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Scale 3813: "Aeologyllic"

Scale 3813: Aeologyllic, 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
Aeologyllic

Analysis

Cardinality

Cardinality is the count of how many pitches are in the scale.

8 (octatonic)

Pitch Class Set

The tones in this scale, expressed as numbers from 0 to 11

{0,2,5,6,7,9,10,11}

Forte Number

A code assigned by theorist Alan Forte, for this pitch class set and all of its transpositional (rotation) and inversional (reflection) transformations.

8-14

Rotational Symmetry

Some scales have rotational symmetry, sometimes known as "limited transposition". If there are any rotational symmetries, these are the intervals of periodicity.

none

Reflection Axes

If a scale has an axis of reflective symmetry, then it can transform into itself by inversion. It also implies that the scale has Ridge Tones. Notably an axis of reflection can occur directly on a tone or half way between two tones.

none

Palindromicity

A palindromic scale has the same pattern of intervals both ascending and descending.

no

Chirality

A chiral scale can not be transformed into its inverse by rotation. If a scale is chiral, then it has an enantiomorph.

yes
enantiomorph: 1263

Hemitonia

A hemitone is two tones separated by a semitone interval. Hemitonia describes how many such hemitones exist.

5 (multihemitonic)

Cohemitonia

A cohemitone is an instance of two adjacent hemitones. Cohemitonia describes how many such cohemitones exist.

3 (tricohemitonic)

Imperfections

An imperfection is a tone which does not have a perfect fifth above it in the scale. This value is the quantity of imperfections in this scale.

2

Modes

Modes are the rotational transformations of this scale. This number does not include the scale itself, so the number is usually one less than its cardinality; unless there are rotational symmetries then there are even fewer modes.

7

Prime Form

Describes if this scale is in prime form, using the Rahn/Ring formula.

no
prime: 759

Deep Scale

A deep scale is one where the interval vector has 6 different digits.

no

Interval Vector

Describes the intervallic content of the scale, read from left to right as the number of occurences of each interval size from semitone, up to six semitones.

[5, 5, 5, 5, 6, 2]

Interval Spectrum

The same as the Interval Vector, but expressed in a syntax used by Howard Hansen.

p6m5n5s5d5t2

Distribution Spectra

Describes the specific interval sizes that exist for each generic interval size. Each generic <g> has a spectrum {n,...}. The Spectrum Width is the difference between the highest and lowest values in each spectrum.

<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {3,4,5,6}
<4> = {5,7}
<5> = {6,7,8,9}
<6> = {7,8,9,10}
<7> = {9,10,11}

Spectra Variation

Determined by the Distribution Spectra; this is the sum of all spectrum widths divided by the scale cardinality.

2.25

Maximally Even

A scale is maximally even if the tones are optimally spaced apart from each other.

no

Maximal Area Set

A scale is a maximal area set if a polygon described by vertices dodecimetrically placed around a circle produces the maximal interior area for scales of the same cardinality. All maximally even sets have maximal area, but not all maximal area sets are maximally even.

no

Interior Area

Area of the polygon described by vertices placed for each tone of the scale dodecimetrically around a unit circle, ie a circle with radius of 1.

2.616

Polygon Perimeter

Perimeter of the polygon described by vertices placed for each tone of the scale dodecimetrically around a unit circle.

6.002

Myhill Property

A scale has Myhill Property if the Interval Spectra has exactly two specific intervals for every generic interval.

no

Balanced

A scale is balanced if the distribution of its tones would satisfy the "centrifuge problem", ie are placed such that it would balance on its centre point.

no

Ridge Tones

Ridge Tones are those that appear in all transpositions of a scale upon the members of that scale. Ridge Tones correspond directly with axes of reflective symmetry.

none

Propriety

Also known as Rothenberg Propriety, named after its inventor. Propriety describes whether every specific interval is uniquely mapped to a generic interval. A scale is either "Proper", "Strictly Proper", or "Improper".

Improper

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 TriadsD{2,6,9}331.7
F{5,9,0}252.5
G{7,11,2}252.5
A♯{10,2,5}331.7
Minor Triadsdm{2,5,9}341.9
gm{7,10,2}242.1
bm{11,2,6}341.9
Augmented TriadsD+{2,6,10}431.5
Diminished Triadsf♯°{6,9,0}242.3
{11,2,5}242.1
Parsimonious Voice Leading Between Common Triads of Scale 3813. Created by Ian Ring ©2019 dm dm D D dm->D F F dm->F A# A# dm->A# D+ D+ D->D+ f#° f#° D->f#° gm gm D+->gm D+->A# bm bm D+->bm F->f#° Parsimonious Voice Leading Between Common Triads of Scale 3813. Created by Ian Ring ©2019 G gm->G G->bm A#->b° b°->bm

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 VerticesD, D+, A♯
Peripheral VerticesF, G

Modes

Modes are the rotational transformation of this scale. Scale 3813 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 1977
Scale 1977: Dagyllic, Ian Ring Music TheoryDagyllic
3rd mode:
Scale 759
Scale 759: Katalyllic, Ian Ring Music TheoryKatalyllicThis is the prime mode
4th mode:
Scale 2427
Scale 2427: Katoryllic, Ian Ring Music TheoryKatoryllic
5th mode:
Scale 3261
Scale 3261: Dodyllic, Ian Ring Music TheoryDodyllic
6th mode:
Scale 1839
Scale 1839: Zogyllic, Ian Ring Music TheoryZogyllic
7th mode:
Scale 2967
Scale 2967: Madyllic, Ian Ring Music TheoryMadyllic
8th mode:
Scale 3531
Scale 3531: Neveseri, Ian Ring Music TheoryNeveseri

Prime

The prime form of this scale is Scale 759

Scale 759Scale 759: Katalyllic, Ian Ring Music TheoryKatalyllic

Complement

The octatonic modal family [3813, 1977, 759, 2427, 3261, 1839, 2967, 3531] (Forte: 8-14) is the complement of the tetratonic modal family [141, 417, 1059, 2577] (Forte: 4-14)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3813 is 1263

Scale 1263Scale 1263: Stynyllic, Ian Ring Music TheoryStynyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3813 is chiral, and its enantiomorph is scale 1263

Scale 1263Scale 1263: Stynyllic, Ian Ring Music TheoryStynyllic

Transformations:

T0 3813  T0I 1263
T1 3531  T1I 2526
T2 2967  T2I 957
T3 1839  T3I 1914
T4 3678  T4I 3828
T5 3261  T5I 3561
T6 2427  T6I 3027
T7 759  T7I 1959
T8 1518  T8I 3918
T9 3036  T9I 3741
T10 1977  T10I 3387
T11 3954  T11I 2679

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 3815Scale 3815: Galygic, Ian Ring Music TheoryGalygic
Scale 3809Scale 3809, Ian Ring Music Theory
Scale 3811Scale 3811: Epogyllic, Ian Ring Music TheoryEpogyllic
Scale 3817Scale 3817: Zoryllic, Ian Ring Music TheoryZoryllic
Scale 3821Scale 3821: Epyrygic, Ian Ring Music TheoryEpyrygic
Scale 3829Scale 3829: Taishikicho, Ian Ring Music TheoryTaishikicho
Scale 3781Scale 3781: Gyphian, Ian Ring Music TheoryGyphian
Scale 3797Scale 3797: Rocryllic, Ian Ring Music TheoryRocryllic
Scale 3749Scale 3749: Raga Sorati, Ian Ring Music TheoryRaga Sorati
Scale 3685Scale 3685: Kodian, Ian Ring Music TheoryKodian
Scale 3941Scale 3941: Stathyllic, Ian Ring Music TheoryStathyllic
Scale 4069Scale 4069: Starygic, Ian Ring Music TheoryStarygic
Scale 3301Scale 3301: Chromatic Mixolydian Inverse, Ian Ring Music TheoryChromatic Mixolydian Inverse
Scale 3557Scale 3557, Ian Ring Music Theory
Scale 2789Scale 2789: Zolian, Ian Ring Music TheoryZolian
Scale 1765Scale 1765: Lonian, Ian Ring Music TheoryLonian

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.