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Scale 2991: "Zanygic"

Scale 2991: Zanygic, 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
Zanygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,1,2,3,5,7,8,9,11}
Forte Number9-8
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3771
Hemitonia6 (multihemitonic)
Cohemitonia4 (multicohemitonic)
Imperfections3
Modes8
Prime?no
prime: 1503
Deep Scaleno
Interval Vector676764
Interval Spectrump6m7n6s7d6t4
Distribution Spectra<1> = {1,2}
<2> = {2,3,4}
<3> = {3,4,5}
<4> = {4,5,6}
<5> = {6,7,8}
<6> = {7,8,9}
<7> = {8,9,10}
<8> = {10,11}
Spectra Variation1.556
Maximally Evenno
Maximal Area Setyes
Interior Area2.799
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}342.33
F{5,9,0}342.33
G{7,11,2}342.47
G♯{8,0,3}442.07
Minor Triadscm{0,3,7}242.47
dm{2,5,9}342.47
fm{5,8,0}442.07
g♯m{8,11,3}442.2
Augmented TriadsC♯+{1,5,9}342.4
D♯+{3,7,11}342.4
Diminished Triads{2,5,8}242.67
{5,8,11}242.33
g♯°{8,11,2}242.53
{9,0,3}242.47
{11,2,5}242.53
Parsimonious Voice Leading Between Common Triads of Scale 2991. Created by Ian Ring ©2019 cm cm D#+ D#+ cm->D#+ G# G# cm->G# C# C# C#+ C#+ C#->C#+ C#->d° fm fm C#->fm dm dm C#+->dm F F C#+->F d°->dm dm->b° Parsimonious Voice Leading Between Common Triads of Scale 2991. Created by Ian Ring ©2019 G D#+->G g#m g#m D#+->g#m f°->fm f°->g#m fm->F fm->G# F->a° g#° g#° G->g#° G->b° g#°->g#m g#m->G# G#->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 2991 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 3543
Scale 3543: Aeolonygic, Ian Ring Music TheoryAeolonygic
3rd mode:
Scale 3819
Scale 3819: Aeolanygic, Ian Ring Music TheoryAeolanygic
4th mode:
Scale 3957
Scale 3957: Porygic, Ian Ring Music TheoryPorygic
5th mode:
Scale 2013
Scale 2013: Mocrygic, Ian Ring Music TheoryMocrygic
6th mode:
Scale 1527
Scale 1527: Aeolyrigic, Ian Ring Music TheoryAeolyrigic
7th mode:
Scale 2811
Scale 2811: Barygic, Ian Ring Music TheoryBarygic
8th mode:
Scale 3453
Scale 3453: Katarygic, Ian Ring Music TheoryKatarygic
9th mode:
Scale 1887
Scale 1887: Aerocrygic, Ian Ring Music TheoryAerocrygic

Prime

The prime form of this scale is Scale 1503

Scale 1503Scale 1503: Padygic, Ian Ring Music TheoryPadygic

Complement

The nonatonic modal family [2991, 3543, 3819, 3957, 2013, 1527, 2811, 3453, 1887] (Forte: 9-8) is the complement of the tritonic modal family [69, 321, 1041] (Forte: 3-8)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2991 is 3771

Scale 3771Scale 3771: Stophygic, Ian Ring Music TheoryStophygic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2991 is chiral, and its enantiomorph is scale 3771

Scale 3771Scale 3771: Stophygic, Ian Ring Music TheoryStophygic

Transformations:

T0 2991  T0I 3771
T1 1887  T1I 3447
T2 3774  T2I 2799
T3 3453  T3I 1503
T4 2811  T4I 3006
T5 1527  T5I 1917
T6 3054  T6I 3834
T7 2013  T7I 3573
T8 4026  T8I 3051
T9 3957  T9I 2007
T10 3819  T10I 4014
T11 3543  T11I 3933

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 2989Scale 2989: Bebop Minor, Ian Ring Music TheoryBebop Minor
Scale 2987Scale 2987: Neapolitan Major and Minor Mixed, Ian Ring Music TheoryNeapolitan Major and Minor Mixed
Scale 2983Scale 2983: Zythyllic, Ian Ring Music TheoryZythyllic
Scale 2999Scale 2999: Chromatic and Permuted Diatonic Dorian Mixed, Ian Ring Music TheoryChromatic and Permuted Diatonic Dorian Mixed
Scale 3007Scale 3007: Zyryllian, Ian Ring Music TheoryZyryllian
Scale 2959Scale 2959: Dygyllic, Ian Ring Music TheoryDygyllic
Scale 2975Scale 2975: Aeroptygic, Ian Ring Music TheoryAeroptygic
Scale 3023Scale 3023: Mothygic, Ian Ring Music TheoryMothygic
Scale 3055Scale 3055: Messiaen Mode 7, Ian Ring Music TheoryMessiaen Mode 7
Scale 2863Scale 2863: Aerogyllic, Ian Ring Music TheoryAerogyllic
Scale 2927Scale 2927: Rodygic, Ian Ring Music TheoryRodygic
Scale 2735Scale 2735: Gynyllic, Ian Ring Music TheoryGynyllic
Scale 2479Scale 2479: Harmonic and Neapolitan Minor Mixed, Ian Ring Music TheoryHarmonic and Neapolitan Minor Mixed
Scale 3503Scale 3503: Zyphygic, Ian Ring Music TheoryZyphygic
Scale 4015Scale 4015: Phradyllian, Ian Ring Music TheoryPhradyllian
Scale 943Scale 943: Aerygyllic, Ian Ring Music TheoryAerygyllic
Scale 1967Scale 1967: Diatonic Dorian Mixed, Ian Ring Music TheoryDiatonic Dorian Mixed

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.