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Scale 863: "Pyryllic"

Scale 863: Pyryllic, 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
Pyryllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,2,3,4,6,8,9}
Forte Number8-Z15
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3929
Hemitonia5 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections3
Modes7
Prime?yes
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 TriadsD{2,6,9}242.27
G♯{8,0,3}342
A{9,1,4}341.91
Minor Triadsc♯m{1,4,8}242.18
f♯m{6,9,1}342
am{9,0,4}441.82
Augmented TriadsC+{0,4,8}341.91
Diminished Triads{0,3,6}242.27
d♯°{3,6,9}242.36
f♯°{6,9,0}242.09
{9,0,3}242.09
Parsimonious Voice Leading Between Common Triads of Scale 863. Created by Ian Ring ©2019 d#° d#° c°->d#° G# G# c°->G# C+ C+ c#m c#m C+->c#m C+->G# am am C+->am A A c#m->A D D D->d#° f#m f#m D->f#m f#° f#° f#°->f#m f#°->am f#m->A G#->a° a°->am am->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.

Diameter4
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 863 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 2479
Scale 2479: Harmonic and Neapolitan Minor Mixed, Ian Ring Music TheoryHarmonic and Neapolitan Minor Mixed
3rd mode:
Scale 3287
Scale 3287: Phrathyllic, Ian Ring Music TheoryPhrathyllic
4th mode:
Scale 3691
Scale 3691: Badyllic, Ian Ring Music TheoryBadyllic
5th mode:
Scale 3893
Scale 3893: Phrocryllic, Ian Ring Music TheoryPhrocryllic
6th mode:
Scale 1997
Scale 1997: Raga Cintamani, Ian Ring Music TheoryRaga Cintamani
7th mode:
Scale 1523
Scale 1523: Zothyllic, Ian Ring Music TheoryZothyllic
8th mode:
Scale 2809
Scale 2809: Gythyllic, Ian Ring Music TheoryGythyllic

Prime

This is the prime form of this scale.

Complement

The octatonic modal family [863, 2479, 3287, 3691, 3893, 1997, 1523, 2809] (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 863 is 3929

Scale 3929Scale 3929: Aeolothyllic, Ian Ring Music TheoryAeolothyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 863 is chiral, and its enantiomorph is scale 3929

Scale 3929Scale 3929: Aeolothyllic, Ian Ring Music TheoryAeolothyllic

Transformations:

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

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 861Scale 861: Rylian, Ian Ring Music TheoryRylian
Scale 859Scale 859: Ultralocrian, Ian Ring Music TheoryUltralocrian
Scale 855Scale 855: Porian, Ian Ring Music TheoryPorian
Scale 847Scale 847: Ganian, Ian Ring Music TheoryGanian
Scale 879Scale 879: Aeranyllic, Ian Ring Music TheoryAeranyllic
Scale 895Scale 895: Aeolathygic, Ian Ring Music TheoryAeolathygic
Scale 799Scale 799: Lolian, Ian Ring Music TheoryLolian
Scale 831Scale 831: Rodyllic, Ian Ring Music TheoryRodyllic
Scale 927Scale 927: Gaptyllic, Ian Ring Music TheoryGaptyllic
Scale 991Scale 991: Aeolygic, Ian Ring Music TheoryAeolygic
Scale 607Scale 607: Kadian, Ian Ring Music TheoryKadian
Scale 735Scale 735: Sylyllic, Ian Ring Music TheorySylyllic
Scale 351Scale 351: Epanian, Ian Ring Music TheoryEpanian
Scale 1375Scale 1375: Bothyllic, Ian Ring Music TheoryBothyllic
Scale 1887Scale 1887: Aerocrygic, Ian Ring Music TheoryAerocrygic
Scale 2911Scale 2911: Katygic, Ian Ring Music TheoryKatygic

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.