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Scale 3207

Scale 3207, 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{0,1,2,7,10,11}
Forte Number6-Z36
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3111
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 TriadsG{7,11,2}121
Minor Triadsgm{7,10,2}210.67
Diminished Triads{7,10,1}121
Parsimonious Voice Leading Between Common Triads of Scale 3207. Created by Ian Ring ©2019 gm gm g°->gm Parsimonious Voice Leading Between Common Triads of Scale 3207. Created by Ian Ring ©2019 G gm->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.

Diameter2
Radius1
Self-Centeredno
Central Verticesgm
Peripheral Verticesg°, G

Modes

Modes are the rotational transformation of this scale. Scale 3207 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 3651
Scale 3651, Ian Ring Music Theory
3rd mode:
Scale 3873
Scale 3873, Ian Ring Music Theory
4th mode:
Scale 249
Scale 249, Ian Ring Music Theory
5th mode:
Scale 543
Scale 543, Ian Ring Music Theory
6th mode:
Scale 2319
Scale 2319, 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 [3207, 3651, 3873, 249, 543, 2319] (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 3207 is 3111

Scale 3111Scale 3111, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3207 is chiral, and its enantiomorph is scale 3111

Scale 3111Scale 3111, Ian Ring Music Theory

Transformations:

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

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 3205Scale 3205, Ian Ring Music Theory
Scale 3203Scale 3203, Ian Ring Music Theory
Scale 3211Scale 3211: Epacrimic, Ian Ring Music TheoryEpacrimic
Scale 3215Scale 3215: Katydian, Ian Ring Music TheoryKatydian
Scale 3223Scale 3223: Thyphian, Ian Ring Music TheoryThyphian
Scale 3239Scale 3239: Mela Tanarupi, Ian Ring Music TheoryMela Tanarupi
Scale 3271Scale 3271: Mela Raghupriya, Ian Ring Music TheoryMela Raghupriya
Scale 3079Scale 3079, Ian Ring Music Theory
Scale 3143Scale 3143: Polimic, Ian Ring Music TheoryPolimic
Scale 3335Scale 3335, Ian Ring Music Theory
Scale 3463Scale 3463, Ian Ring Music Theory
Scale 3719Scale 3719, Ian Ring Music Theory
Scale 2183Scale 2183, Ian Ring Music Theory
Scale 2695Scale 2695, Ian Ring Music Theory
Scale 1159Scale 1159, 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.