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Scale 3943: "Zynygic"

Scale 3943: Zynygic, 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
Zynygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,1,2,5,6,8,9,10,11}
Forte Number9-3
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3295
Hemitonia7 (multihemitonic)
Cohemitonia5 (multicohemitonic)
Imperfections3
Modes8
Prime?no
prime: 895
Deep Scaleno
Interval Vector767763
Interval Spectrump6m7n7s6d7t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4}
<3> = {3,4,5,6}
<4> = {4,5,6,7}
<5> = {5,6,7,8}
<6> = {6,7,8,9}
<7> = {8,9,10}
<8> = {9,10,11}
Spectra Variation2.222
Maximally Evenno
Maximal Area Setno
Interior Area2.683
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♯{1,5,8}342.35
D{2,6,9}342.24
F{5,9,0}342.35
F♯{6,10,1}342.35
A♯{10,2,5}442.24
Minor Triadsdm{2,5,9}442.12
fm{5,8,0}342.53
f♯m{6,9,1}442.24
a♯m{10,1,5}342.24
bm{11,2,6}342.53
Augmented TriadsC♯+{1,5,9}542
D+{2,6,10}442.24
Diminished Triads{2,5,8}242.59
{5,8,11}242.76
f♯°{6,9,0}252.71
g♯°{8,11,2}242.76
{11,2,5}252.71
Parsimonious Voice Leading Between Common Triads of Scale 3943. Created by Ian Ring ©2019 C# C# C#+ C#+ C#->C#+ C#->d° fm fm C#->fm dm dm C#+->dm F F C#+->F f#m f#m C#+->f#m a#m a#m C#+->a#m d°->dm D D dm->D A# A# dm->A# D+ D+ D->D+ D->f#m F# F# D+->F# D+->A# bm bm D+->bm f°->fm g#° g#° f°->g#° fm->F f#° f#° F->f#° f#°->f#m f#m->F# F#->a#m g#°->bm a#m->A# A#->b° b°->bm

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.

Diameter5
Radius4
Self-Centeredno
Central VerticesC♯, C♯+, d°, dm, D, D+, f°, fm, F, f♯m, F♯, g♯°, a♯m, A♯, bm
Peripheral Verticesf♯°, b°

Modes

Modes are the rotational transformation of this scale. Scale 3943 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 4019
Scale 4019: Lonygic, Ian Ring Music TheoryLonygic
3rd mode:
Scale 4057
Scale 4057: Phrygic, Ian Ring Music TheoryPhrygic
4th mode:
Scale 1019
Scale 1019: Aeranygic, Ian Ring Music TheoryAeranygic
5th mode:
Scale 2557
Scale 2557: Dothygic, Ian Ring Music TheoryDothygic
6th mode:
Scale 1663
Scale 1663: Lydygic, Ian Ring Music TheoryLydygic
7th mode:
Scale 2879
Scale 2879: Stadygic, Ian Ring Music TheoryStadygic
8th mode:
Scale 3487
Scale 3487: Byptygic, Ian Ring Music TheoryByptygic
9th mode:
Scale 3791
Scale 3791: Stodygic, Ian Ring Music TheoryStodygic

Prime

The prime form of this scale is Scale 895

Scale 895Scale 895: Aeolathygic, Ian Ring Music TheoryAeolathygic

Complement

The nonatonic modal family [3943, 4019, 4057, 1019, 2557, 1663, 2879, 3487, 3791] (Forte: 9-3) is the complement of the tritonic modal family [19, 769, 2057] (Forte: 3-3)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3943 is 3295

Scale 3295Scale 3295: Phroptygic, Ian Ring Music TheoryPhroptygic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3943 is chiral, and its enantiomorph is scale 3295

Scale 3295Scale 3295: Phroptygic, Ian Ring Music TheoryPhroptygic

Transformations:

T0 3943  T0I 3295
T1 3791  T1I 2495
T2 3487  T2I 895
T3 2879  T3I 1790
T4 1663  T4I 3580
T5 3326  T5I 3065
T6 2557  T6I 2035
T7 1019  T7I 4070
T8 2038  T8I 4045
T9 4076  T9I 3995
T10 4057  T10I 3895
T11 4019  T11I 3695

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 3941Scale 3941: Stathyllic, Ian Ring Music TheoryStathyllic
Scale 3939Scale 3939: Dogyllic, Ian Ring Music TheoryDogyllic
Scale 3947Scale 3947: Ryptygic, Ian Ring Music TheoryRyptygic
Scale 3951Scale 3951: Mathyllian, Ian Ring Music TheoryMathyllian
Scale 3959Scale 3959: Katagyllian, Ian Ring Music TheoryKatagyllian
Scale 3911Scale 3911: Katyryllic, Ian Ring Music TheoryKatyryllic
Scale 3927Scale 3927: Monygic, Ian Ring Music TheoryMonygic
Scale 3879Scale 3879: Pathyllic, Ian Ring Music TheoryPathyllic
Scale 4007Scale 4007: Doptygic, Ian Ring Music TheoryDoptygic
Scale 4071Scale 4071: Rygyllian, Ian Ring Music TheoryRygyllian
Scale 3687Scale 3687: Zonyllic, Ian Ring Music TheoryZonyllic
Scale 3815Scale 3815: Galygic, Ian Ring Music TheoryGalygic
Scale 3431Scale 3431: Zyptyllic, Ian Ring Music TheoryZyptyllic
Scale 2919Scale 2919: Molyllic, Ian Ring Music TheoryMolyllic
Scale 1895Scale 1895: Salyllic, Ian Ring Music TheorySalyllic

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.