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Scale 3737: "Phrocrian"

Scale 3737: Phrocrian, 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
Phrocrian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,3,4,7,9,10,11}
Forte Number7-Z18
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 815
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections3
Modes6
Prime?no
prime: 755
Deep Scaleno
Interval Vector434442
Interval Spectrump4m4n4s3d4t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {3,4,5,6,7}
<4> = {5,6,7,8,9}
<5> = {7,8,9,10}
<6> = {9,10,11}
Spectra Variation2.571
Maximally Evenno
Maximal Area Setno
Interior Area2.433
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicyes

Harmonic Chords

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}331.5
D♯{3,7,10}242
Minor Triadscm{0,3,7}331.5
em{4,7,11}331.5
am{9,0,4}242
Augmented TriadsD♯+{3,7,11}331.5
Diminished Triads{4,7,10}242
{9,0,3}242
Parsimonious Voice Leading Between Common Triads of Scale 3737. Created by Ian Ring ©2019 cm cm C C cm->C D#+ D#+ cm->D#+ cm->a° em em C->em am am C->am D# D# D#->D#+ D#->e° D#+->em e°->em a°->am

view full size

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.

Diameter4
Radius3
Self-Centeredno
Central Verticescm, C, D♯+, em
Peripheral VerticesD♯, e°, a°, am

Modes

Modes are the rotational transformation of this scale. Scale 3737 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 979
Scale 979: Mela Dhavalambari, Ian Ring Music TheoryMela Dhavalambari
3rd mode:
Scale 2537
Scale 2537: Laptian, Ian Ring Music TheoryLaptian
4th mode:
Scale 829
Scale 829: Lygian, Ian Ring Music TheoryLygian
5th mode:
Scale 1231
Scale 1231: Logian, Ian Ring Music TheoryLogian
6th mode:
Scale 2663
Scale 2663: Lalian, Ian Ring Music TheoryLalian
7th mode:
Scale 3379
Scale 3379: Verdi's Scala Enigmatica Descending, Ian Ring Music TheoryVerdi's Scala Enigmatica Descending

Prime

The prime form of this scale is Scale 755

Scale 755Scale 755: Phrythian, Ian Ring Music TheoryPhrythian

Complement

The heptatonic modal family [3737, 979, 2537, 829, 1231, 2663, 3379] (Forte: 7-Z18) is the complement of the pentatonic modal family [179, 779, 1633, 2137, 2437] (Forte: 5-Z18)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3737 is 815

Scale 815Scale 815: Bolian, Ian Ring Music TheoryBolian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3737 is chiral, and its enantiomorph is scale 815

Scale 815Scale 815: Bolian, Ian Ring Music TheoryBolian

Transformations:

T0 3737  T0I 815
T1 3379  T1I 1630
T2 2663  T2I 3260
T3 1231  T3I 2425
T4 2462  T4I 755
T5 829  T5I 1510
T6 1658  T6I 3020
T7 3316  T7I 1945
T8 2537  T8I 3890
T9 979  T9I 3685
T10 1958  T10I 3275
T11 3916  T11I 2455

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 3739Scale 3739: Epanyllic, Ian Ring Music TheoryEpanyllic
Scale 3741Scale 3741: Zydyllic, Ian Ring Music TheoryZydyllic
Scale 3729Scale 3729: Starimic, Ian Ring Music TheoryStarimic
Scale 3733Scale 3733: Gycrian, Ian Ring Music TheoryGycrian
Scale 3721Scale 3721: Phragimic, Ian Ring Music TheoryPhragimic
Scale 3753Scale 3753: Phraptian, Ian Ring Music TheoryPhraptian
Scale 3769Scale 3769: Eponyllic, Ian Ring Music TheoryEponyllic
Scale 3801Scale 3801: Maptyllic, Ian Ring Music TheoryMaptyllic
Scale 3609Scale 3609, Ian Ring Music Theory
Scale 3673Scale 3673: Ranian, Ian Ring Music TheoryRanian
Scale 3865Scale 3865: Starian, Ian Ring Music TheoryStarian
Scale 3993Scale 3993: Ioniptyllic, Ian Ring Music TheoryIoniptyllic
Scale 3225Scale 3225: Ionalimic, Ian Ring Music TheoryIonalimic
Scale 3481Scale 3481: Katathian, Ian Ring Music TheoryKatathian
Scale 2713Scale 2713: Porimic, Ian Ring Music TheoryPorimic
Scale 1689Scale 1689: Lorimic, Ian Ring Music TheoryLorimic

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.