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Scale 603: "Aeolygimic"

Scale 603: Aeolygimic, 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
Aeolygimic

Analysis

Cardinality

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

6 (hexatonic)

Pitch Class Set

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

{0,1,3,4,6,9}

Forte Number

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

6-27

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: 2889

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.

0 (ancohemitonic)

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.

4

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.

5

Prime Form

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

yes

Deep Scale

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

no

Interval Formula

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

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

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, 2, 5, 2, 2, 2>

Interval Spectrum

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

p2m2n5s2d2t2

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

Spectra Variation

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

2.333

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.

2.366

Polygon Perimeter

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

5.864

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 TriadsA{9,1,4}231.57
Minor Triadsf♯m{6,9,1}331.43
am{9,0,4}331.43
Diminished Triads{0,3,6}231.71
d♯°{3,6,9}231.57
f♯°{6,9,0}231.57
{9,0,3}231.57
Parsimonious Voice Leading Between Common Triads of Scale 603. Created by Ian Ring ©2019 d#° d#° c°->d#° c°->a° f#m f#m d#°->f#m f#° f#° f#°->f#m am am f#°->am A A f#m->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.

Diameter3
Radius3
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 603 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 2349
Scale 2349: Raga Ghantana, Ian Ring Music TheoryRaga Ghantana
3rd mode:
Scale 1611
Scale 1611: Dacrimic, Ian Ring Music TheoryDacrimic
4th mode:
Scale 2853
Scale 2853: Baptimic, Ian Ring Music TheoryBaptimic
5th mode:
Scale 1737
Scale 1737: Raga Madhukauns, Ian Ring Music TheoryRaga Madhukauns
6th mode:
Scale 729
Scale 729: Stygimic, Ian Ring Music TheoryStygimic

Prime

This is the prime form of this scale.

Complement

The hexatonic modal family [603, 2349, 1611, 2853, 1737, 729] (Forte: 6-27) is the complement of the hexatonic modal family [603, 729, 1611, 1737, 2349, 2853] (Forte: 6-27)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 603 is 2889

Scale 2889Scale 2889: Thoptimic, Ian Ring Music TheoryThoptimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 603 is chiral, and its enantiomorph is scale 2889

Scale 2889Scale 2889: Thoptimic, Ian Ring Music TheoryThoptimic

Transformations:

T0 603  T0I 2889
T1 1206  T1I 1683
T2 2412  T2I 3366
T3 729  T3I 2637
T4 1458  T4I 1179
T5 2916  T5I 2358
T6 1737  T6I 621
T7 3474  T7I 1242
T8 2853  T8I 2484
T9 1611  T9I 873
T10 3222  T10I 1746
T11 2349  T11I 3492

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 601Scale 601: Bycritonic, Ian Ring Music TheoryBycritonic
Scale 605Scale 605: Dycrimic, Ian Ring Music TheoryDycrimic
Scale 607Scale 607: Kadian, Ian Ring Music TheoryKadian
Scale 595Scale 595: Sogitonic, Ian Ring Music TheorySogitonic
Scale 599Scale 599: Thyrimic, Ian Ring Music TheoryThyrimic
Scale 587Scale 587: Pathitonic, Ian Ring Music TheoryPathitonic
Scale 619Scale 619: Double-Phrygian Hexatonic, Ian Ring Music TheoryDouble-Phrygian Hexatonic
Scale 635Scale 635: Epolian, Ian Ring Music TheoryEpolian
Scale 539Scale 539, Ian Ring Music Theory
Scale 571Scale 571: Kynimic, Ian Ring Music TheoryKynimic
Scale 667Scale 667: Rodimic, Ian Ring Music TheoryRodimic
Scale 731Scale 731: Alternating Heptamode, Ian Ring Music TheoryAlternating Heptamode
Scale 859Scale 859: Ultralocrian, Ian Ring Music TheoryUltralocrian
Scale 91Scale 91, Ian Ring Music Theory
Scale 347Scale 347: Barimic, Ian Ring Music TheoryBarimic
Scale 1115Scale 1115: Superlocrian Hexamirror, Ian Ring Music TheorySuperlocrian Hexamirror
Scale 1627Scale 1627: Zyptian, Ian Ring Music TheoryZyptian
Scale 2651Scale 2651: Panian, Ian Ring Music TheoryPanian

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. 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.