,8,9}
Forte Number6-Z19
Rotational Symmetrynone
Reflection Axesnone
enantiomorph: 2265
Hemitonia3 (trihemitonic)
Cohemitonia0 (ancohemitonic)
prime: 411
Deep Scaleno
Interval Vector313431
Interval Spectrump3m4n3sd3t
Distribution Spectra<1> = {1,2,3,4}
<2> = {3,4,5}
<3> = {4,5,6,7,8}
<4> = {7,8,9}
<5> = {8,9,10,11}
Spectra Variation2.333
Maximally Evenno
Myhill Propertyno
Ridge Tonesnone


Modes are the rotational transformation of this scale. Scale 867 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 2481
Scale 2481: Raga Paraju, Ian Ring Music TheoryRaga Paraju
3rd mode:
Scale 411
Scale 411: Lygimic, Ian Ring Music TheoryLygimicThis is the prime mode
4th mode:
Scale 2253
Scale 2253: Raga Amarasenapriya, Ian Ring Music TheoryRaga Amarasenapriya
5th mode:
Scale 1587
Scale 1587: Raga Rudra Pancama, Ian Ring Music TheoryRaga Rudra Pancama
6th mode:
Scale 2841
Scale 2841: Sothimic, Ian Ring Music TheorySothimic


The prime form of this scale is Scale 411

Scale 411Scale 411: Lygimic, Ian Ring Music TheoryLygimic


The hexatonic modal family [867, 2481, 411, 2253, 1587, 2841] (Forte: 6-Z19) is the complement of the hexatonic modal family [615, 825, 915, 2355, 2505, 3225] (Forte: 6-Z44)


The inverse of a scale is a reflection using the root as its axis. The inverse of 867 is 2265

Scale 2265Scale 2265: Raga Rasamanjari, Ian Ring Music TheoryRaga Rasamanjari


Only scales that are chiral will have an enantiomorph. Scale 867 is chiral, and its enantiomorph is scale 2265

Scale 2265Scale 2265: Raga Rasamanjari, Ian Ring Music TheoryRaga Rasamanjari


T0 867  T0I 2265
T1 1734  T1I 435
T2 3468  T2I 870
T3 2841  T3I 1740
T4 1587  T4I 3480
T5 3174  T5I 2865
T6 2253  T6I 1635
T7 411  T7I 3270
T8 822  T8I 2445
T9 1644  T9I 795
T10 3288  T10I 1590
T11 2481  T11I 3180

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 865Scale 865, Ian Ring Music Theory
Scale 869Scale 869: Kothimic, Ian Ring Music TheoryKothimic
Scale 871Scale 871: Locrian Double-flat 3 Double-flat 7, Ian Ring Music TheoryLocrian Double-flat 3 Double-flat 7
Scale 875Scale 875: Locrian Double-flat 7, Ian Ring Music TheoryLocrian Double-flat 7
Scale 883Scale 883: Ralian, Ian Ring Music TheoryRalian
Scale 835Scale 835, Ian Ring Music Theory
Scale 851Scale 851: Raga Hejjajji, Ian Ring Music TheoryRaga Hejjajji
Scale 803Scale 803: Loritonic, Ian Ring Music TheoryLoritonic
Scale 931Scale 931: Raga Kalakanthi, Ian Ring Music TheoryRaga Kalakanthi
Scale 995Scale 995: Phrathian, Ian Ring Music TheoryPhrathian
Scale 611Scale 611: Anchihoye, Ian Ring Music TheoryAnchihoye
Scale 739Scale 739: Rorimic, Ian Ring Music TheoryRorimic
Scale 355Scale 355: Aeoloritonic, Ian Ring Music TheoryAeoloritonic
Scale 1379Scale 1379: Kycrimic, Ian Ring Music TheoryKycrimic
Scale 1891Scale 1891: Thalian, Ian Ring Music TheoryThalian
Scale 2915Scale 2915: Aeolydian, Ian Ring Music TheoryAeolydian

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