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Scale 583: "Aeritonic"

Scale 583: Aeritonic, 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
Aeritonic

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

{0,1,2,6,9}

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-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: 3145

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: 295

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, 2, 2, 1]

Interval Spectrum

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

p2m2n2sd2t

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> = {2,4,5,6,7}
<3> = {5,6,7,8,10}
<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.

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}121
Minor Triadsf♯m{6,9,1}210.67
Diminished Triadsf♯°{6,9,0}121
Parsimonious Voice Leading Between Common Triads of Scale 583. Created by Ian Ring ©2019 D D f#m f#m D->f#m f#° f#° f#°->f#m

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 Verticesf♯m
Peripheral VerticesD, f♯°

Modes

Modes are the rotational transformation of this scale. Scale 583 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 2339
Scale 2339: Raga Kshanika, Ian Ring Music TheoryRaga Kshanika
3rd mode:
Scale 3217
Scale 3217: Molitonic, Ian Ring Music TheoryMolitonic
4th mode:
Scale 457
Scale 457: Staptitonic, Ian Ring Music TheoryStaptitonic
5th mode:
Scale 569
Scale 569: Mothitonic, Ian Ring Music TheoryMothitonic

Prime

The prime form of this scale is Scale 295

Scale 295Scale 295: Gyritonic, Ian Ring Music TheoryGyritonic

Complement

The pentatonic modal family [583, 2339, 3217, 457, 569] (Forte: 5-Z38) is the complement of the heptatonic modal family [439, 1763, 1819, 2267, 2929, 2957, 3181] (Forte: 7-Z38)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 583 is 3145

Scale 3145Scale 3145: Stolitonic, Ian Ring Music TheoryStolitonic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 583 is chiral, and its enantiomorph is scale 3145

Scale 3145Scale 3145: Stolitonic, Ian Ring Music TheoryStolitonic

Transformations:

T0 583  T0I 3145
T1 1166  T1I 2195
T2 2332  T2I 295
T3 569  T3I 590
T4 1138  T4I 1180
T5 2276  T5I 2360
T6 457  T6I 625
T7 914  T7I 1250
T8 1828  T8I 2500
T9 3656  T9I 905
T10 3217  T10I 1810
T11 2339  T11I 3620

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 581Scale 581: Eporic 2, Ian Ring Music TheoryEporic 2
Scale 579Scale 579, Ian Ring Music Theory
Scale 587Scale 587: Pathitonic, Ian Ring Music TheoryPathitonic
Scale 591Scale 591: Gaptimic, Ian Ring Music TheoryGaptimic
Scale 599Scale 599: Thyrimic, Ian Ring Music TheoryThyrimic
Scale 615Scale 615: Phrothimic, Ian Ring Music TheoryPhrothimic
Scale 519Scale 519, Ian Ring Music Theory
Scale 551Scale 551: Aeoloditonic, Ian Ring Music TheoryAeoloditonic
Scale 647Scale 647, Ian Ring Music Theory
Scale 711Scale 711: Raga Chandrajyoti, Ian Ring Music TheoryRaga Chandrajyoti
Scale 839Scale 839: Ionathimic, Ian Ring Music TheoryIonathimic
Scale 71Scale 71, Ian Ring Music Theory
Scale 327Scale 327: Syptitonic, Ian Ring Music TheorySyptitonic
Scale 1095Scale 1095: Phrythitonic, Ian Ring Music TheoryPhrythitonic
Scale 1607Scale 1607: Epytimic, Ian Ring Music TheoryEpytimic
Scale 2631Scale 2631: Macrimic, Ian Ring Music TheoryMacrimic

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.