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Scale 2623: "Aerylyllic"

Scale 2623: Aerylyllic, 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
Aerylyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,2,3,4,5,9,11}
Forte Number8-2
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3979
Hemitonia6 (multihemitonic)
Cohemitonia5 (multicohemitonic)
Imperfections4
Modes7
Prime?no
prime: 383
Deep Scaleno
Interval Vector665542
Interval Spectrump4m5n5s6d6t2
Distribution Spectra<1> = {1,2,4}
<2> = {2,3,5,6}
<3> = {3,4,6,7}
<4> = {4,5,7,8}
<5> = {5,6,8,9}
<6> = {6,7,9,10}
<7> = {8,10,11}
Spectra Variation3.25
Maximally Evenno
Maximal Area Setno
Interior Area2.366
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 TriadsF{5,9,0}231.57
A{9,1,4}231.57
Minor Triadsdm{2,5,9}241.86
am{9,0,4}341.71
Augmented TriadsC♯+{1,5,9}331.43
Diminished Triads{9,0,3}152.43
{11,2,5}152.57
Parsimonious Voice Leading Between Common Triads of Scale 2623. Created by Ian Ring ©2019 C#+ C#+ dm dm C#+->dm F F C#+->F A A C#+->A dm->b° am am F->am a°->am am->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.

Diameter5
Radius3
Self-Centeredno
Central VerticesC♯+, F, A
Peripheral Verticesa°, b°

Modes

Modes are the rotational transformation of this scale. Scale 2623 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3359
Scale 3359: Bonyllic, Ian Ring Music TheoryBonyllic
3rd mode:
Scale 3727
Scale 3727: Tholyllic, Ian Ring Music TheoryTholyllic
4th mode:
Scale 3911
Scale 3911: Katyryllic, Ian Ring Music TheoryKatyryllic
5th mode:
Scale 4003
Scale 4003: Sadyllic, Ian Ring Music TheorySadyllic
6th mode:
Scale 4049
Scale 4049: Stycryllic, Ian Ring Music TheoryStycryllic
7th mode:
Scale 509
Scale 509: Ionothyllic, Ian Ring Music TheoryIonothyllic
8th mode:
Scale 1151
Scale 1151: Mythyllic, Ian Ring Music TheoryMythyllic

Prime

The prime form of this scale is Scale 383

Scale 383Scale 383: Logyllic, Ian Ring Music TheoryLogyllic

Complement

The octatonic modal family [2623, 3359, 3727, 3911, 4003, 4049, 509, 1151] (Forte: 8-2) is the complement of the tetratonic modal family [23, 1793, 2059, 3077] (Forte: 4-2)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2623 is 3979

Scale 3979Scale 3979: Dynyllic, Ian Ring Music TheoryDynyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2623 is chiral, and its enantiomorph is scale 3979

Scale 3979Scale 3979: Dynyllic, Ian Ring Music TheoryDynyllic

Transformations:

T0 2623  T0I 3979
T1 1151  T1I 3863
T2 2302  T2I 3631
T3 509  T3I 3167
T4 1018  T4I 2239
T5 2036  T5I 383
T6 4072  T6I 766
T7 4049  T7I 1532
T8 4003  T8I 3064
T9 3911  T9I 2033
T10 3727  T10I 4066
T11 3359  T11I 4037

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 2621Scale 2621: Ionogian, Ian Ring Music TheoryIonogian
Scale 2619Scale 2619: Ionyrian, Ian Ring Music TheoryIonyrian
Scale 2615Scale 2615: Thoptian, Ian Ring Music TheoryThoptian
Scale 2607Scale 2607: Aerolian, Ian Ring Music TheoryAerolian
Scale 2591Scale 2591, Ian Ring Music Theory
Scale 2655Scale 2655, Ian Ring Music Theory
Scale 2687Scale 2687: Thacrygic, Ian Ring Music TheoryThacrygic
Scale 2751Scale 2751: Sylygic, Ian Ring Music TheorySylygic
Scale 2879Scale 2879: Stadygic, Ian Ring Music TheoryStadygic
Scale 2111Scale 2111, Ian Ring Music Theory
Scale 2367Scale 2367: Laryllic, Ian Ring Music TheoryLaryllic
Scale 3135Scale 3135, Ian Ring Music Theory
Scale 3647Scale 3647: Eporygic, Ian Ring Music TheoryEporygic
Scale 575Scale 575: Ionydian, Ian Ring Music TheoryIonydian
Scale 1599Scale 1599: Pocryllic, Ian Ring Music TheoryPocryllic

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.