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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

Cardinality6 (hexatonic)
Pitch Class Set{0,1,2,6,8,11}
Forte Number6-Z41
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3155
Hemitonia3 (trihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections3
Modes5
Prime?no
prime: 335
Deep Scaleno
Interval Vector332232
Interval Spectrump3m2n2s3d3t2
Distribution Spectra<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 Variation3.333
Maximally Evenno
Maximal Area Setno
Interior Area2.116
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicno

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
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.