The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 1987

Scale 1987, 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

Cardinality7 (heptatonic)
Pitch Class Set{0,1,6,7,8,9,10}
Forte Number7-4
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2173
Hemitonia5 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections4
Modes6
Prime?no
prime: 223
Deep Scaleno
Interval Vector544332
Interval Spectrump3m3n4s4d5t2
Distribution Spectra<1> = {1,2,5}
<2> = {2,3,6}
<3> = {3,4,7,8}
<4> = {4,5,8,9}
<5> = {6,9,10}
<6> = {7,10,11}
Spectra Variation3.714
Maximally Evenno
Maximal Area Setno
Interior Area1.933
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicyes

Harmonic Chords

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 TriadsF♯{6,10,1}221
Minor Triadsf♯m{6,9,1}221
Diminished Triadsf♯°{6,9,0}131.5
{7,10,1}131.5
Parsimonious Voice Leading Between Common Triads of Scale 1987. Created by Ian Ring ©2019 f#° f#° f#m f#m f#°->f#m F# F# f#m->F# F#->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.

Diameter3
Radius2
Self-Centeredno
Central Verticesf♯m, F♯
Peripheral Verticesf♯°, g°

Modes

Modes are the rotational transformation of this scale. Scale 1987 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 3041
Scale 3041, Ian Ring Music Theory
3rd mode:
Scale 223
Scale 223, Ian Ring Music TheoryThis is the prime mode
4th mode:
Scale 2159
Scale 2159, Ian Ring Music Theory
5th mode:
Scale 3127
Scale 3127, Ian Ring Music Theory
6th mode:
Scale 3611
Scale 3611, Ian Ring Music Theory
7th mode:
Scale 3853
Scale 3853, Ian Ring Music Theory

Prime

The prime form of this scale is Scale 223

Scale 223Scale 223, Ian Ring Music Theory

Complement

The heptatonic modal family [1987, 3041, 223, 2159, 3127, 3611, 3853] (Forte: 7-4) is the complement of the pentatonic modal family [79, 961, 2087, 3091, 3593] (Forte: 5-4)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1987 is 2173

Scale 2173Scale 2173, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1987 is chiral, and its enantiomorph is scale 2173

Scale 2173Scale 2173, Ian Ring Music Theory

Transformations:

T0 1987  T0I 2173
T1 3974  T1I 251
T2 3853  T2I 502
T3 3611  T3I 1004
T4 3127  T4I 2008
T5 2159  T5I 4016
T6 223  T6I 3937
T7 446  T7I 3779
T8 892  T8I 3463
T9 1784  T9I 2831
T10 3568  T10I 1567
T11 3041  T11I 3134

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 1985Scale 1985, Ian Ring Music Theory
Scale 1989Scale 1989: Dydian, Ian Ring Music TheoryDydian
Scale 1991Scale 1991: Phryptyllic, Ian Ring Music TheoryPhryptyllic
Scale 1995Scale 1995: Aeolacryllic, Ian Ring Music TheoryAeolacryllic
Scale 2003Scale 2003: Podyllic, Ian Ring Music TheoryPodyllic
Scale 2019Scale 2019: Palyllic, Ian Ring Music TheoryPalyllic
Scale 1923Scale 1923, Ian Ring Music Theory
Scale 1955Scale 1955: Sonian, Ian Ring Music TheorySonian
Scale 1859Scale 1859, Ian Ring Music Theory
Scale 1731Scale 1731, Ian Ring Music Theory
Scale 1475Scale 1475, Ian Ring Music Theory
Scale 963Scale 963, Ian Ring Music Theory
Scale 3011Scale 3011, Ian Ring Music Theory
Scale 4035Scale 4035, 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.