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Scale 2139

Scale 2139, 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{0,1,3,4,6,11}
Forte Number6-Z11
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2883
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes5
Prime?no
prime: 183
Deep Scaleno
Interval Vector333231
Interval Spectrump3m2n3s3d3t
Distribution Spectra<1> = {1,2,5}
<2> = {2,3,6,7}
<3> = {4,5,7,8}
<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 TriadsB{11,3,6}110.5
Diminished Triads{0,3,6}110.5
Parsimonious Voice Leading Between Common Triads of Scale 2139. Created by Ian Ring ©2019 B B c°->B

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.

Diameter1
Radius1
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 2139 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 3117
Scale 3117, Ian Ring Music Theory
3rd mode:
Scale 1803
Scale 1803, Ian Ring Music Theory
4th mode:
Scale 2949
Scale 2949, Ian Ring Music Theory
5th mode:
Scale 1761
Scale 1761, Ian Ring Music Theory
6th mode:
Scale 183
Scale 183, Ian Ring Music TheoryThis is the prime mode

Prime

The prime form of this scale is Scale 183

Scale 183Scale 183, Ian Ring Music Theory

Complement

The hexatonic modal family [2139, 3117, 1803, 2949, 1761, 183] (Forte: 6-Z11) is the complement of the hexatonic modal family [303, 753, 1929, 2199, 3147, 3621] (Forte: 6-Z40)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2139 is 2883

Scale 2883Scale 2883, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2139 is chiral, and its enantiomorph is scale 2883

Scale 2883Scale 2883, Ian Ring Music Theory

Transformations:

T0 2139  T0I 2883
T1 183  T1I 1671
T2 366  T2I 3342
T3 732  T3I 2589
T4 1464  T4I 1083
T5 2928  T5I 2166
T6 1761  T6I 237
T7 3522  T7I 474
T8 2949  T8I 948
T9 1803  T9I 1896
T10 3606  T10I 3792
T11 3117  T11I 3489

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 2137Scale 2137, Ian Ring Music Theory
Scale 2141Scale 2141, Ian Ring Music Theory
Scale 2143Scale 2143, Ian Ring Music Theory
Scale 2131Scale 2131, Ian Ring Music Theory
Scale 2135Scale 2135, Ian Ring Music Theory
Scale 2123Scale 2123, Ian Ring Music Theory
Scale 2155Scale 2155, Ian Ring Music Theory
Scale 2171Scale 2171, Ian Ring Music Theory
Scale 2075Scale 2075, Ian Ring Music Theory
Scale 2107Scale 2107, Ian Ring Music Theory
Scale 2203Scale 2203: Dorimic, Ian Ring Music TheoryDorimic
Scale 2267Scale 2267: Padian, Ian Ring Music TheoryPadian
Scale 2395Scale 2395: Zoptian, Ian Ring Music TheoryZoptian
Scale 2651Scale 2651: Panian, Ian Ring Music TheoryPanian
Scale 3163Scale 3163: Rogian, Ian Ring Music TheoryRogian
Scale 91Scale 91, Ian Ring Music Theory
Scale 1115Scale 1115: Superlocrian Hexamirror, Ian Ring Music TheorySuperlocrian Hexamirror

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.