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Scale 2375: "Aeolaptimic"

Scale 2375: Aeolaptimic, 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

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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
Aeolaptimic

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

{0,1,2,6,8,11}

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-Z41

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: 3155

Hemitonia

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

3 (trihemitonic)

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.

5

Prime Form

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

no
prime: 335

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.

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

Interval Spectrum

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

p3m2n2s3d3t2

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> = {1,2,3,4}
<2> = {2,4,5,6}
<3> = {3,5,6,7,9}
<4> = {6,7,8,10}
<5> = {8,9,10,11}

Spectra Variation

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

3.333

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.

2.116

Polygon Perimeter

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

5.699

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
Minor Triadsbm{11,2,6}110.5
Diminished Triadsg♯°{8,11,2}110.5

The following pitch classes are not present in any of the common triads: {0,1}

Parsimonious Voice Leading Between Common Triads of Scale 2375. Created by Ian Ring ©2019 g#° g#° bm bm g#°->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.

Diameter1
Radius1
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 2375 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 3235
Scale 3235: Pothimic, Ian Ring Music TheoryPothimic
3rd mode:
Scale 3665
Scale 3665: Stalimic, Ian Ring Music TheoryStalimic
4th mode:
Scale 485
Scale 485: Stoptimic, Ian Ring Music TheoryStoptimic
5th mode:
Scale 1145
Scale 1145: Zygimic, Ian Ring Music TheoryZygimic
6th mode:
Scale 655
Scale 655: Kataptimic, Ian Ring Music TheoryKataptimic

Prime

The prime form of this scale is Scale 335

Scale 335Scale 335: Zanimic, Ian Ring Music TheoryZanimic

Complement

The hexatonic modal family [2375, 3235, 3665, 485, 1145, 655] (Forte: 6-Z41) is the complement of the hexatonic modal family [215, 1475, 1805, 2155, 2785, 3125] (Forte: 6-Z12)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2375 is 3155

Scale 3155Scale 3155: Ladimic, Ian Ring Music TheoryLadimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2375 is chiral, and its enantiomorph is scale 3155

Scale 3155Scale 3155: Ladimic, Ian Ring Music TheoryLadimic

Transformations:

T0 2375  T0I 3155
T1 655  T1I 2215
T2 1310  T2I 335
T3 2620  T3I 670
T4 1145  T4I 1340
T5 2290  T5I 2680
T6 485  T6I 1265
T7 970  T7I 2530
T8 1940  T8I 965
T9 3880  T9I 1930
T10 3665  T10I 3860
T11 3235  T11I 3625

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 2373Scale 2373: Dyptitonic, Ian Ring Music TheoryDyptitonic
Scale 2371Scale 2371, Ian Ring Music Theory
Scale 2379Scale 2379: Raga Gurjari Todi, Ian Ring Music TheoryRaga Gurjari Todi
Scale 2383Scale 2383: Katorian, Ian Ring Music TheoryKatorian
Scale 2391Scale 2391: Molian, Ian Ring Music TheoryMolian
Scale 2407Scale 2407: Zylian, Ian Ring Music TheoryZylian
Scale 2311Scale 2311: Raga Kumarapriya, Ian Ring Music TheoryRaga Kumarapriya
Scale 2343Scale 2343: Tharimic, Ian Ring Music TheoryTharimic
Scale 2439Scale 2439, Ian Ring Music Theory
Scale 2503Scale 2503: Mela Jhalavarali, Ian Ring Music TheoryMela Jhalavarali
Scale 2119Scale 2119, Ian Ring Music Theory
Scale 2247Scale 2247: Raga Vijayasri, Ian Ring Music TheoryRaga Vijayasri
Scale 2631Scale 2631: Macrimic, Ian Ring Music TheoryMacrimic
Scale 2887Scale 2887: Gaptian, Ian Ring Music TheoryGaptian
Scale 3399Scale 3399: Zonian, Ian Ring Music TheoryZonian
Scale 327Scale 327: Syptitonic, Ian Ring Music TheorySyptitonic
Scale 1351Scale 1351: Aeraptimic, Ian Ring Music TheoryAeraptimic

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.