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Scale 3873

Scale 3873, 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

Cardinality6 (hexatonic)
Pitch Class Set{0,5,8,9,10,11}
Forte Number6-Z36
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 159
Hemitonia4 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections4
Modes5
Prime?no
prime: 159
Deep Scaleno
Interval Vector433221
Interval Spectrump2m2n3s3d4t
Distribution Spectra<1> = {1,3,5}
<2> = {2,4,6,8}
<3> = {3,5,7,9}
<4> = {4,6,8,10}
<5> = {7,9,11}
Spectra Variation4.333
Maximally Evenno
Maximal Area Setno
Interior Area1.75
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 TriadsF{5,9,0}121
Minor Triadsfm{5,8,0}210.67
Diminished Triads{5,8,11}121
Parsimonious Voice Leading Between Common Triads of Scale 3873. Created by Ian Ring ©2019 fm fm f°->fm F F fm->F

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 Verticesfm
Peripheral Verticesf°, F

Modes

Modes are the rotational transformation of this scale. Scale 3873 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 249
Scale 249, Ian Ring Music Theory
3rd mode:
Scale 543
Scale 543, Ian Ring Music Theory
4th mode:
Scale 2319
Scale 2319, Ian Ring Music Theory
5th mode:
Scale 3207
Scale 3207, Ian Ring Music Theory
6th mode:
Scale 3651
Scale 3651, Ian Ring Music Theory

Prime

The prime form of this scale is Scale 159

Scale 159Scale 159, Ian Ring Music Theory

Complement

The hexatonic modal family [3873, 249, 543, 2319, 3207, 3651] (Forte: 6-Z36) is the complement of the hexatonic modal family [111, 1923, 2103, 3009, 3099, 3597] (Forte: 6-Z3)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3873 is 159

Scale 159Scale 159, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3873 is chiral, and its enantiomorph is scale 159

Scale 159Scale 159, Ian Ring Music Theory

Transformations:

T0 3873  T0I 159
T1 3651  T1I 318
T2 3207  T2I 636
T3 2319  T3I 1272
T4 543  T4I 2544
T5 1086  T5I 993
T6 2172  T6I 1986
T7 249  T7I 3972
T8 498  T8I 3849
T9 996  T9I 3603
T10 1992  T10I 3111
T11 3984  T11I 2127

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 3875Scale 3875: Aeryptian, Ian Ring Music TheoryAeryptian
Scale 3877Scale 3877: Thanian, Ian Ring Music TheoryThanian
Scale 3881Scale 3881: Morian, Ian Ring Music TheoryMorian
Scale 3889Scale 3889: Parian, Ian Ring Music TheoryParian
Scale 3841Scale 3841, Ian Ring Music Theory
Scale 3857Scale 3857: Ponimic, Ian Ring Music TheoryPonimic
Scale 3905Scale 3905, Ian Ring Music Theory
Scale 3937Scale 3937, Ian Ring Music Theory
Scale 4001Scale 4001, Ian Ring Music Theory
Scale 3617Scale 3617, Ian Ring Music Theory
Scale 3745Scale 3745, Ian Ring Music Theory
Scale 3361Scale 3361, Ian Ring Music Theory
Scale 2849Scale 2849, Ian Ring Music Theory
Scale 1825Scale 1825, 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.