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Scale 397: "Aeolian Pentatonic"

Scale 397: Aeolian Pentatonic, 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

Western Modern
Aeolian Pentatonic
Japanese
Hira-joshi
Hirajoshi
Hira-choshi
Kata-kumoi
Yona Nuki Minor
Ethiopian
Tizita Minor
Half Tizita
Zeitler
Epogitonic

Analysis

Cardinality5 (pentatonic)
Pitch Class Set{0,2,3,7,8}
Forte Number5-20
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1585
Hemitonia2 (dihemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections2
Modes4
Prime?no
prime: 355
Deep Scaleno
Interval Vector211231
Interval Spectrump3m2nsd2t
Distribution Spectra<1> = {1,2,4}
<2> = {3,5,6}
<3> = {6,7,9}
<4> = {8,10,11}
Spectra Variation2.4
Maximally Evenno
Maximal Area Setno
Interior Area1.799
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
Major TriadsG♯{8,0,3}110.5
Minor Triadscm{0,3,7}110.5
Parsimonious Voice Leading Between Common Triads of Scale 397. Created by Ian Ring ©2019 cm cm G# G# cm->G#

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 397 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 1123
Scale 1123: Iwato, Ian Ring Music TheoryIwato
3rd mode:
Scale 2609
Scale 2609: Raga Bhinna Shadja, Ian Ring Music TheoryRaga Bhinna Shadja
4th mode:
Scale 419
Scale 419: Hon-kumoi-joshi, Ian Ring Music TheoryHon-kumoi-joshi
5th mode:
Scale 2257
Scale 2257: Lydian Pentatonic, Ian Ring Music TheoryLydian Pentatonic

Prime

The prime form of this scale is Scale 355

Scale 355Scale 355: Aeoloritonic, Ian Ring Music TheoryAeoloritonic

Complement

The pentatonic modal family [397, 1123, 2609, 419, 2257] (Forte: 5-20) is the complement of the heptatonic modal family [743, 919, 1849, 2419, 2507, 3257, 3301] (Forte: 7-20)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 397 is 1585

Scale 1585Scale 1585: Raga Khamaji Durga, Ian Ring Music TheoryRaga Khamaji Durga

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 397 is chiral, and its enantiomorph is scale 1585

Scale 1585Scale 1585: Raga Khamaji Durga, Ian Ring Music TheoryRaga Khamaji Durga

Transformations:

T0 397  T0I 1585
T1 794  T1I 3170
T2 1588  T2I 2245
T3 3176  T3I 395
T4 2257  T4I 790
T5 419  T5I 1580
T6 838  T6I 3160
T7 1676  T7I 2225
T8 3352  T8I 355
T9 2609  T9I 710
T10 1123  T10I 1420
T11 2246  T11I 2840

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 399Scale 399: Zynimic, Ian Ring Music TheoryZynimic
Scale 393Scale 393: Lothic, Ian Ring Music TheoryLothic
Scale 395Scale 395: Phrygian Pentatonic, Ian Ring Music TheoryPhrygian Pentatonic
Scale 389Scale 389, Ian Ring Music Theory
Scale 405Scale 405: Raga Bhupeshwari, Ian Ring Music TheoryRaga Bhupeshwari
Scale 413Scale 413: Ganimic, Ian Ring Music TheoryGanimic
Scale 429Scale 429: Koptimic, Ian Ring Music TheoryKoptimic
Scale 461Scale 461: Raga Syamalam, Ian Ring Music TheoryRaga Syamalam
Scale 269Scale 269, Ian Ring Music Theory
Scale 333Scale 333: Bogitonic, Ian Ring Music TheoryBogitonic
Scale 141Scale 141, Ian Ring Music Theory
Scale 653Scale 653: Dorian Pentatonic, Ian Ring Music TheoryDorian Pentatonic
Scale 909Scale 909: Katarimic, Ian Ring Music TheoryKatarimic
Scale 1421Scale 1421: Raga Trimurti, Ian Ring Music TheoryRaga Trimurti
Scale 2445Scale 2445: Zadimic, Ian Ring Music TheoryZadimic

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.