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Scale 2813: "Zolygic"

Scale 2813: Zolygic, 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
Zolygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,2,3,4,5,6,7,9,11}
Forte Number9-7
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2027
Hemitonia6 (multihemitonic)
Cohemitonia4 (multicohemitonic)
Imperfections2
Modes8
Prime?no
prime: 1471
Deep Scaleno
Interval Vector677673
Interval Spectrump7m6n7s7d6t3
Distribution Spectra<1> = {1,2}
<2> = {2,3,4}
<3> = {3,4,5}
<4> = {4,5,6,7}
<5> = {5,6,7,8}
<6> = {7,8,9}
<7> = {8,9,10}
<8> = {10,11}
Spectra Variation1.778
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{0,4,7}342.44
D{2,6,9}442.31
F{5,9,0}342.44
G{7,11,2}242.38
B{11,3,6}442.13
Minor Triadscm{0,3,7}442.31
dm{2,5,9}342.44
em{4,7,11}242.56
am{9,0,4}342.44
bm{11,2,6}442.19
Augmented TriadsD♯+{3,7,11}442.19
Diminished Triads{0,3,6}242.44
d♯°{3,6,9}242.44
f♯°{6,9,0}242.56
{9,0,3}242.56
{11,2,5}242.56
Parsimonious Voice Leading Between Common Triads of Scale 2813. Created by Ian Ring ©2019 cm cm c°->cm B B c°->B C C cm->C D#+ D#+ cm->D#+ cm->a° em em C->em am am C->am dm dm D D dm->D F F dm->F dm->b° d#° d#° D->d#° f#° f#° D->f#° bm bm D->bm d#°->B D#+->em Parsimonious Voice Leading Between Common Triads of Scale 2813. Created by Ian Ring ©2019 G D#+->G D#+->B F->f#° F->am G->bm a°->am b°->bm bm->B

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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 2813 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 1727
Scale 1727: Sydygic, Ian Ring Music TheorySydygic
3rd mode:
Scale 2911
Scale 2911: Katygic, Ian Ring Music TheoryKatygic
4th mode:
Scale 3503
Scale 3503: Zyphygic, Ian Ring Music TheoryZyphygic
5th mode:
Scale 3799
Scale 3799: Aeralygic, Ian Ring Music TheoryAeralygic
6th mode:
Scale 3947
Scale 3947: Ryptygic, Ian Ring Music TheoryRyptygic
7th mode:
Scale 4021
Scale 4021: Raga Pahadi, Ian Ring Music TheoryRaga Pahadi
8th mode:
Scale 2029
Scale 2029: Kiourdi, Ian Ring Music TheoryKiourdi
9th mode:
Scale 1531
Scale 1531: Styptygic, Ian Ring Music TheoryStyptygic

Prime

The prime form of this scale is Scale 1471

Scale 1471Scale 1471: Radygic, Ian Ring Music TheoryRadygic

Complement

The nonatonic modal family [2813, 1727, 2911, 3503, 3799, 3947, 4021, 2029, 1531] (Forte: 9-7) is the complement of the tritonic modal family [37, 641, 1033] (Forte: 3-7)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2813 is 2027

Scale 2027Scale 2027: Boptygic, Ian Ring Music TheoryBoptygic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2813 is chiral, and its enantiomorph is scale 2027

Scale 2027Scale 2027: Boptygic, Ian Ring Music TheoryBoptygic

Transformations:

T0 2813  T0I 2027
T1 1531  T1I 4054
T2 3062  T2I 4013
T3 2029  T3I 3931
T4 4058  T4I 3767
T5 4021  T5I 3439
T6 3947  T6I 2783
T7 3799  T7I 1471
T8 3503  T8I 2942
T9 2911  T9I 1789
T10 1727  T10I 3578
T11 3454  T11I 3061

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 2815Scale 2815: Aeradyllian, Ian Ring Music TheoryAeradyllian
Scale 2809Scale 2809: Gythyllic, Ian Ring Music TheoryGythyllic
Scale 2811Scale 2811: Barygic, Ian Ring Music TheoryBarygic
Scale 2805Scale 2805: Ishikotsucho, Ian Ring Music TheoryIshikotsucho
Scale 2797Scale 2797: Stalyllic, Ian Ring Music TheoryStalyllic
Scale 2781Scale 2781: Gycryllic, Ian Ring Music TheoryGycryllic
Scale 2749Scale 2749: Katagyllic, Ian Ring Music TheoryKatagyllic
Scale 2685Scale 2685: Ionoryllic, Ian Ring Music TheoryIonoryllic
Scale 2941Scale 2941: Laptygic, Ian Ring Music TheoryLaptygic
Scale 3069Scale 3069: Maqam Shawq Afza, Ian Ring Music TheoryMaqam Shawq Afza
Scale 2301Scale 2301: Bydyllic, Ian Ring Music TheoryBydyllic
Scale 2557Scale 2557: Dothygic, Ian Ring Music TheoryDothygic
Scale 3325Scale 3325: Mixolygic, Ian Ring Music TheoryMixolygic
Scale 3837Scale 3837: Minor Pentatonic With Leading Tones, Ian Ring Music TheoryMinor Pentatonic With Leading Tones
Scale 765Scale 765, Ian Ring Music Theory
Scale 1789Scale 1789: Blues Enneatonic II, Ian Ring Music TheoryBlues Enneatonic II

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.