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Scale 3893: "Phrocryllic"

Scale 3893: Phrocryllic, 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
Phrocryllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,2,4,5,8,9,10,11}
Forte Number8-Z15
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1439
Hemitonia5 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections3
Modes7
Prime?no
prime: 863
Deep Scaleno
Interval Vector555553
Interval Spectrump5m5n5s5d5t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4}
<3> = {3,4,5,6}
<4> = {4,5,6,7,8}
<5> = {6,7,8,9}
<6> = {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 TriadsE{4,8,11}342
F{5,9,0}341.91
A♯{10,2,5}242.27
Minor Triadsdm{2,5,9}342
fm{5,8,0}441.82
am{9,0,4}242.18
Augmented TriadsC+{0,4,8}341.91
Diminished Triads{2,5,8}242.09
{5,8,11}242.09
g♯°{8,11,2}242.27
{11,2,5}242.36
Parsimonious Voice Leading Between Common Triads of Scale 3893. Created by Ian Ring ©2019 C+ C+ E E C+->E fm fm C+->fm am am C+->am dm dm d°->dm d°->fm F F dm->F A# A# dm->A# E->f° g#° g#° E->g#° f°->fm fm->F F->am g#°->b° A#->b°

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
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 3893 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 1997
Scale 1997: Raga Cintamani, Ian Ring Music TheoryRaga Cintamani
3rd mode:
Scale 1523
Scale 1523: Zothyllic, Ian Ring Music TheoryZothyllic
4th mode:
Scale 2809
Scale 2809: Gythyllic, Ian Ring Music TheoryGythyllic
5th mode:
Scale 863
Scale 863: Pyryllic, Ian Ring Music TheoryPyryllicThis is the prime mode
6th mode:
Scale 2479
Scale 2479: Harmonic and Neapolitan Minor Mixed, Ian Ring Music TheoryHarmonic and Neapolitan Minor Mixed
7th mode:
Scale 3287
Scale 3287: Phrathyllic, Ian Ring Music TheoryPhrathyllic
8th mode:
Scale 3691
Scale 3691: Badyllic, Ian Ring Music TheoryBadyllic

Prime

The prime form of this scale is Scale 863

Scale 863Scale 863: Pyryllic, Ian Ring Music TheoryPyryllic

Complement

The octatonic modal family [3893, 1997, 1523, 2809, 863, 2479, 3287, 3691] (Forte: 8-Z15) is the complement of the tetratonic modal family [83, 773, 1217, 2089] (Forte: 4-Z15)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3893 is 1439

Scale 1439Scale 1439: Rolyllic, Ian Ring Music TheoryRolyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3893 is chiral, and its enantiomorph is scale 1439

Scale 1439Scale 1439: Rolyllic, Ian Ring Music TheoryRolyllic

Transformations:

T0 3893  T0I 1439
T1 3691  T1I 2878
T2 3287  T2I 1661
T3 2479  T3I 3322
T4 863  T4I 2549
T5 1726  T5I 1003
T6 3452  T6I 2006
T7 2809  T7I 4012
T8 1523  T8I 3929
T9 3046  T9I 3763
T10 1997  T10I 3431
T11 3994  T11I 2767

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 3895Scale 3895: Eparygic, Ian Ring Music TheoryEparygic
Scale 3889Scale 3889: Parian, Ian Ring Music TheoryParian
Scale 3891Scale 3891: Ryryllic, Ian Ring Music TheoryRyryllic
Scale 3897Scale 3897: Kalyllic, Ian Ring Music TheoryKalyllic
Scale 3901Scale 3901: Bycrygic, Ian Ring Music TheoryBycrygic
Scale 3877Scale 3877: Thanian, Ian Ring Music TheoryThanian
Scale 3885Scale 3885: Styryllic, Ian Ring Music TheoryStyryllic
Scale 3861Scale 3861: Phroptian, Ian Ring Music TheoryPhroptian
Scale 3925Scale 3925: Thyryllic, Ian Ring Music TheoryThyryllic
Scale 3957Scale 3957: Porygic, Ian Ring Music TheoryPorygic
Scale 4021Scale 4021: Raga Pahadi, Ian Ring Music TheoryRaga Pahadi
Scale 3637Scale 3637: Raga Rageshri, Ian Ring Music TheoryRaga Rageshri
Scale 3765Scale 3765: Dominant Bebop, Ian Ring Music TheoryDominant Bebop
Scale 3381Scale 3381: Katanian, Ian Ring Music TheoryKatanian
Scale 2869Scale 2869: Major Augmented, Ian Ring Music TheoryMajor Augmented
Scale 1845Scale 1845: Lagian, Ian Ring Music TheoryLagian

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.