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Scale 2915: "Aeolydian"

Scale 2915: Aeolydian, 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

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
Aeolydian
Dozenal
Argian

Analysis

Cardinality

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

7 (heptatonic)

Pitch Class Set

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

{0,1,5,6,8,9,11}

Forte Number

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

7-Z38

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: 2267

Hemitonia

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

4 (multihemitonic)

Cohemitonia

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

1 (uncohemitonic)

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.

3

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.

6

Prime Form

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

no
prime: 439

Generator

Indicates if the scale can be constructed using a generator, and an origin.

none

Deep Scale

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

no

Interval Structure

Defines the scale as the sequence of intervals between one tone and the next.

[1, 4, 1, 2, 1, 2, 1]

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.

<4, 3, 4, 4, 4, 2>

Interval Spectrum

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

p4m4n4s3d4t2

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

Spectra Variation

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

2.571

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.

2.299

Polygon Perimeter

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

5.803

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

Heteromorphic Profile

Defined by Norman Carey (2002), the heteromorphic profile is an ordered triple of (c, a, d) where c is the number of contradictions, a is the number of ambiguities, and d is the number of differences. When c is zero, the scale is Proper. When a is also zero, the scale is Strictly Proper.

(27, 24, 90)

Tertian Harmonic Chords

Tertian chords are made from alternating members of the scale, ie built from "stacked thirds". Not all scales lend themselves well to tertian harmony.

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}231.57
F{5,9,0}321.29
Minor Triadsfm{5,8,0}331.43
f♯m{6,9,1}241.86
Augmented TriadsC♯+{1,5,9}331.43
Diminished Triads{5,8,11}142.14
f♯°{6,9,0}231.71
Parsimonious Voice Leading Between Common Triads of Scale 2915. Created by Ian Ring ©2019 C# C# C#+ C#+ C#->C#+ fm fm C#->fm F F C#+->F f#m f#m C#+->f#m f°->fm fm->F f#° f#° F->f#° f#°->f#m

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
Radius2
Self-Centeredno
Central VerticesF
Peripheral Verticesf°, f♯m

Modes

Modes are the rotational transformation of this scale. Scale 2915 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 3505
Scale 3505: Stygian, Ian Ring Music TheoryStygian
3rd mode:
Scale 475
Scale 475: Aeolygian, Ian Ring Music TheoryAeolygian
4th mode:
Scale 2285
Scale 2285: Aerogian, Ian Ring Music TheoryAerogian
5th mode:
Scale 1595
Scale 1595: Dacrian, Ian Ring Music TheoryDacrian
6th mode:
Scale 2845
Scale 2845: Baptian, Ian Ring Music TheoryBaptian
7th mode:
Scale 1735
Scale 1735: Mela Navanitam, Ian Ring Music TheoryMela Navanitam

Prime

The prime form of this scale is Scale 439

Scale 439Scale 439: Bythian, Ian Ring Music TheoryBythian

Complement

The heptatonic modal family [2915, 3505, 475, 2285, 1595, 2845, 1735] (Forte: 7-Z38) is the complement of the pentatonic modal family [295, 625, 905, 2195, 3145] (Forte: 5-Z38)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2915 is 2267

Scale 2267Scale 2267: Padian, Ian Ring Music TheoryPadian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2915 is chiral, and its enantiomorph is scale 2267

Scale 2267Scale 2267: Padian, Ian Ring Music TheoryPadian

Transformations:

In the abbreviation, the subscript number after "T" is the number of semitones of tranposition, "M" means the pitch class is multiplied by 5, and "I" means the result is inverted. Operation is an identical way to express the same thing; the syntax is <a,b> where each tone of the set x is transformed by the equation y = ax + b

Abbrev Operation Result Abbrev Operation Result
T0 <1,0> 2915       T0I <11,0> 2267
T1 <1,1> 1735      T1I <11,1> 439
T2 <1,2> 3470      T2I <11,2> 878
T3 <1,3> 2845      T3I <11,3> 1756
T4 <1,4> 1595      T4I <11,4> 3512
T5 <1,5> 3190      T5I <11,5> 2929
T6 <1,6> 2285      T6I <11,6> 1763
T7 <1,7> 475      T7I <11,7> 3526
T8 <1,8> 950      T8I <11,8> 2957
T9 <1,9> 1900      T9I <11,9> 1819
T10 <1,10> 3800      T10I <11,10> 3638
T11 <1,11> 3505      T11I <11,11> 3181
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 755      T0MI <7,0> 2537
T1M <5,1> 1510      T1MI <7,1> 979
T2M <5,2> 3020      T2MI <7,2> 1958
T3M <5,3> 1945      T3MI <7,3> 3916
T4M <5,4> 3890      T4MI <7,4> 3737
T5M <5,5> 3685      T5MI <7,5> 3379
T6M <5,6> 3275      T6MI <7,6> 2663
T7M <5,7> 2455      T7MI <7,7> 1231
T8M <5,8> 815      T8MI <7,8> 2462
T9M <5,9> 1630      T9MI <7,9> 829
T10M <5,10> 3260      T10MI <7,10> 1658
T11M <5,11> 2425      T11MI <7,11> 3316

The transformations that map this set to itself are: T0

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 2913Scale 2913: Senian, Ian Ring Music TheorySenian
Scale 2917Scale 2917: Nohkan Flute Scale, Ian Ring Music TheoryNohkan Flute Scale
Scale 2919Scale 2919: Molyllic, Ian Ring Music TheoryMolyllic
Scale 2923Scale 2923: Baryllic, Ian Ring Music TheoryBaryllic
Scale 2931Scale 2931: Zathyllic, Ian Ring Music TheoryZathyllic
Scale 2883Scale 2883: Savian, Ian Ring Music TheorySavian
Scale 2899Scale 2899: Kagian, Ian Ring Music TheoryKagian
Scale 2851Scale 2851: Katoptimic, Ian Ring Music TheoryKatoptimic
Scale 2979Scale 2979: Gyptian, Ian Ring Music TheoryGyptian
Scale 3043Scale 3043: Ionayllic, Ian Ring Music TheoryIonayllic
Scale 2659Scale 2659: Katynimic, Ian Ring Music TheoryKatynimic
Scale 2787Scale 2787: Zyrian, Ian Ring Music TheoryZyrian
Scale 2403Scale 2403: Lycrimic, Ian Ring Music TheoryLycrimic
Scale 3427Scale 3427: Zacrian, Ian Ring Music TheoryZacrian
Scale 3939Scale 3939: Dogyllic, Ian Ring Music TheoryDogyllic
Scale 867Scale 867: Phrocrimic, Ian Ring Music TheoryPhrocrimic
Scale 1891Scale 1891: Thalian, Ian Ring Music TheoryThalian

This scale analysis was created by Ian Ring, Canadian Composer of works for Piano, and total music theory nerd. Scale notation generated by VexFlow, graph visualization by Graphviz, and MIDI playback by MIDI.js. All other diagrams and visualizations are © Ian Ring. 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, and George Howlett for assistance with the Carnatic ragas.