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Scale 3981: "Phrycryllic"

Scale 3981: Phrycryllic, 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
Phrycryllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,2,3,7,8,9,10,11}
Forte Number8-4
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1599
Hemitonia6 (multihemitonic)
Cohemitonia4 (multicohemitonic)
Imperfections3
Modes7
Prime?no
prime: 447
Deep Scaleno
Interval Vector655552
Interval Spectrump5m5n5s5d6t2
Distribution Spectra<1> = {1,2,4}
<2> = {2,3,5}
<3> = {3,4,6,7}
<4> = {4,5,7,8}
<5> = {5,6,8,9}
<6> = {7,9,10}
<7> = {8,10,11}
Spectra Variation3
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 TriadsD♯{3,7,10}242
G{7,11,2}341.78
G♯{8,0,3}341.89
Minor Triadscm{0,3,7}231.78
gm{7,10,2}252.33
g♯m{8,11,3}331.56
Augmented TriadsD♯+{3,7,11}431.44
Diminished Triadsg♯°{8,11,2}231.89
{9,0,3}152.67
Parsimonious Voice Leading Between Common Triads of Scale 3981. Created by Ian Ring ©2019 cm cm D#+ D#+ cm->D#+ G# G# cm->G# D# D# D#->D#+ gm gm D#->gm Parsimonious Voice Leading Between Common Triads of Scale 3981. Created by Ian Ring ©2019 G D#+->G g#m g#m D#+->g#m gm->G g#° g#° G->g#° g#°->g#m g#m->G# G#->a°

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 Verticescm, D♯+, g♯°, g♯m
Peripheral Verticesgm, a°

Modes

Modes are the rotational transformation of this scale. Scale 3981 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 2019
Scale 2019: Palyllic, Ian Ring Music TheoryPalyllic
3rd mode:
Scale 3057
Scale 3057: Phroryllic, Ian Ring Music TheoryPhroryllic
4th mode:
Scale 447
Scale 447: Thyphyllic, Ian Ring Music TheoryThyphyllicThis is the prime mode
5th mode:
Scale 2271
Scale 2271: Poptyllic, Ian Ring Music TheoryPoptyllic
6th mode:
Scale 3183
Scale 3183: Mixonyllic, Ian Ring Music TheoryMixonyllic
7th mode:
Scale 3639
Scale 3639: Paptyllic, Ian Ring Music TheoryPaptyllic
8th mode:
Scale 3867
Scale 3867: Storyllic, Ian Ring Music TheoryStoryllic

Prime

The prime form of this scale is Scale 447

Scale 447Scale 447: Thyphyllic, Ian Ring Music TheoryThyphyllic

Complement

The octatonic modal family [3981, 2019, 3057, 447, 2271, 3183, 3639, 3867] (Forte: 8-4) is the complement of the tetratonic modal family [39, 897, 2067, 3081] (Forte: 4-4)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3981 is 1599

Scale 1599Scale 1599: Pocryllic, Ian Ring Music TheoryPocryllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3981 is chiral, and its enantiomorph is scale 1599

Scale 1599Scale 1599: Pocryllic, Ian Ring Music TheoryPocryllic

Transformations:

T0 3981  T0I 1599
T1 3867  T1I 3198
T2 3639  T2I 2301
T3 3183  T3I 507
T4 2271  T4I 1014
T5 447  T5I 2028
T6 894  T6I 4056
T7 1788  T7I 4017
T8 3576  T8I 3939
T9 3057  T9I 3783
T10 2019  T10I 3471
T11 4038  T11I 2847

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 3983Scale 3983: Thyptygic, Ian Ring Music TheoryThyptygic
Scale 3977Scale 3977: Kythian, Ian Ring Music TheoryKythian
Scale 3979Scale 3979: Dynyllic, Ian Ring Music TheoryDynyllic
Scale 3973Scale 3973, Ian Ring Music Theory
Scale 3989Scale 3989: Sythyllic, Ian Ring Music TheorySythyllic
Scale 3997Scale 3997: Dogygic, Ian Ring Music TheoryDogygic
Scale 4013Scale 4013: Raga Pilu, Ian Ring Music TheoryRaga Pilu
Scale 4045Scale 4045: Gyptygic, Ian Ring Music TheoryGyptygic
Scale 3853Scale 3853, Ian Ring Music Theory
Scale 3917Scale 3917: Katoptyllic, Ian Ring Music TheoryKatoptyllic
Scale 3725Scale 3725: Kyrian, Ian Ring Music TheoryKyrian
Scale 3469Scale 3469: Monian, Ian Ring Music TheoryMonian
Scale 2957Scale 2957: Thygian, Ian Ring Music TheoryThygian
Scale 1933Scale 1933: Mocrian, Ian Ring Music TheoryMocrian

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. Special thanks to Richard Repp for helping with technical accuracy.