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Scale 2587

Scale 2587, 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).

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,1,3,4,9,11}
Forte Number6-Z10
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2827
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections4
Modes5
Prime?no
prime: 187
Deep Scaleno
Interval Vector333321
Interval Spectrump2m3n3s3d3t
Distribution Spectra<1> = {1,2,5}
<2> = {2,3,6,7}
<3> = {4,8}
<4> = {5,6,9,10}
<5> = {7,10,11}
Spectra Variation3.667
Maximally Evenno
Maximal Area Setno
Interior Area1.866
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 2587. 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 2587 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 3341
Scale 3341, Ian Ring Music Theory
3rd mode:
Scale 1859
Scale 1859, Ian Ring Music Theory
4th mode:
Scale 2977
Scale 2977, Ian Ring Music Theory
5th mode:
Scale 221
Scale 221, Ian Ring Music Theory
6th mode:
Scale 1079
Scale 1079, Ian Ring Music Theory

Prime

The prime form of this scale is Scale 187

Scale 187Scale 187, Ian Ring Music Theory

Complement

The hexatonic modal family [2587, 3341, 1859, 2977, 221, 1079] (Forte: 6-Z10) is the complement of the hexatonic modal family [317, 977, 1103, 2599, 3347, 3721] (Forte: 6-Z39)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2587 is 2827

Scale 2827Scale 2827, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2587 is chiral, and its enantiomorph is scale 2827

Scale 2827Scale 2827, Ian Ring Music Theory

Transformations:

T0 2587  T0I 2827
T1 1079  T1I 1559
T2 2158  T2I 3118
T3 221  T3I 2141
T4 442  T4I 187
T5 884  T5I 374
T6 1768  T6I 748
T7 3536  T7I 1496
T8 2977  T8I 2992
T9 1859  T9I 1889
T10 3718  T10I 3778
T11 3341  T11I 3461

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 2585Scale 2585, Ian Ring Music Theory
Scale 2589Scale 2589, Ian Ring Music Theory
Scale 2591Scale 2591, Ian Ring Music Theory
Scale 2579Scale 2579, Ian Ring Music Theory
Scale 2583Scale 2583, Ian Ring Music Theory
Scale 2571Scale 2571, Ian Ring Music Theory
Scale 2603Scale 2603: Gadimic, Ian Ring Music TheoryGadimic
Scale 2619Scale 2619: Ionyrian, Ian Ring Music TheoryIonyrian
Scale 2651Scale 2651: Panian, Ian Ring Music TheoryPanian
Scale 2715Scale 2715: Kynian, Ian Ring Music TheoryKynian
Scale 2843Scale 2843: Sorian, Ian Ring Music TheorySorian
Scale 2075Scale 2075, Ian Ring Music Theory
Scale 2331Scale 2331: Dylimic, Ian Ring Music TheoryDylimic
Scale 3099Scale 3099, Ian Ring Music Theory
Scale 3611Scale 3611, Ian Ring Music Theory
Scale 539Scale 539, Ian Ring Music Theory
Scale 1563Scale 1563, 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.