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Scale 957: "Phronyllic"

Scale 957: Phronyllic, 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
Phronyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,2,3,4,5,7,8,9}
Forte Number8-14
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1977
Hemitonia5 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections2
Modes7
Prime?no
prime: 759
Deep Scaleno
Interval Vector555562
Interval Spectrump6m5n5s5d5t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {3,4,5,6}
<4> = {5,7}
<5> = {6,7,8,9}
<6> = {7,8,9,10}
<7> = {9,10,11}
Spectra Variation2.25
Maximally Evenno
Maximal Area Setno
Interior Area2.616
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}242.1
F{5,9,0}341.9
G♯{8,0,3}341.9
Minor Triadscm{0,3,7}252.5
dm{2,5,9}252.5
fm{5,8,0}331.7
am{9,0,4}331.7
Augmented TriadsC+{0,4,8}431.5
Diminished Triads{2,5,8}242.3
{9,0,3}242.1
Parsimonious Voice Leading Between Common Triads of Scale 957. Created by Ian Ring ©2019 cm cm C C cm->C G# G# cm->G# C+ C+ C->C+ fm fm C+->fm C+->G# am am C+->am dm dm d°->dm d°->fm F F dm->F fm->F F->am G#->a° 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.

Diameter5
Radius3
Self-Centeredno
Central VerticesC+, fm, am
Peripheral Verticescm, dm

Modes

Modes are the rotational transformation of this scale. Scale 957 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 1263
Scale 1263: Stynyllic, Ian Ring Music TheoryStynyllic
3rd mode:
Scale 2679
Scale 2679: Rathyllic, Ian Ring Music TheoryRathyllic
4th mode:
Scale 3387
Scale 3387: Aeryptyllic, Ian Ring Music TheoryAeryptyllic
5th mode:
Scale 3741
Scale 3741: Zydyllic, Ian Ring Music TheoryZydyllic
6th mode:
Scale 1959
Scale 1959: Katolyllic, Ian Ring Music TheoryKatolyllic
7th mode:
Scale 3027
Scale 3027: Rythyllic, Ian Ring Music TheoryRythyllic
8th mode:
Scale 3561
Scale 3561: Pothyllic, Ian Ring Music TheoryPothyllic

Prime

The prime form of this scale is Scale 759

Scale 759Scale 759: Katalyllic, Ian Ring Music TheoryKatalyllic

Complement

The octatonic modal family [957, 1263, 2679, 3387, 3741, 1959, 3027, 3561] (Forte: 8-14) is the complement of the tetratonic modal family [141, 417, 1059, 2577] (Forte: 4-14)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 957 is 1977

Scale 1977Scale 1977: Dagyllic, Ian Ring Music TheoryDagyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 957 is chiral, and its enantiomorph is scale 1977

Scale 1977Scale 1977: Dagyllic, Ian Ring Music TheoryDagyllic

Transformations:

T0 957  T0I 1977
T1 1914  T1I 3954
T2 3828  T2I 3813
T3 3561  T3I 3531
T4 3027  T4I 2967
T5 1959  T5I 1839
T6 3918  T6I 3678
T7 3741  T7I 3261
T8 3387  T8I 2427
T9 2679  T9I 759
T10 1263  T10I 1518
T11 2526  T11I 3036

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 959Scale 959: Katylygic, Ian Ring Music TheoryKatylygic
Scale 953Scale 953: Mela Yagapriya, Ian Ring Music TheoryMela Yagapriya
Scale 955Scale 955: Ionogyllic, Ian Ring Music TheoryIonogyllic
Scale 949Scale 949: Mela Mararanjani, Ian Ring Music TheoryMela Mararanjani
Scale 941Scale 941: Mela Jhankaradhvani, Ian Ring Music TheoryMela Jhankaradhvani
Scale 925Scale 925: Chromatic Hypodorian, Ian Ring Music TheoryChromatic Hypodorian
Scale 989Scale 989: Phrolyllic, Ian Ring Music TheoryPhrolyllic
Scale 1021Scale 1021: Ladygic, Ian Ring Music TheoryLadygic
Scale 829Scale 829: Lygian, Ian Ring Music TheoryLygian
Scale 893Scale 893: Dadyllic, Ian Ring Music TheoryDadyllic
Scale 701Scale 701: Mixonyphian, Ian Ring Music TheoryMixonyphian
Scale 445Scale 445: Gocrian, Ian Ring Music TheoryGocrian
Scale 1469Scale 1469: Epiryllic, Ian Ring Music TheoryEpiryllic
Scale 1981Scale 1981: Houseini, Ian Ring Music TheoryHouseini
Scale 3005Scale 3005: Gycrygic, Ian Ring Music TheoryGycrygic

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.

Pitch spelling algorithm employed here is adapted from a method by Uzay Bora, Baris Tekin Tezel, and Alper Vahaplar. (An algorithm for spelling the pitches of any musical scale) Contact authors Patent owner: Dokuz Eylül University, Used with Permission. Contact TTO

Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography.