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Scale 895: "Aeolathygic"

Scale 895: Aeolathygic, 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
Aeolathygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,1,2,3,4,5,6,8,9}
Forte Number9-3
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 4057
Hemitonia7 (multihemitonic)
Cohemitonia5 (multicohemitonic)
Imperfections3
Modes8
Prime?yes
Deep Scaleno
Interval Vector767763
Interval Spectrump6m7n7s6d7t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4}
<3> = {3,4,5,6}
<4> = {4,5,6,7}
<5> = {5,6,7,8}
<6> = {6,7,8,9}
<7> = {8,9,10}
<8> = {9,10,11}
Spectra Variation2.222
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♯{1,5,8}442.24
D{2,6,9}342.53
F{5,9,0}442.12
G♯{8,0,3}342.53
A{9,1,4}342.24
Minor Triadsc♯m{1,4,8}342.35
dm{2,5,9}342.35
fm{5,8,0}342.24
f♯m{6,9,1}342.35
am{9,0,4}442.24
Augmented TriadsC+{0,4,8}442.24
C♯+{1,5,9}542
Diminished Triads{0,3,6}242.76
{2,5,8}252.71
d♯°{3,6,9}242.76
f♯°{6,9,0}242.59
{9,0,3}252.71
Parsimonious Voice Leading Between Common Triads of Scale 895. Created by Ian Ring ©2019 d#° d#° c°->d#° G# G# c°->G# C+ C+ c#m c#m C+->c#m fm fm C+->fm C+->G# am am C+->am C# C# c#m->C# A A c#m->A C#+ C#+ C#->C#+ C#->d° C#->fm dm dm C#+->dm F F C#+->F f#m f#m C#+->f#m C#+->A d°->dm D D dm->D D->d#° D->f#m fm->F f#° f#° F->f#° F->am f#°->f#m 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
Radius4
Self-Centeredno
Central Verticesc°, C+, c♯m, C♯, C♯+, dm, D, d♯°, fm, F, f♯°, f♯m, G♯, am, A
Peripheral Verticesd°, a°

Modes

Modes are the rotational transformation of this scale. Scale 895 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 2495
Scale 2495: Aeolocrygic, Ian Ring Music TheoryAeolocrygic
3rd mode:
Scale 3295
Scale 3295: Phroptygic, Ian Ring Music TheoryPhroptygic
4th mode:
Scale 3695
Scale 3695: Kodygic, Ian Ring Music TheoryKodygic
5th mode:
Scale 3895
Scale 3895: Eparygic, Ian Ring Music TheoryEparygic
6th mode:
Scale 3995
Scale 3995: Ionygic, Ian Ring Music TheoryIonygic
7th mode:
Scale 4045
Scale 4045: Gyptygic, Ian Ring Music TheoryGyptygic
8th mode:
Scale 2035
Scale 2035: Aerythygic, Ian Ring Music TheoryAerythygic
9th mode:
Scale 3065
Scale 3065: Zothygic, Ian Ring Music TheoryZothygic

Prime

This is the prime form of this scale.

Complement

The nonatonic modal family [895, 2495, 3295, 3695, 3895, 3995, 4045, 2035, 3065] (Forte: 9-3) is the complement of the tritonic modal family [19, 769, 2057] (Forte: 3-3)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 895 is 4057

Scale 4057Scale 4057: Phrygic, Ian Ring Music TheoryPhrygic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 895 is chiral, and its enantiomorph is scale 4057

Scale 4057Scale 4057: Phrygic, Ian Ring Music TheoryPhrygic

Transformations:

T0 895  T0I 4057
T1 1790  T1I 4019
T2 3580  T2I 3943
T3 3065  T3I 3791
T4 2035  T4I 3487
T5 4070  T5I 2879
T6 4045  T6I 1663
T7 3995  T7I 3326
T8 3895  T8I 2557
T9 3695  T9I 1019
T10 3295  T10I 2038
T11 2495  T11I 4076

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 893Scale 893: Dadyllic, Ian Ring Music TheoryDadyllic
Scale 891Scale 891: Ionilyllic, Ian Ring Music TheoryIonilyllic
Scale 887Scale 887: Sathyllic, Ian Ring Music TheorySathyllic
Scale 879Scale 879: Aeranyllic, Ian Ring Music TheoryAeranyllic
Scale 863Scale 863: Pyryllic, Ian Ring Music TheoryPyryllic
Scale 831Scale 831: Rodyllic, Ian Ring Music TheoryRodyllic
Scale 959Scale 959: Katylygic, Ian Ring Music TheoryKatylygic
Scale 1023Scale 1023: Dodyllian, Ian Ring Music TheoryDodyllian
Scale 639Scale 639: Ionaryllic, Ian Ring Music TheoryIonaryllic
Scale 767Scale 767: Raptygic, Ian Ring Music TheoryRaptygic
Scale 383Scale 383: Logyllic, Ian Ring Music TheoryLogyllic
Scale 1407Scale 1407: Tharygic, Ian Ring Music TheoryTharygic
Scale 1919Scale 1919: Rocryllian, Ian Ring Music TheoryRocryllian
Scale 2943Scale 2943: Dathyllian, Ian Ring Music TheoryDathyllian

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.