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Scale 735: "Sylyllic"

Scale 735: Sylyllic, 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
Sylyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,2,3,4,6,7,9}
Forte Number8-13
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3945
Hemitonia5 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections3
Modes7
Prime?yes
Deep Scaleno
Interval Vector556453
Interval Spectrump5m4n6s5d5t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {3,4,5,6}
<4> = {4,5,6,7,8}
<5> = {6,7,8,9}
<6> = {7,8,9,10}
<7> = {9,10,11}
Spectra Variation2.5
Maximally Evenno
Maximal Area Setno
Interior Area2.616
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 TriadsC{0,4,7}341.91
D{2,6,9}242.27
A{9,1,4}341.91
Minor Triadscm{0,3,7}342
f♯m{6,9,1}342
am{9,0,4}441.82
Diminished Triads{0,3,6}242.27
c♯°{1,4,7}242.18
d♯°{3,6,9}242.36
f♯°{6,9,0}242.09
{9,0,3}242.09
Parsimonious Voice Leading Between Common Triads of Scale 735. Created by Ian Ring ©2019 cm cm c°->cm d#° d#° c°->d#° C C cm->C cm->a° c#° c#° C->c#° am am C->am A A c#°->A D D D->d#° f#m f#m D->f#m f#° f#° f#°->f#m f#°->am f#m->A a°->am am->A

view full size

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.

Diameter4
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 735 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 2415
Scale 2415: Lothyllic, Ian Ring Music TheoryLothyllic
3rd mode:
Scale 3255
Scale 3255: Daryllic, Ian Ring Music TheoryDaryllic
4th mode:
Scale 3675
Scale 3675: Monyllic, Ian Ring Music TheoryMonyllic
5th mode:
Scale 3885
Scale 3885: Styryllic, Ian Ring Music TheoryStyryllic
6th mode:
Scale 1995
Scale 1995: Aeolacryllic, Ian Ring Music TheoryAeolacryllic
7th mode:
Scale 3045
Scale 3045: Raptyllic, Ian Ring Music TheoryRaptyllic
8th mode:
Scale 1785
Scale 1785: Tharyllic, Ian Ring Music TheoryTharyllic

Prime

This is the prime form of this scale.

Complement

The octatonic modal family [735, 2415, 3255, 3675, 3885, 1995, 3045, 1785] (Forte: 8-13) is the complement of the tetratonic modal family [75, 705, 1545, 2085] (Forte: 4-13)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 735 is 3945

Scale 3945Scale 3945: Lydyllic, Ian Ring Music TheoryLydyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 735 is chiral, and its enantiomorph is scale 3945

Scale 3945Scale 3945: Lydyllic, Ian Ring Music TheoryLydyllic

Transformations:

T0 735  T0I 3945
T1 1470  T1I 3795
T2 2940  T2I 3495
T3 1785  T3I 2895
T4 3570  T4I 1695
T5 3045  T5I 3390
T6 1995  T6I 2685
T7 3990  T7I 1275
T8 3885  T8I 2550
T9 3675  T9I 1005
T10 3255  T10I 2010
T11 2415  T11I 4020

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 733Scale 733: Donian, Ian Ring Music TheoryDonian
Scale 731Scale 731: Ionorian, Ian Ring Music TheoryIonorian
Scale 727Scale 727: Phradian, Ian Ring Music TheoryPhradian
Scale 719Scale 719: Kanian, Ian Ring Music TheoryKanian
Scale 751Scale 751, Ian Ring Music Theory
Scale 767Scale 767: Raptygic, Ian Ring Music TheoryRaptygic
Scale 671Scale 671: Stycrian, Ian Ring Music TheoryStycrian
Scale 703Scale 703: Aerocryllic, Ian Ring Music TheoryAerocryllic
Scale 607Scale 607: Kadian, Ian Ring Music TheoryKadian
Scale 863Scale 863: Pyryllic, Ian Ring Music TheoryPyryllic
Scale 991Scale 991: Aeolygic, Ian Ring Music TheoryAeolygic
Scale 223Scale 223, Ian Ring Music Theory
Scale 479Scale 479: Kocryllic, Ian Ring Music TheoryKocryllic
Scale 1247Scale 1247: Aeodyllic, Ian Ring Music TheoryAeodyllic
Scale 1759Scale 1759: Pylygic, Ian Ring Music TheoryPylygic
Scale 2783Scale 2783: Gothygic, Ian Ring Music TheoryGothygic

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.