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Scale 309: "Palitonic"

Scale 309: Palitonic, 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
Palitonic

Analysis

Cardinality5 (pentatonic)
Pitch Class Set{0,2,4,5,8}
Forte Number5-26
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1425
Hemitonia1 (unhemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections4
Modes4
Prime?yes
Deep Scaleno
Interval Vector122311
Interval Spectrumpm3n2s2dt
Distribution Spectra<1> = {1,2,3,4}
<2> = {3,4,6,7}
<3> = {5,6,8,9}
<4> = {8,9,10,11}
Spectra Variation2.8
Maximally Evenno
Maximal Area Setno
Interior Area2.049
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 Triadsfm{5,8,0}210.67
Augmented TriadsC+{0,4,8}121
Diminished Triads{2,5,8}121
Parsimonious Voice Leading Between Common Triads of Scale 309. Created by Ian Ring ©2019 C+ C+ fm fm C+->fm d°->fm

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 VerticesC+, d°

Modes

Modes are the rotational transformation of this scale. Scale 309 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 1101
Scale 1101: Stothitonic, Ian Ring Music TheoryStothitonic
3rd mode:
Scale 1299
Scale 1299: Aerophitonic, Ian Ring Music TheoryAerophitonic
4th mode:
Scale 2697
Scale 2697: Katagitonic, Ian Ring Music TheoryKatagitonic
5th mode:
Scale 849
Scale 849: Aerynitonic, Ian Ring Music TheoryAerynitonic

Prime

This is the prime form of this scale.

Complement

The pentatonic modal family [309, 1101, 1299, 2697, 849] (Forte: 5-26) is the complement of the heptatonic modal family [699, 1497, 1623, 1893, 2397, 2859, 3477] (Forte: 7-26)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 309 is 1425

Scale 1425Scale 1425: Ryphitonic, Ian Ring Music TheoryRyphitonic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 309 is chiral, and its enantiomorph is scale 1425

Scale 1425Scale 1425: Ryphitonic, Ian Ring Music TheoryRyphitonic

Transformations:

T0 309  T0I 1425
T1 618  T1I 2850
T2 1236  T2I 1605
T3 2472  T3I 3210
T4 849  T4I 2325
T5 1698  T5I 555
T6 3396  T6I 1110
T7 2697  T7I 2220
T8 1299  T8I 345
T9 2598  T9I 690
T10 1101  T10I 1380
T11 2202  T11I 2760

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 311Scale 311: Stagimic, Ian Ring Music TheoryStagimic
Scale 305Scale 305: Gonic, Ian Ring Music TheoryGonic
Scale 307Scale 307: Raga Megharanjani, Ian Ring Music TheoryRaga Megharanjani
Scale 313Scale 313: Goritonic, Ian Ring Music TheoryGoritonic
Scale 317Scale 317: Korimic, Ian Ring Music TheoryKorimic
Scale 293Scale 293: Raga Haripriya, Ian Ring Music TheoryRaga Haripriya
Scale 301Scale 301: Raga Audav Tukhari, Ian Ring Music TheoryRaga Audav Tukhari
Scale 277Scale 277: Mixolyric, Ian Ring Music TheoryMixolyric
Scale 341Scale 341: Bothitonic, Ian Ring Music TheoryBothitonic
Scale 373Scale 373: Epagimic, Ian Ring Music TheoryEpagimic
Scale 437Scale 437: Ronimic, Ian Ring Music TheoryRonimic
Scale 53Scale 53, Ian Ring Music Theory
Scale 181Scale 181: Raga Budhamanohari, Ian Ring Music TheoryRaga Budhamanohari
Scale 565Scale 565: Aeolyphritonic, Ian Ring Music TheoryAeolyphritonic
Scale 821Scale 821: Aeranimic, Ian Ring Music TheoryAeranimic
Scale 1333Scale 1333: Lyptimic, Ian Ring Music TheoryLyptimic
Scale 2357Scale 2357: Raga Sarasanana, Ian Ring Music TheoryRaga Sarasanana

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.