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Scale 991: "Aeolygic"

Scale 991: Aeolygic, 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
Aeolygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,1,2,3,4,6,7,8,9}
Forte Number9-5
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3961
Hemitonia7 (multihemitonic)
Cohemitonia5 (multicohemitonic)
Imperfections2
Modes8
Prime?yes
Deep Scaleno
Interval Vector766674
Interval Spectrump7m6n6s6d7t4
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4}
<3> = {3,4,5}
<4> = {4,5,6}
<5> = {6,7,8}
<6> = {7,8,9}
<7> = {8,9,10}
<8> = {9,10,11}
Spectra Variation1.778
Maximally Evenno
Maximal Area Setno
Interior Area2.683
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}342.21
D{2,6,9}242.64
G♯{8,0,3}342.21
A{9,1,4}342.14
Minor Triadscm{0,3,7}342.29
c♯m{1,4,8}342.21
f♯m{6,9,1}342.36
am{9,0,4}442.07
Augmented TriadsC+{0,4,8}442
Diminished Triads{0,3,6}242.57
c♯°{1,4,7}242.57
d♯°{3,6,9}242.71
f♯°{6,9,0}242.43
{9,0,3}242.43
Parsimonious Voice Leading Between Common Triads of Scale 991. Created by Ian Ring ©2019 cm cm c°->cm d#° d#° c°->d#° C C cm->C G# G# cm->G# C+ C+ C->C+ c#° c#° C->c#° c#m c#m C+->c#m C+->G# am am C+->am c#°->c#m 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 991 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 2543
Scale 2543: Dydygic, Ian Ring Music TheoryDydygic
3rd mode:
Scale 3319
Scale 3319: Tholygic, Ian Ring Music TheoryTholygic
4th mode:
Scale 3707
Scale 3707: Rynygic, Ian Ring Music TheoryRynygic
5th mode:
Scale 3901
Scale 3901: Bycrygic, Ian Ring Music TheoryBycrygic
6th mode:
Scale 1999
Scale 1999: Zacrygic, Ian Ring Music TheoryZacrygic
7th mode:
Scale 3047
Scale 3047: Panygic, Ian Ring Music TheoryPanygic
8th mode:
Scale 3571
Scale 3571: Dyrygic, Ian Ring Music TheoryDyrygic
9th mode:
Scale 3833
Scale 3833: Dycrygic, Ian Ring Music TheoryDycrygic

Prime

This is the prime form of this scale.

Complement

The nonatonic modal family [991, 2543, 3319, 3707, 3901, 1999, 3047, 3571, 3833] (Forte: 9-5) is the complement of the tritonic modal family [67, 193, 2081] (Forte: 3-5)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 991 is 3961

Scale 3961Scale 3961: Zathygic, Ian Ring Music TheoryZathygic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 991 is chiral, and its enantiomorph is scale 3961

Scale 3961Scale 3961: Zathygic, Ian Ring Music TheoryZathygic

Transformations:

T0 991  T0I 3961
T1 1982  T1I 3827
T2 3964  T2I 3559
T3 3833  T3I 3023
T4 3571  T4I 1951
T5 3047  T5I 3902
T6 1999  T6I 3709
T7 3998  T7I 3323
T8 3901  T8I 2551
T9 3707  T9I 1007
T10 3319  T10I 2014
T11 2543  T11I 4028

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 989Scale 989: Phrolyllic, Ian Ring Music TheoryPhrolyllic
Scale 987Scale 987: Aeraptyllic, Ian Ring Music TheoryAeraptyllic
Scale 983Scale 983: Thocryllic, Ian Ring Music TheoryThocryllic
Scale 975Scale 975: Messiaen Mode 4, Ian Ring Music TheoryMessiaen Mode 4
Scale 1007Scale 1007: Epitygic, Ian Ring Music TheoryEpitygic
Scale 1023Scale 1023: Dodyllian, Ian Ring Music TheoryDodyllian
Scale 927Scale 927: Gaptyllic, Ian Ring Music TheoryGaptyllic
Scale 959Scale 959: Katylygic, Ian Ring Music TheoryKatylygic
Scale 863Scale 863: Pyryllic, Ian Ring Music TheoryPyryllic
Scale 735Scale 735: Sylyllic, Ian Ring Music TheorySylyllic
Scale 479Scale 479: Kocryllic, Ian Ring Music TheoryKocryllic
Scale 1503Scale 1503: Epiryllian, Ian Ring Music TheoryEpiryllian
Scale 2015Scale 2015: Messiaen Mode 7, Ian Ring Music TheoryMessiaen Mode 7
Scale 3039Scale 3039: Godyllian, Ian Ring Music TheoryGodyllian

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.