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Scale 551: "Aeoloditonic"

Scale 551: Aeoloditonic, 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
Aeoloditonic

Analysis

Cardinality

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

5 (pentatonic)

Pitch Class Set

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

{0,1,2,5,9}

Forte Number

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

5-Z37

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.

[1]

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.

no

Hemitonia

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

2 (dihemitonic)

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.

4

Prime Form

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

no
prime: 313

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.

[2, 1, 2, 3, 2, 0]

Interval Spectrum

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

p2m3n2sd2

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

Spectra Variation

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

3.2

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.

1.933

Polygon Perimeter

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

5.596

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.

[2]

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 TriadsF{5,9,0}121
Minor Triadsdm{2,5,9}121
Augmented TriadsC♯+{1,5,9}210.67
Parsimonious Voice Leading Between Common Triads of Scale 551. Created by Ian Ring ©2019 C#+ C#+ dm dm C#+->dm F F C#+->F

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.

Diameter2
Radius1
Self-Centeredno
Central VerticesC♯+
Peripheral Verticesdm, F

Modes

Modes are the rotational transformation of this scale. Scale 551 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 2323
Scale 2323: Doptitonic, Ian Ring Music TheoryDoptitonic
3rd mode:
Scale 3209
Scale 3209: Aeraphitonic, Ian Ring Music TheoryAeraphitonic
4th mode:
Scale 913
Scale 913: Aeolyritonic, Ian Ring Music TheoryAeolyritonic
5th mode:
Scale 313
Scale 313: Goritonic, Ian Ring Music TheoryGoritonicThis is the prime mode

Prime

The prime form of this scale is Scale 313

Scale 313Scale 313: Goritonic, Ian Ring Music TheoryGoritonic

Complement

The pentatonic modal family [551, 2323, 3209, 913, 313] (Forte: 5-Z37) is the complement of the heptatonic modal family [443, 1591, 1891, 2269, 2843, 2993, 3469] (Forte: 7-Z37)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 551 is 3209

Scale 3209Scale 3209: Aeraphitonic, Ian Ring Music TheoryAeraphitonic

Transformations:

T0 551  T0I 3209
T1 1102  T1I 2323
T2 2204  T2I 551
T3 313  T3I 1102
T4 626  T4I 2204
T5 1252  T5I 313
T6 2504  T6I 626
T7 913  T7I 1252
T8 1826  T8I 2504
T9 3652  T9I 913
T10 3209  T10I 1826
T11 2323  T11I 3652

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 549Scale 549: Raga Bhavani, Ian Ring Music TheoryRaga Bhavani
Scale 547Scale 547: Pyrric, Ian Ring Music TheoryPyrric
Scale 555Scale 555: Aeolycritonic, Ian Ring Music TheoryAeolycritonic
Scale 559Scale 559: Lylimic, Ian Ring Music TheoryLylimic
Scale 567Scale 567: Aeoladimic, Ian Ring Music TheoryAeoladimic
Scale 519Scale 519, Ian Ring Music Theory
Scale 535Scale 535, Ian Ring Music Theory
Scale 583Scale 583: Aeritonic, Ian Ring Music TheoryAeritonic
Scale 615Scale 615: Phrothimic, Ian Ring Music TheoryPhrothimic
Scale 679Scale 679: Lanimic, Ian Ring Music TheoryLanimic
Scale 807Scale 807: Raga Suddha Mukhari, Ian Ring Music TheoryRaga Suddha Mukhari
Scale 39Scale 39, Ian Ring Music Theory
Scale 295Scale 295: Gyritonic, Ian Ring Music TheoryGyritonic
Scale 1063Scale 1063, Ian Ring Music Theory
Scale 1575Scale 1575: Zycrimic, Ian Ring Music TheoryZycrimic
Scale 2599Scale 2599: Malimic, Ian Ring Music TheoryMalimic

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.