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Scale 3053: "Zycrygic"

Scale 3053: Zycrygic, 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
Zycrygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,2,3,5,6,7,8,9,11}
Forte Number9-10
Rotational Symmetrynone
Reflection Axes1
Palindromicno
Chiralityno
Hemitonia6 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections3
Modes8
Prime?no
prime: 1759
Deep Scaleno
Interval Vector668664
Interval Spectrump6m6n8s6d6t4
Distribution Spectra<1> = {1,2}
<2> = {2,3}
<3> = {3,4,5}
<4> = {4,5,6}
<5> = {6,7,8}
<6> = {7,8,9}
<7> = {9,10}
<8> = {10,11}
Spectra Variation1.333
Maximally Evenno
Maximal Area Setyes
Interior Area2.799
Myhill Propertyno
Balancedno
Ridge Tones[2]
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 TriadsD{2,6,9}442.37
F{5,9,0}442.42
G{7,11,2}342.47
G♯{8,0,3}442.32
B{11,3,6}442.37
Minor Triadscm{0,3,7}342.47
dm{2,5,9}442.42
fm{5,8,0}442.37
g♯m{8,11,3}442.37
bm{11,2,6}442.32
Augmented TriadsD♯+{3,7,11}442.32
Diminished Triads{0,3,6}242.74
{2,5,8}242.63
d♯°{3,6,9}242.63
{5,8,11}242.63
f♯°{6,9,0}242.63
g♯°{8,11,2}242.74
{9,0,3}242.58
{11,2,5}242.58
Parsimonious Voice Leading Between Common Triads of Scale 3053. Created by Ian Ring ©2019 cm cm c°->cm B B c°->B D#+ D#+ cm->D#+ G# G# cm->G# dm dm d°->dm fm fm d°->fm D D dm->D F F dm->F dm->b° d#° d#° D->d#° f#° f#° D->f#° bm bm D->bm d#°->B Parsimonious Voice Leading Between Common Triads of Scale 3053. Created by Ian Ring ©2019 G D#+->G g#m g#m D#+->g#m D#+->B f°->fm f°->g#m fm->F fm->G# F->f#° F->a° g#° g#° G->g#° G->bm g#°->g#m g#m->G# G#->a° b°->bm bm->B

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 3053 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 1787
Scale 1787: Mycrygic, Ian Ring Music TheoryMycrygic
3rd mode:
Scale 2941
Scale 2941: Laptygic, Ian Ring Music TheoryLaptygic
4th mode:
Scale 1759
Scale 1759: Pylygic, Ian Ring Music TheoryPylygicThis is the prime mode
5th mode:
Scale 2927
Scale 2927: Rodygic, Ian Ring Music TheoryRodygic
6th mode:
Scale 3511
Scale 3511: Epolygic, Ian Ring Music TheoryEpolygic
7th mode:
Scale 3803
Scale 3803: Epidygic, Ian Ring Music TheoryEpidygic
8th mode:
Scale 3949
Scale 3949: Koptygic, Ian Ring Music TheoryKoptygic
9th mode:
Scale 2011
Scale 2011: Raphygic, Ian Ring Music TheoryRaphygic

Prime

The prime form of this scale is Scale 1759

Scale 1759Scale 1759: Pylygic, Ian Ring Music TheoryPylygic

Complement

The nonatonic modal family [3053, 1787, 2941, 1759, 2927, 3511, 3803, 3949, 2011] (Forte: 9-10) is the complement of the tritonic modal family [73, 521, 577] (Forte: 3-10)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3053 is 1787

Scale 1787Scale 1787: Mycrygic, Ian Ring Music TheoryMycrygic

Transformations:

T0 3053  T0I 1787
T1 2011  T1I 3574
T2 4022  T2I 3053
T3 3949  T3I 2011
T4 3803  T4I 4022
T5 3511  T5I 3949
T6 2927  T6I 3803
T7 1759  T7I 3511
T8 3518  T8I 2927
T9 2941  T9I 1759
T10 1787  T10I 3518
T11 3574  T11I 2941

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 3055Scale 3055: Messiaen Mode 7, Ian Ring Music TheoryMessiaen Mode 7
Scale 3049Scale 3049: Phrydyllic, Ian Ring Music TheoryPhrydyllic
Scale 3051Scale 3051: Stalygic, Ian Ring Music TheoryStalygic
Scale 3045Scale 3045: Raptyllic, Ian Ring Music TheoryRaptyllic
Scale 3061Scale 3061: Apinygic, Ian Ring Music TheoryApinygic
Scale 3069Scale 3069: Maqam Shawq Afza, Ian Ring Music TheoryMaqam Shawq Afza
Scale 3021Scale 3021: Stodyllic, Ian Ring Music TheoryStodyllic
Scale 3037Scale 3037: Nine Tone Scale, Ian Ring Music TheoryNine Tone Scale
Scale 2989Scale 2989: Bebop Minor, Ian Ring Music TheoryBebop Minor
Scale 2925Scale 2925: Diminished, Ian Ring Music TheoryDiminished
Scale 2797Scale 2797: Stalyllic, Ian Ring Music TheoryStalyllic
Scale 2541Scale 2541: Algerian, Ian Ring Music TheoryAlgerian
Scale 3565Scale 3565: Aeolorygic, Ian Ring Music TheoryAeolorygic
Scale 4077Scale 4077: Gothyllian, Ian Ring Music TheoryGothyllian
Scale 1005Scale 1005: Radyllic, Ian Ring Music TheoryRadyllic
Scale 2029Scale 2029: Kiourdi, Ian Ring Music TheoryKiourdi

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.