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Scale 187

Scale 187, 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{0,1,3,4,5,7}
Forte Number6-Z10
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2977
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections4
Modes5
Prime?yes
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 TriadsC{0,4,7}210.67
Minor Triadscm{0,3,7}121
Diminished Triadsc♯°{1,4,7}121
Parsimonious Voice Leading Between Common Triads of Scale 187. Created by Ian Ring ©2019 cm cm C C cm->C c#° c#° C->c#°

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 VerticesC
Peripheral Verticescm, c♯°

Modes

Modes are the rotational transformation of this scale. Scale 187 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 2141
Scale 2141, Ian Ring Music Theory
3rd mode:
Scale 1559
Scale 1559, Ian Ring Music Theory
4th mode:
Scale 2827
Scale 2827, Ian Ring Music Theory
5th mode:
Scale 3461
Scale 3461, Ian Ring Music Theory
6th mode:
Scale 1889
Scale 1889, Ian Ring Music Theory

Prime

This is the prime form of this scale.

Complement

The hexatonic modal family [187, 2141, 1559, 2827, 3461, 1889] (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 187 is 2977

Scale 2977Scale 2977, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 187 is chiral, and its enantiomorph is scale 2977

Scale 2977Scale 2977, Ian Ring Music Theory

Transformations:

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

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 185Scale 185, Ian Ring Music Theory
Scale 189Scale 189, Ian Ring Music Theory
Scale 191Scale 191, Ian Ring Music Theory
Scale 179Scale 179, Ian Ring Music Theory
Scale 183Scale 183, Ian Ring Music Theory
Scale 171Scale 171, Ian Ring Music Theory
Scale 155Scale 155, Ian Ring Music Theory
Scale 219Scale 219: Istrian, Ian Ring Music TheoryIstrian
Scale 251Scale 251, Ian Ring Music Theory
Scale 59Scale 59, Ian Ring Music Theory
Scale 123Scale 123, Ian Ring Music Theory
Scale 315Scale 315: Stodimic, Ian Ring Music TheoryStodimic
Scale 443Scale 443: Kothian, Ian Ring Music TheoryKothian
Scale 699Scale 699: Aerothian, Ian Ring Music TheoryAerothian
Scale 1211Scale 1211: Zadian, Ian Ring Music TheoryZadian
Scale 2235Scale 2235: Bathian, Ian Ring Music TheoryBathian

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.