The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 3721: "Phragimic"

Scale 3721: Phragimic, 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
Phragimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,3,7,9,10,11}
Forte Number6-Z39
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 559
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
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicno

Modes

Modes are the rotational transformation of this scale. Scale 3721 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 977
Scale 977: Kocrimic, Ian Ring Music TheoryKocrimic
3rd mode:
Scale 317
Scale 317: Korimic, Ian Ring Music TheoryKorimicThis is the prime mode
4th mode:
Scale 1103
Scale 1103: Lynimic, Ian Ring Music TheoryLynimic
5th mode:
Scale 2599
Scale 2599: Malimic, Ian Ring Music TheoryMalimic
6th mode:
Scale 3347
Scale 3347: Synimic, Ian Ring Music TheorySynimic

Prime

The prime form of this scale is Scale 317

Scale 317Scale 317: Korimic, Ian Ring Music TheoryKorimic

Complement

The hexatonic modal family [3721, 977, 317, 1103, 2599, 3347] (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 3721 is 559

Scale 559Scale 559: Lylimic, Ian Ring Music TheoryLylimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3721 is chiral, and its enantiomorph is scale 559

Scale 559Scale 559: Lylimic, Ian Ring Music TheoryLylimic

Transformations:

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

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 3723Scale 3723: Myptian, Ian Ring Music TheoryMyptian
Scale 3725Scale 3725: Kyrian, Ian Ring Music TheoryKyrian
Scale 3713Scale 3713, Ian Ring Music Theory
Scale 3717Scale 3717, Ian Ring Music Theory
Scale 3729Scale 3729: Starimic, Ian Ring Music TheoryStarimic
Scale 3737Scale 3737: Phrocrian, Ian Ring Music TheoryPhrocrian
Scale 3753Scale 3753: Phraptian, Ian Ring Music TheoryPhraptian
Scale 3785Scale 3785: Epagian, Ian Ring Music TheoryEpagian
Scale 3593Scale 3593, Ian Ring Music Theory
Scale 3657Scale 3657: Epynimic, Ian Ring Music TheoryEpynimic
Scale 3849Scale 3849, Ian Ring Music Theory
Scale 3977Scale 3977: Kythian, Ian Ring Music TheoryKythian
Scale 3209Scale 3209: Aeraphitonic, Ian Ring Music TheoryAeraphitonic
Scale 3465Scale 3465: Katathimic, Ian Ring Music TheoryKatathimic
Scale 2697Scale 2697: Katagitonic, Ian Ring Music TheoryKatagitonic
Scale 1673Scale 1673: Thocritonic, Ian Ring Music TheoryThocritonic

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.