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Scale 139

Scale 139, 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

Cardinality4 (tetratonic)
Pitch Class Set{0,1,3,7}
Forte Number4-Z29
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2593
Hemitonia1 (unhemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections3
Modes3
Prime?yes
Deep Scaleno
Interval Vector111111
Interval Spectrumpmnsdt
Distribution Spectra<1> = {1,2,4,5}
<2> = {3,6,9}
<3> = {7,8,10,11}
Spectra Variation3.5
Maximally Evenno
Maximal Area Setno
Interior Area1.366
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
Minor Triadscm{0,3,7}000

Since there is only one common triad in this scale, there are no opportunities for parsimonious voice leading between triads.

Modes

Modes are the rotational transformation of this scale. Scale 139 can be rotated to make 3 other scales. The 1st mode is itself.

2nd mode:
Scale 2117
Scale 2117: Raga Sumukam, Ian Ring Music TheoryRaga Sumukam
3rd mode:
Scale 1553
Scale 1553, Ian Ring Music Theory
4th mode:
Scale 353
Scale 353, Ian Ring Music Theory

Prime

This is the prime form of this scale.

Complement

The tetratonic modal family [139, 2117, 1553, 353] (Forte: 4-Z29) is the complement of the octatonic modal family [751, 1913, 1943, 2423, 3019, 3259, 3557, 3677] (Forte: 8-Z29)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 139 is 2593

Scale 2593Scale 2593, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 139 is chiral, and its enantiomorph is scale 2593

Scale 2593Scale 2593, Ian Ring Music Theory

Transformations:

T0 139  T0I 2593
T1 278  T1I 1091
T2 556  T2I 2182
T3 1112  T3I 269
T4 2224  T4I 538
T5 353  T5I 1076
T6 706  T6I 2152
T7 1412  T7I 209
T8 2824  T8I 418
T9 1553  T9I 836
T10 3106  T10I 1672
T11 2117  T11I 3344

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 137Scale 137: Ute Tritonic, Ian Ring Music TheoryUte Tritonic
Scale 141Scale 141, Ian Ring Music Theory
Scale 143Scale 143, Ian Ring Music Theory
Scale 131Scale 131, Ian Ring Music Theory
Scale 135Scale 135, Ian Ring Music Theory
Scale 147Scale 147, Ian Ring Music Theory
Scale 155Scale 155, Ian Ring Music Theory
Scale 171Scale 171, Ian Ring Music Theory
Scale 203Scale 203, Ian Ring Music Theory
Scale 11Scale 11, Ian Ring Music Theory
Scale 75Scale 75, Ian Ring Music Theory
Scale 267Scale 267, Ian Ring Music Theory
Scale 395Scale 395: Phrygian Pentatonic, Ian Ring Music TheoryPhrygian Pentatonic
Scale 651Scale 651: Golitonic, Ian Ring Music TheoryGolitonic
Scale 1163Scale 1163: Raga Rukmangi, Ian Ring Music TheoryRaga Rukmangi
Scale 2187Scale 2187: Ionothitonic, Ian Ring Music TheoryIonothitonic

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.