The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 663: "Phrynimic"

Scale 663: Phrynimic, 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
Phrynimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,1,2,4,7,9}
Forte Number6-Z47
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3369
Hemitonia2 (dihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections2
Modes5
Prime?yes
Deep Scaleno
Interval Vector233241
Interval Spectrump4m2n3s3d2t
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {4,5,6,7,8}
<4> = {7,8,9,10}
<5> = {9,10,11}
Spectra Variation2.333
Maximally Evenno
Maximal Area Setno
Interior Area2.366
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{0,4,7}221
A{9,1,4}221
Minor Triadsam{9,0,4}221
Diminished Triadsc♯°{1,4,7}221
Parsimonious Voice Leading Between Common Triads of Scale 663. Created by Ian Ring ©2019 C C c#° c#° C->c#° am am C->am A A c#°->A am->A

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.

Diameter2
Radius2
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 663 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 2379
Scale 2379: Raga Gurjari Todi, Ian Ring Music TheoryRaga Gurjari Todi
3rd mode:
Scale 3237
Scale 3237: Raga Brindabani Sarang, Ian Ring Music TheoryRaga Brindabani Sarang
4th mode:
Scale 1833
Scale 1833: Ionacrimic, Ian Ring Music TheoryIonacrimic
5th mode:
Scale 741
Scale 741: Gathimic, Ian Ring Music TheoryGathimic
6th mode:
Scale 1209
Scale 1209: Raga Bhanumanjari, Ian Ring Music TheoryRaga Bhanumanjari

Prime

This is the prime form of this scale.

Complement

The hexatonic modal family [663, 2379, 3237, 1833, 741, 1209] (Forte: 6-Z47) is the complement of the hexatonic modal family [363, 1419, 1581, 1713, 2229, 2757] (Forte: 6-Z25)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 663 is 3369

Scale 3369Scale 3369: Mixolimic, Ian Ring Music TheoryMixolimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 663 is chiral, and its enantiomorph is scale 3369

Scale 3369Scale 3369: Mixolimic, Ian Ring Music TheoryMixolimic

Transformations:

T0 663  T0I 3369
T1 1326  T1I 2643
T2 2652  T2I 1191
T3 1209  T3I 2382
T4 2418  T4I 669
T5 741  T5I 1338
T6 1482  T6I 2676
T7 2964  T7I 1257
T8 1833  T8I 2514
T9 3666  T9I 933
T10 3237  T10I 1866
T11 2379  T11I 3732

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 661Scale 661: Major Pentatonic, Ian Ring Music TheoryMajor Pentatonic
Scale 659Scale 659: Raga Rasika Ranjani, Ian Ring Music TheoryRaga Rasika Ranjani
Scale 667Scale 667: Rodimic, Ian Ring Music TheoryRodimic
Scale 671Scale 671: Stycrian, Ian Ring Music TheoryStycrian
Scale 647Scale 647, Ian Ring Music Theory
Scale 655Scale 655: Kataptimic, Ian Ring Music TheoryKataptimic
Scale 679Scale 679: Lanimic, Ian Ring Music TheoryLanimic
Scale 695Scale 695: Sarian, Ian Ring Music TheorySarian
Scale 727Scale 727: Phradian, Ian Ring Music TheoryPhradian
Scale 535Scale 535, Ian Ring Music Theory
Scale 599Scale 599: Thyrimic, Ian Ring Music TheoryThyrimic
Scale 791Scale 791: Aeoloptimic, Ian Ring Music TheoryAeoloptimic
Scale 919Scale 919: Chromatic Phrygian Inverse, Ian Ring Music TheoryChromatic Phrygian Inverse
Scale 151Scale 151, Ian Ring Music Theory
Scale 407Scale 407: Zylimic, Ian Ring Music TheoryZylimic
Scale 1175Scale 1175: Epycrimic, Ian Ring Music TheoryEpycrimic
Scale 1687Scale 1687: Phralian, Ian Ring Music TheoryPhralian
Scale 2711Scale 2711: Stolian, Ian Ring Music TheoryStolian

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.