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Scale 4059: "Zolyllian"

Scale 4059: Zolyllian, 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
Zolyllian

Analysis

Cardinality10 (decatonic)
Pitch Class Set{0,1,3,4,6,7,8,9,10,11}
Forte Number10-3
Rotational Symmetrynone
Reflection Axes3.5
Palindromicno
Chiralityno
Hemitonia8 (multihemitonic)
Cohemitonia6 (multicohemitonic)
Imperfections2
Modes9
Prime?no
prime: 1791
Deep Scaleno
Interval Vector889884
Interval Spectrump8m8n9s8d8t4
Distribution Spectra<1> = {1,2}
<2> = {2,3}
<3> = {3,4,5}
<4> = {4,5,6}
<5> = {5,6,7}
<6> = {6,7,8}
<7> = {7,8,9}
<8> = {9,10}
<9> = {10,11}
Spectra Variation1.4
Maximally Evenno
Maximal Area Setyes
Interior Area2.866
Myhill Propertyno
Balancedno
Ridge Tones[7]
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}452.58
D♯{3,7,10}452.67
E{4,8,11}352.75
F♯{6,10,1}452.83
G♯{8,0,3}452.67
A{9,1,4}452.75
B{11,3,6}352.75
Minor Triadscm{0,3,7}452.58
c♯m{1,4,8}352.75
d♯m{3,6,10}452.75
em{4,7,11}452.67
f♯m{6,9,1}452.83
g♯m{8,11,3}352.75
am{9,0,4}452.67
Augmented TriadsC+{0,4,8}552.5
D♯+{3,7,11}552.5
Diminished Triads{0,3,6}253
c♯°{1,4,7}253
d♯°{3,6,9}253
{4,7,10}253
f♯°{6,9,0}253
{7,10,1}253
{9,0,3}253
a♯°{10,1,4}253
Parsimonious Voice Leading Between Common Triads of Scale 4059. Created by Ian Ring ©2019 cm cm c°->cm B B c°->B C C cm->C D#+ D#+ cm->D#+ G# G# cm->G# C+ C+ C->C+ c#° c#° C->c#° em em C->em c#m c#m C+->c#m E E C+->E C+->G# am am C+->am c#°->c#m A A c#m->A d#° d#° d#m d#m d#°->d#m f#m f#m d#°->f#m D# D# d#m->D# F# F# d#m->F# d#m->B D#->D#+ D#->e° D#->g° D#+->em g#m g#m D#+->g#m D#+->B e°->em em->E E->g#m f#° f#° f#°->f#m f#°->am f#m->F# f#m->A F#->g° a#° a#° F#->a#° g#m->G# G#->a° a°->am am->A A->a#°

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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.

Diameter5
Radius5
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 4059 can be rotated to make 9 other scales. The 1st mode is itself.

2nd mode:
Scale 4077
Scale 4077: Gothyllian, Ian Ring Music TheoryGothyllian
3rd mode:
Scale 2043
Scale 2043: Maqam Tarzanuyn, Ian Ring Music TheoryMaqam Tarzanuyn
4th mode:
Scale 3069
Scale 3069: Maqam Shawq Afza, Ian Ring Music TheoryMaqam Shawq Afza
5th mode:
Scale 1791
Scale 1791: Aerygyllian, Ian Ring Music TheoryAerygyllianThis is the prime mode
6th mode:
Scale 2943
Scale 2943: Dathyllian, Ian Ring Music TheoryDathyllian
7th mode:
Scale 3519
Scale 3519: Raga Sindhi-Bhairavi, Ian Ring Music TheoryRaga Sindhi-Bhairavi
8th mode:
Scale 3807
Scale 3807: Bagyllian, Ian Ring Music TheoryBagyllian
9th mode:
Scale 3951
Scale 3951: Mathyllian, Ian Ring Music TheoryMathyllian
10th mode:
Scale 4023
Scale 4023: Styptyllian, Ian Ring Music TheoryStyptyllian

Prime

The prime form of this scale is Scale 1791

Scale 1791Scale 1791: Aerygyllian, Ian Ring Music TheoryAerygyllian

Complement

The decatonic modal family [4059, 4077, 2043, 3069, 1791, 2943, 3519, 3807, 3951, 4023] (Forte: 10-3) is the complement of the modal family [9, 513] (Forte: 2-3)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 4059 is 2943

Scale 2943Scale 2943: Dathyllian, Ian Ring Music TheoryDathyllian

Transformations:

T0 4059  T0I 2943
T1 4023  T1I 1791
T2 3951  T2I 3582
T3 3807  T3I 3069
T4 3519  T4I 2043
T5 2943  T5I 4086
T6 1791  T6I 4077
T7 3582  T7I 4059
T8 3069  T8I 4023
T9 2043  T9I 3951
T10 4086  T10I 3807
T11 4077  T11I 3519

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 4057Scale 4057: Phrygic, Ian Ring Music TheoryPhrygic
Scale 4061Scale 4061: Staptyllian, Ian Ring Music TheoryStaptyllian
Scale 4063Scale 4063: Eptatic, Ian Ring Music TheoryEptatic
Scale 4051Scale 4051: Ionilygic, Ian Ring Music TheoryIonilygic
Scale 4055Scale 4055: Dagyllian, Ian Ring Music TheoryDagyllian
Scale 4043Scale 4043: Phrocrygic, Ian Ring Music TheoryPhrocrygic
Scale 4075Scale 4075: Katyllian, Ian Ring Music TheoryKatyllian
Scale 4091Scale 4091: Thydatic, Ian Ring Music TheoryThydatic
Scale 3995Scale 3995: Ionygic, Ian Ring Music TheoryIonygic
Scale 4027Scale 4027: Ragyllian, Ian Ring Music TheoryRagyllian
Scale 3931Scale 3931: Aerygic, Ian Ring Music TheoryAerygic
Scale 3803Scale 3803: Epidygic, Ian Ring Music TheoryEpidygic
Scale 3547Scale 3547: Sadygic, Ian Ring Music TheorySadygic
Scale 3035Scale 3035: Gocrygic, Ian Ring Music TheoryGocrygic
Scale 2011Scale 2011: Raphygic, Ian Ring Music TheoryRaphygic

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.