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Scale 2971: "Aeolynyllic"

Scale 2971: Aeolynyllic, 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
Aeolynyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,3,4,7,8,9,11}
Forte Number8-19
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2875
Hemitonia5 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections3
Modes7
Prime?no
prime: 887
Deep Scaleno
Interval Vector545752
Interval Spectrump5m7n5s4d5t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4}
<3> = {4,5,6}
<4> = {5,6,7}
<5> = {6,7,8}
<6> = {8,9,10}
<7> = {9,10,11}
Spectra Variation1.75
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{0,4,7}431.77
E{4,8,11}331.92
G♯{8,0,3}431.77
A{9,1,4}252.62
Minor Triadscm{0,3,7}342
c♯m{1,4,8}342.08
em{4,7,11}342.15
g♯m{8,11,3}342.15
am{9,0,4}342.08
Augmented TriadsC+{0,4,8}531.54
D♯+{3,7,11}352.38
Diminished Triadsc♯°{1,4,7}242.31
{9,0,3}242.31
Parsimonious Voice Leading Between Common Triads of Scale 2971. Created by Ian Ring ©2019 cm cm C C cm->C D#+ D#+ cm->D#+ G# G# cm->G# C+ C+ C->C+ c#° c#° C->c#° em em C->em c#m c#m C+->c#m E E C+->E C+->G# am am C+->am c#°->c#m A A c#m->A D#+->em g#m g#m D#+->g#m em->E E->g#m g#m->G# 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.

Diameter5
Radius3
Self-Centeredno
Central VerticesC, C+, E, G♯
Peripheral VerticesD♯+, A

Modes

Modes are the rotational transformation of this scale. Scale 2971 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3533
Scale 3533: Thadyllic, Ian Ring Music TheoryThadyllic
3rd mode:
Scale 1907
Scale 1907: Lynyllic, Ian Ring Music TheoryLynyllic
4th mode:
Scale 3001
Scale 3001: Lonyllic, Ian Ring Music TheoryLonyllic
5th mode:
Scale 887
Scale 887: Sathyllic, Ian Ring Music TheorySathyllicThis is the prime mode
6th mode:
Scale 2491
Scale 2491: Layllic, Ian Ring Music TheoryLayllic
7th mode:
Scale 3293
Scale 3293: Saryllic, Ian Ring Music TheorySaryllic
8th mode:
Scale 1847
Scale 1847: Thacryllic, Ian Ring Music TheoryThacryllic

Prime

The prime form of this scale is Scale 887

Scale 887Scale 887: Sathyllic, Ian Ring Music TheorySathyllic

Complement

The octatonic modal family [2971, 3533, 1907, 3001, 887, 2491, 3293, 1847] (Forte: 8-19) is the complement of the tetratonic modal family [275, 305, 785, 2185] (Forte: 4-19)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2971 is 2875

Scale 2875Scale 2875: Ganyllic, Ian Ring Music TheoryGanyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2971 is chiral, and its enantiomorph is scale 2875

Scale 2875Scale 2875: Ganyllic, Ian Ring Music TheoryGanyllic

Transformations:

T0 2971  T0I 2875
T1 1847  T1I 1655
T2 3694  T2I 3310
T3 3293  T3I 2525
T4 2491  T4I 955
T5 887  T5I 1910
T6 1774  T6I 3820
T7 3548  T7I 3545
T8 3001  T8I 2995
T9 1907  T9I 1895
T10 3814  T10I 3790
T11 3533  T11I 3485

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 2969Scale 2969: Tholian, Ian Ring Music TheoryTholian
Scale 2973Scale 2973: Panyllic, Ian Ring Music TheoryPanyllic
Scale 2975Scale 2975: Aeroptygic, Ian Ring Music TheoryAeroptygic
Scale 2963Scale 2963: Bygian, Ian Ring Music TheoryBygian
Scale 2967Scale 2967: Madyllic, Ian Ring Music TheoryMadyllic
Scale 2955Scale 2955: Thorian, Ian Ring Music TheoryThorian
Scale 2987Scale 2987: Neapolitan Major and Minor Mixed, Ian Ring Music TheoryNeapolitan Major and Minor Mixed
Scale 3003Scale 3003: Genus Chromaticum, Ian Ring Music TheoryGenus Chromaticum
Scale 3035Scale 3035: Gocrygic, Ian Ring Music TheoryGocrygic
Scale 2843Scale 2843: Sorian, Ian Ring Music TheorySorian
Scale 2907Scale 2907: Magen Abot 2, Ian Ring Music TheoryMagen Abot 2
Scale 2715Scale 2715: Kynian, Ian Ring Music TheoryKynian
Scale 2459Scale 2459: Ionocrian, Ian Ring Music TheoryIonocrian
Scale 3483Scale 3483: Mixotharyllic, Ian Ring Music TheoryMixotharyllic
Scale 3995Scale 3995: Ionygic, Ian Ring Music TheoryIonygic
Scale 923Scale 923: Ultraphrygian, Ian Ring Music TheoryUltraphrygian
Scale 1947Scale 1947: Byptyllic, Ian Ring Music TheoryByptyllic

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.