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Scale 3377: "Phralimic"

Scale 3377: Phralimic, 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

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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
Phralimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,4,5,8,10,11}
Forte Number6-Z17
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 407
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes5
Prime?no
prime: 407
Deep Scaleno
Interval Vector322332
Interval Spectrump3m3n2s2d3t2
Distribution Spectra<1> = {1,2,3,4}
<2> = {2,3,4,5}
<3> = {4,6,8}
<4> = {7,8,9,10}
<5> = {8,9,10,11}
Spectra Variation2.667
Maximally Evenno
Maximal Area Setno
Interior Area2.116
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 TriadsE{4,8,11}221
Minor Triadsfm{5,8,0}221
Augmented TriadsC+{0,4,8}221
Diminished Triads{5,8,11}221
Parsimonious Voice Leading Between Common Triads of Scale 3377. Created by Ian Ring ©2019 C+ C+ E E C+->E fm fm C+->fm E->f° f°->fm

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 3377 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 467
Scale 467: Raga Dhavalangam, Ian Ring Music TheoryRaga Dhavalangam
3rd mode:
Scale 2281
Scale 2281: Rathimic, Ian Ring Music TheoryRathimic
4th mode:
Scale 797
Scale 797: Katocrimic, Ian Ring Music TheoryKatocrimic
5th mode:
Scale 1223
Scale 1223: Phryptimic, Ian Ring Music TheoryPhryptimic
6th mode:
Scale 2659
Scale 2659: Katynimic, Ian Ring Music TheoryKatynimic

Prime

The prime form of this scale is Scale 407

Scale 407Scale 407: Zylimic, Ian Ring Music TheoryZylimic

Complement

The hexatonic modal family [3377, 467, 2281, 797, 1223, 2659] (Forte: 6-Z17) is the complement of the hexatonic modal family [359, 907, 1649, 2227, 2501, 3161] (Forte: 6-Z43)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3377 is 407

Scale 407Scale 407: Zylimic, Ian Ring Music TheoryZylimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3377 is chiral, and its enantiomorph is scale 407

Scale 407Scale 407: Zylimic, Ian Ring Music TheoryZylimic

Transformations:

T0 3377  T0I 407
T1 2659  T1I 814
T2 1223  T2I 1628
T3 2446  T3I 3256
T4 797  T4I 2417
T5 1594  T5I 739
T6 3188  T6I 1478
T7 2281  T7I 2956
T8 467  T8I 1817
T9 934  T9I 3634
T10 1868  T10I 3173
T11 3736  T11I 2251

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 3379Scale 3379: Verdi's Scala Enigmatica Descending, Ian Ring Music TheoryVerdi's Scala Enigmatica Descending
Scale 3381Scale 3381: Katanian, Ian Ring Music TheoryKatanian
Scale 3385Scale 3385: Chromatic Phrygian, Ian Ring Music TheoryChromatic Phrygian
Scale 3361Scale 3361, Ian Ring Music Theory
Scale 3369Scale 3369: Mixolimic, Ian Ring Music TheoryMixolimic
Scale 3345Scale 3345: Zylitonic, Ian Ring Music TheoryZylitonic
Scale 3409Scale 3409: Katanimic, Ian Ring Music TheoryKatanimic
Scale 3441Scale 3441: Thacrian, Ian Ring Music TheoryThacrian
Scale 3505Scale 3505: Stygian, Ian Ring Music TheoryStygian
Scale 3121Scale 3121, Ian Ring Music Theory
Scale 3249Scale 3249: Raga Tilang, Ian Ring Music TheoryRaga Tilang
Scale 3633Scale 3633: Daptimic, Ian Ring Music TheoryDaptimic
Scale 3889Scale 3889: Parian, Ian Ring Music TheoryParian
Scale 2353Scale 2353: Raga Girija, Ian Ring Music TheoryRaga Girija
Scale 2865Scale 2865: Solimic, Ian Ring Music TheorySolimic
Scale 1329Scale 1329: Epygitonic, Ian Ring Music TheoryEpygitonic

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.