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Scale 1597: "Aeolodian"

Scale 1597: Aeolodian, 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
Aeolodian

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

{0,2,3,4,5,9,10}

Forte Number

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

7-14

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: 1933

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.

2

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: 431

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.

[4, 4, 3, 3, 5, 2]

Interval Spectrum

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

p5m3n3s4d4t2

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

2.857

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

Harmonic Chords

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}221.2
A♯{10,2,5}142
Minor Triadsdm{2,5,9}231.4
am{9,0,4}231.4
Diminished Triads{9,0,3}142
Parsimonious Voice Leading Between Common Triads of Scale 1597. Created by Ian Ring ©2019 dm dm F F dm->F A# A# dm->A# am am F->am a°->am

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 Verticesa°, A♯

Modes

Modes are the rotational transformation of this scale. Scale 1597 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 1423
Scale 1423: Doptian, Ian Ring Music TheoryDoptian
3rd mode:
Scale 2759
Scale 2759: Mela Pavani, Ian Ring Music TheoryMela Pavani
4th mode:
Scale 3427
Scale 3427: Zacrian, Ian Ring Music TheoryZacrian
5th mode:
Scale 3761
Scale 3761: Raga Madhuri, Ian Ring Music TheoryRaga Madhuri
6th mode:
Scale 491
Scale 491: Aeolyrian, Ian Ring Music TheoryAeolyrian
7th mode:
Scale 2293
Scale 2293: Gorian, Ian Ring Music TheoryGorian

Prime

The prime form of this scale is Scale 431

Scale 431Scale 431: Epyrian, Ian Ring Music TheoryEpyrian

Complement

The heptatonic modal family [1597, 1423, 2759, 3427, 3761, 491, 2293] (Forte: 7-14) is the complement of the pentatonic modal family [167, 901, 1249, 2131, 3113] (Forte: 5-14)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1597 is 1933

Scale 1933Scale 1933: Mocrian, Ian Ring Music TheoryMocrian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1597 is chiral, and its enantiomorph is scale 1933

Scale 1933Scale 1933: Mocrian, Ian Ring Music TheoryMocrian

Transformations:

T0 1597  T0I 1933
T1 3194  T1I 3866
T2 2293  T2I 3637
T3 491  T3I 3179
T4 982  T4I 2263
T5 1964  T5I 431
T6 3928  T6I 862
T7 3761  T7I 1724
T8 3427  T8I 3448
T9 2759  T9I 2801
T10 1423  T10I 1507
T11 2846  T11I 3014

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 1599Scale 1599: Pocryllic, Ian Ring Music TheoryPocryllic
Scale 1593Scale 1593: Zogimic, Ian Ring Music TheoryZogimic
Scale 1595Scale 1595: Dacrian, Ian Ring Music TheoryDacrian
Scale 1589Scale 1589: Raga Rageshri, Ian Ring Music TheoryRaga Rageshri
Scale 1581Scale 1581: Raga Bagesri, Ian Ring Music TheoryRaga Bagesri
Scale 1565Scale 1565, Ian Ring Music Theory
Scale 1629Scale 1629: Synian, Ian Ring Music TheorySynian
Scale 1661Scale 1661: Gonyllic, Ian Ring Music TheoryGonyllic
Scale 1725Scale 1725: Minor Bebop, Ian Ring Music TheoryMinor Bebop
Scale 1853Scale 1853: Maryllic, Ian Ring Music TheoryMaryllic
Scale 1085Scale 1085, Ian Ring Music Theory
Scale 1341Scale 1341: Madian, Ian Ring Music TheoryMadian
Scale 573Scale 573: Saptimic, Ian Ring Music TheorySaptimic
Scale 2621Scale 2621: Ionogian, Ian Ring Music TheoryIonogian
Scale 3645Scale 3645: Zycryllic, Ian Ring Music TheoryZycryllic

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.