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Scale 1559

Scale 1559, 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{0,1,2,4,9,10}
Forte Number6-Z10
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3341
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}210.67
Minor Triadsam{9,0,4}121
Diminished Triadsa♯°{10,1,4}121
Parsimonious Voice Leading Between Common Triads of Scale 1559. Created by Ian Ring ©2019 am am A A am->A a#° a#° A->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 VerticesA
Peripheral Verticesam, a♯°

Modes

Modes are the rotational transformation of this scale. Scale 1559 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 2827
Scale 2827, Ian Ring Music Theory
3rd mode:
Scale 3461
Scale 3461, Ian Ring Music Theory
4th mode:
Scale 1889
Scale 1889, Ian Ring Music Theory
5th mode:
Scale 187
Scale 187, Ian Ring Music TheoryThis is the prime mode
6th mode:
Scale 2141
Scale 2141, 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 [1559, 2827, 3461, 1889, 187, 2141] (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 1559 is 3341

Scale 3341Scale 3341, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1559 is chiral, and its enantiomorph is scale 3341

Scale 3341Scale 3341, Ian Ring Music Theory

Transformations:

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

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 1557Scale 1557, Ian Ring Music Theory
Scale 1555Scale 1555, Ian Ring Music Theory
Scale 1563Scale 1563, Ian Ring Music Theory
Scale 1567Scale 1567, Ian Ring Music Theory
Scale 1543Scale 1543, Ian Ring Music Theory
Scale 1551Scale 1551, Ian Ring Music Theory
Scale 1575Scale 1575: Zycrimic, Ian Ring Music TheoryZycrimic
Scale 1591Scale 1591: Rodian, Ian Ring Music TheoryRodian
Scale 1623Scale 1623: Lothian, Ian Ring Music TheoryLothian
Scale 1687Scale 1687: Phralian, Ian Ring Music TheoryPhralian
Scale 1815Scale 1815: Godian, Ian Ring Music TheoryGodian
Scale 1047Scale 1047, Ian Ring Music Theory
Scale 1303Scale 1303: Epolimic, Ian Ring Music TheoryEpolimic
Scale 535Scale 535, Ian Ring Music Theory
Scale 2583Scale 2583, Ian Ring Music Theory
Scale 3607Scale 3607, 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.