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Scale 2863: "Aerogyllic"

Scale 2863: Aerogyllic, 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
Aerogyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,2,3,5,8,9,11}
Forte Number8-12
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3739
Hemitonia5 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections4
Modes7
Prime?no
prime: 763
Deep Scaleno
Interval Vector556543
Interval Spectrump4m5n6s5d5t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {3,4,6}
<4> = {4,5,7,8}
<5> = {6,8,9}
<6> = {7,8,9,10}
<7> = {9,10,11}
Spectra Variation2.5
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♯{1,5,8}342
F{5,9,0}342
G♯{8,0,3}342
Minor Triadsdm{2,5,9}342.17
fm{5,8,0}441.83
g♯m{8,11,3}342.17
Augmented TriadsC♯+{1,5,9}342
Diminished Triadsd°{2,5,8}242.33
f°{5,8,11}242.17
g♯°{8,11,2}242.33
a°{9,0,3}242.33
b°{11,2,5}242.33
Parsimonious Voice Leading Between Common Triads of Scale 2863. Created by Ian Ring ©2019 C# C# C#+ C#+ C#->C#+ d° d° C#->d° fm fm C#->fm dm dm C#+->dm F F C#+->F d°->dm b° b° dm->b° f° f° f°->fm g#m g#m f°->g#m fm->F G# G# fm->G# a° a° F->a° g#° g#° g#°->g#m g#°->b° g#m->G# G#->a°

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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 2863 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3479		Scale 3479: Rothyllic, Ian Ring Music TheoryRothyllic
3rd mode:
Scale 3787		Scale 3787: Kagyllic, Ian Ring Music TheoryKagyllic
4th mode:
Scale 3941		Scale 3941: Stathyllic, Ian Ring Music TheoryStathyllic
5th mode:
Scale 2009		Scale 2009: Stacryllic, Ian Ring Music TheoryStacryllic
6th mode:
Scale 763		Scale 763: Doryllic, Ian Ring Music TheoryDoryllicThis is the prime mode
7th mode:
Scale 2429		Scale 2429: Kadyllic, Ian Ring Music TheoryKadyllic
8th mode:
Scale 1631		Scale 1631: Rynyllic, Ian Ring Music TheoryRynyllic

Prime

The prime form of this scale is Scale 763

Scale 763Scale 763: Doryllic, Ian Ring Music TheoryDoryllic

Complement

The octatonic modal family [2863, 3479, 3787, 3941, 2009, 763, 2429, 1631] (Forte: 8-12) is the complement of the tetratonic modal family [77, 833, 1043, 2569] (Forte: 4-12)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2863 is 3739

Scale 3739Scale 3739: Epanyllic, Ian Ring Music TheoryEpanyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2863 is chiral, and its enantiomorph is scale 3739

Scale 3739Scale 3739: Epanyllic, Ian Ring Music TheoryEpanyllic

Transformations:

T0 2863  T0I 3739
T1 1631  T1I 3383
T2 3262  T2I 2671
T3 2429  T3I 1247
T4 763  T4I 2494
T5 1526  T5I 893
T6 3052  T6I 1786
T7 2009  T7I 3572
T8 4018  T8I 3049
T9 3941  T9I 2003
T10 3787  T10I 4006
T11 3479  T11I 3917

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 2861Scale 2861: Katothian, Ian Ring Music TheoryKatothian
Scale 2859Scale 2859: Phrycrian, Ian Ring Music TheoryPhrycrian
Scale 2855Scale 2855: Epocrain, Ian Ring Music TheoryEpocrain
Scale 2871Scale 2871: Stanyllic, Ian Ring Music TheoryStanyllic
Scale 2879Scale 2879: Stadygic, Ian Ring Music TheoryStadygic
Scale 2831Scale 2831, Ian Ring Music Theory
Scale 2847Scale 2847: Phracryllic, Ian Ring Music TheoryPhracryllic
Scale 2895Scale 2895: Aeoryllic, Ian Ring Music TheoryAeoryllic
Scale 2927Scale 2927: Rodygic, Ian Ring Music TheoryRodygic
Scale 2991Scale 2991: Zanygic, Ian Ring Music TheoryZanygic
Scale 2607Scale 2607: Aerolian, Ian Ring Music TheoryAerolian
Scale 2735Scale 2735: Gynyllic, Ian Ring Music TheoryGynyllic
Scale 2351Scale 2351: Gynian, Ian Ring Music TheoryGynian
Scale 3375Scale 3375, Ian Ring Music Theory
Scale 3887Scale 3887: Phrathygic, Ian Ring Music TheoryPhrathygic
Scale 815Scale 815: Bolian, Ian Ring Music TheoryBolian
Scale 1839Scale 1839: Zogyllic, Ian Ring Music TheoryZogyllic

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.