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Scale 539

Scale 539, 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).

Analysis

Cardinality5 (pentatonic)
Pitch Class Set{0,1,3,4,9}
Forte Number5-16
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2825
Hemitonia2 (dihemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections4
Modes4
Prime?no
prime: 155
Deep Scaleno
Interval Vector213211
Interval Spectrumpm2n3sd2t
Distribution Spectra<1> = {1,2,3,5}
<2> = {3,4,6,8}
<3> = {4,6,8,9}
<4> = {7,9,10,11}
Spectra Variation3.6
Maximally Evenno
Maximal Area Setno
Interior Area1.683
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 TriadsA{9,1,4}121
Minor Triadsam{9,0,4}210.67
Diminished Triads{9,0,3}121
Parsimonious Voice Leading Between Common Triads of Scale 539. Created by Ian Ring ©2019 am am a°->am A A am->A

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
Radius1
Self-Centeredno
Central Verticesam
Peripheral Verticesa°, A

Modes

Modes are the rotational transformation of this scale. Scale 539 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 2317
Scale 2317, Ian Ring Music Theory
3rd mode:
Scale 1603
Scale 1603, Ian Ring Music Theory
4th mode:
Scale 2849
Scale 2849, Ian Ring Music Theory
5th mode:
Scale 217
Scale 217, Ian Ring Music Theory

Prime

The prime form of this scale is Scale 155

Scale 155Scale 155, Ian Ring Music Theory

Complement

The pentatonic modal family [539, 2317, 1603, 2849, 217] (Forte: 5-16) is the complement of the heptatonic modal family [623, 889, 1939, 2359, 3017, 3227, 3661] (Forte: 7-16)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 539 is 2825

Scale 2825Scale 2825, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 539 is chiral, and its enantiomorph is scale 2825

Scale 2825Scale 2825, Ian Ring Music Theory

Transformations:

T0 539  T0I 2825
T1 1078  T1I 1555
T2 2156  T2I 3110
T3 217  T3I 2125
T4 434  T4I 155
T5 868  T5I 310
T6 1736  T6I 620
T7 3472  T7I 1240
T8 2849  T8I 2480
T9 1603  T9I 865
T10 3206  T10I 1730
T11 2317  T11I 3460

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 537Scale 537, Ian Ring Music Theory
Scale 541Scale 541, Ian Ring Music Theory
Scale 543Scale 543, Ian Ring Music Theory
Scale 531Scale 531, Ian Ring Music Theory
Scale 535Scale 535, Ian Ring Music Theory
Scale 523Scale 523, Ian Ring Music Theory
Scale 555Scale 555: Aeolycritonic, Ian Ring Music TheoryAeolycritonic
Scale 571Scale 571: Kynimic, Ian Ring Music TheoryKynimic
Scale 603Scale 603: Aeolygimic, Ian Ring Music TheoryAeolygimic
Scale 667Scale 667: Rodimic, Ian Ring Music TheoryRodimic
Scale 795Scale 795: Aeologimic, Ian Ring Music TheoryAeologimic
Scale 27Scale 27, Ian Ring Music Theory
Scale 283Scale 283: Aerylitonic, Ian Ring Music TheoryAerylitonic
Scale 1051Scale 1051, Ian Ring Music Theory
Scale 1563Scale 1563, Ian Ring Music Theory
Scale 2587Scale 2587, Ian Ring Music Theory

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.