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Scale 345: "Gylitonic"

Scale 345: Gylitonic, 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
Gylitonic

Analysis

Cardinality5 (pentatonic)
Pitch Class Set{0,3,4,6,8}
Forte Number5-26
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 849
Hemitonia1 (unhemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections4
Modes4
Prime?no
prime: 309
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
Major TriadsG♯{8,0,3}210.67
Augmented TriadsC+{0,4,8}121
Diminished Triads{0,3,6}121
Parsimonious Voice Leading Between Common Triads of Scale 345. Created by Ian Ring ©2019 G# G# c°->G# C+ C+ C+->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 VerticesG♯
Peripheral Verticesc°, C+

Modes

Modes are the rotational transformation of this scale. Scale 345 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 555
Scale 555: Aeolycritonic, Ian Ring Music TheoryAeolycritonic
3rd mode:
Scale 2325
Scale 2325: Pynitonic, Ian Ring Music TheoryPynitonic
4th mode:
Scale 1605
Scale 1605: Zanitonic, Ian Ring Music TheoryZanitonic
5th mode:
Scale 1425
Scale 1425: Ryphitonic, Ian Ring Music TheoryRyphitonic

Prime

The prime form of this scale is Scale 309

Scale 309Scale 309: Palitonic, Ian Ring Music TheoryPalitonic

Complement

The pentatonic modal family [345, 555, 2325, 1605, 1425] (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 345 is 849

Scale 849Scale 849: Aerynitonic, Ian Ring Music TheoryAerynitonic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 345 is chiral, and its enantiomorph is scale 849

Scale 849Scale 849: Aerynitonic, Ian Ring Music TheoryAerynitonic

Transformations:

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

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 347Scale 347: Barimic, Ian Ring Music TheoryBarimic
Scale 349Scale 349: Borimic, Ian Ring Music TheoryBorimic
Scale 337Scale 337: Koptic, Ian Ring Music TheoryKoptic
Scale 341Scale 341: Bothitonic, Ian Ring Music TheoryBothitonic
Scale 329Scale 329: Mynic, Ian Ring Music TheoryMynic
Scale 361Scale 361: Bocritonic, Ian Ring Music TheoryBocritonic
Scale 377Scale 377: Kathimic, Ian Ring Music TheoryKathimic
Scale 281Scale 281: Lanic, Ian Ring Music TheoryLanic
Scale 313Scale 313: Goritonic, Ian Ring Music TheoryGoritonic
Scale 409Scale 409: Laritonic, Ian Ring Music TheoryLaritonic
Scale 473Scale 473: Aeralimic, Ian Ring Music TheoryAeralimic
Scale 89Scale 89, Ian Ring Music Theory
Scale 217Scale 217, Ian Ring Music Theory
Scale 601Scale 601: Bycritonic, Ian Ring Music TheoryBycritonic
Scale 857Scale 857: Aeolydimic, Ian Ring Music TheoryAeolydimic
Scale 1369Scale 1369: Boptimic, Ian Ring Music TheoryBoptimic
Scale 2393Scale 2393: Zathimic, Ian Ring Music TheoryZathimic

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.