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Scale 3189: "Aeolonian"

Scale 3189: Aeolonian, 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
Aeolonian

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

{0,2,4,5,6,10,11}

Forte Number

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

7-15

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.

[2]

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.

4 (multihemitonic)

Cohemitonia

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

2 (dicohemitonic)

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: 471

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.

[2, 2, 1, 1, 4, 1, 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, 4, 2, 4, 4, 3>

Interval Spectrum

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

p4m4n2s4d4t3

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

Spectra Variation

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

2.286

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.

[4]

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

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 TriadsA♯{10,2,5}221
Minor Triadsbm{11,2,6}221
Augmented TriadsD+{2,6,10}221
Diminished Triads{11,2,5}221

The following pitch classes are not present in any of the common triads: {0,4}

Parsimonious Voice Leading Between Common Triads of Scale 3189. Created by Ian Ring ©2019 D+ D+ A# A# D+->A# bm bm D+->bm A#->b° b°->bm

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
Radius2
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 3189 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 1821
Scale 1821: Aeradian, Ian Ring Music TheoryAeradian
3rd mode:
Scale 1479
Scale 1479: Mela Jalarnava, Ian Ring Music TheoryMela Jalarnava
4th mode:
Scale 2787
Scale 2787: Zyrian, Ian Ring Music TheoryZyrian
5th mode:
Scale 3441
Scale 3441: Thacrian, Ian Ring Music TheoryThacrian
6th mode:
Scale 471
Scale 471: Dodian, Ian Ring Music TheoryDodianThis is the prime mode
7th mode:
Scale 2283
Scale 2283: Aeolyptian, Ian Ring Music TheoryAeolyptian

Prime

The prime form of this scale is Scale 471

Scale 471Scale 471: Dodian, Ian Ring Music TheoryDodian

Complement

The heptatonic modal family [3189, 1821, 1479, 2787, 3441, 471, 2283] (Forte: 7-15) is the complement of the pentatonic modal family [327, 453, 1137, 2211, 3153] (Forte: 5-15)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3189 is 1479

Scale 1479Scale 1479: Mela Jalarnava, Ian Ring Music TheoryMela Jalarnava

Transformations:

T0 3189  T0I 1479
T1 2283  T1I 2958
T2 471  T2I 1821
T3 942  T3I 3642
T4 1884  T4I 3189
T5 3768  T5I 2283
T6 3441  T6I 471
T7 2787  T7I 942
T8 1479  T8I 1884
T9 2958  T9I 3768
T10 1821  T10I 3441
T11 3642  T11I 2787

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 3191Scale 3191: Bynyllic, Ian Ring Music TheoryBynyllic
Scale 3185Scale 3185: Messiaen Mode 5 Inverse, Ian Ring Music TheoryMessiaen Mode 5 Inverse
Scale 3187Scale 3187: Koptian, Ian Ring Music TheoryKoptian
Scale 3193Scale 3193: Zathian, Ian Ring Music TheoryZathian
Scale 3197Scale 3197: Gylyllic, Ian Ring Music TheoryGylyllic
Scale 3173Scale 3173: Zarimic, Ian Ring Music TheoryZarimic
Scale 3181Scale 3181: Rolian, Ian Ring Music TheoryRolian
Scale 3157Scale 3157: Zyptimic, Ian Ring Music TheoryZyptimic
Scale 3125Scale 3125, Ian Ring Music Theory
Scale 3253Scale 3253: Mela Naganandini, Ian Ring Music TheoryMela Naganandini
Scale 3317Scale 3317: Katynyllic, Ian Ring Music TheoryKatynyllic
Scale 3445Scale 3445: Messiaen Mode 6 Inverse, Ian Ring Music TheoryMessiaen Mode 6 Inverse
Scale 3701Scale 3701: Bagyllic, Ian Ring Music TheoryBagyllic
Scale 2165Scale 2165, Ian Ring Music Theory
Scale 2677Scale 2677: Thodian, Ian Ring Music TheoryThodian
Scale 1141Scale 1141: Rynimic, Ian Ring Music TheoryRynimic

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.