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Scale 339: "Zaptitonic"

Scale 339: Zaptitonic, 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).

Common Names

Zeitler
Zaptitonic

Analysis

Cardinality5 (pentatonic)
Pitch Class Set{0,1,4,6,8}
Forte Number5-30
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2385
Hemitonia1 (unhemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections3
Modes4
Prime?yes
Deep Scaleno
Interval Vector121321
Interval Spectrump2m3ns2dt
Distribution Spectra<1> = {1,2,3,4}
<2> = {4,5,6}
<3> = {6,7,8}
<4> = {8,9,10,11}
Spectra Variation2
Maximally Evenno
Maximal Area Setno
Interior Area2.049
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyProper
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 Triadsc♯m{1,4,8}110.5
Augmented TriadsC+{0,4,8}110.5
Parsimonious Voice Leading Between Common Triads of Scale 339. Created by Ian Ring ©2019 C+ C+ c#m c#m C+->c#m

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 339 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 2217
Scale 2217: Kagitonic, Ian Ring Music TheoryKagitonic
3rd mode:
Scale 789
Scale 789: Zogitonic, Ian Ring Music TheoryZogitonic
4th mode:
Scale 1221
Scale 1221: Epyritonic, Ian Ring Music TheoryEpyritonic
5th mode:
Scale 1329
Scale 1329: Epygitonic, Ian Ring Music TheoryEpygitonic

Prime

This is the prime form of this scale.

Complement

The pentatonic modal family [339, 2217, 789, 1221, 1329] (Forte: 5-30) is the complement of the heptatonic modal family [855, 1395, 1485, 1845, 2475, 2745, 3285] (Forte: 7-30)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 339 is 2385

Scale 2385Scale 2385: Aeolanitonic, Ian Ring Music TheoryAeolanitonic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 339 is chiral, and its enantiomorph is scale 2385

Scale 2385Scale 2385: Aeolanitonic, Ian Ring Music TheoryAeolanitonic

Transformations:

T0 339  T0I 2385
T1 678  T1I 675
T2 1356  T2I 1350
T3 2712  T3I 2700
T4 1329  T4I 1305
T5 2658  T5I 2610
T6 1221  T6I 1125
T7 2442  T7I 2250
T8 789  T8I 405
T9 1578  T9I 810
T10 3156  T10I 1620
T11 2217  T11I 3240

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 337Scale 337: Koptic, Ian Ring Music TheoryKoptic
Scale 341Scale 341: Bothitonic, Ian Ring Music TheoryBothitonic
Scale 343Scale 343: Ionorimic, Ian Ring Music TheoryIonorimic
Scale 347Scale 347: Barimic, Ian Ring Music TheoryBarimic
Scale 323Scale 323, Ian Ring Music Theory
Scale 331Scale 331: Raga Chhaya Todi, Ian Ring Music TheoryRaga Chhaya Todi
Scale 355Scale 355: Aeoloritonic, Ian Ring Music TheoryAeoloritonic
Scale 371Scale 371: Rythimic, Ian Ring Music TheoryRythimic
Scale 275Scale 275: Dalic, Ian Ring Music TheoryDalic
Scale 307Scale 307: Raga Megharanjani, Ian Ring Music TheoryRaga Megharanjani
Scale 403Scale 403: Raga Reva, Ian Ring Music TheoryRaga Reva
Scale 467Scale 467: Raga Dhavalangam, Ian Ring Music TheoryRaga Dhavalangam
Scale 83Scale 83, Ian Ring Music Theory
Scale 211Scale 211, Ian Ring Music Theory
Scale 595Scale 595: Sogitonic, Ian Ring Music TheorySogitonic
Scale 851Scale 851: Raga Hejjajji, Ian Ring Music TheoryRaga Hejjajji
Scale 1363Scale 1363: Gygimic, Ian Ring Music TheoryGygimic
Scale 2387Scale 2387: Paptimic, Ian Ring Music TheoryPaptimic

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.