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Scale 3007: "Zyryllian"

Scale 3007: Zyryllian, 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
Zyryllian

Analysis

Cardinality10 (decatonic)
Pitch Class Set{0,1,2,3,4,5,7,8,9,11}
Forte Number10-4
Rotational Symmetrynone
Reflection Axes2
Palindromicno
Chiralityno
Hemitonia8 (multihemitonic)
Cohemitonia6 (multicohemitonic)
Imperfections2
Modes9
Prime?no
prime: 1919
Deep Scaleno
Interval Vector888984
Interval Spectrump8m9n8s8d8t4
Distribution Spectra<1> = {1,2}
<2> = {2,3}
<3> = {3,4}
<4> = {4,5,6}
<5> = {5,6,7}
<6> = {6,7,8}
<7> = {8,9}
<8> = {9,10}
<9> = {10,11}
Spectra Variation1.2
Maximally Evenno
Maximal Area Setyes
Interior Area2.866
Myhill Propertyno
Balancedno
Ridge Tones[4]
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}452.52
C♯{1,5,8}452.65
E{4,8,11}452.43
F{5,9,0}352.74
G{7,11,2}353
G♯{8,0,3}452.43
A{9,1,4}352.74
Minor Triadscm{0,3,7}352.74
c♯m{1,4,8}452.43
dm{2,5,9}353
em{4,7,11}352.74
fm{5,8,0}452.43
g♯m{8,11,3}452.65
am{9,0,4}452.52
Augmented TriadsC+{0,4,8}652.13
C♯+{1,5,9}452.78
D♯+{3,7,11}452.78
Diminished Triadsc♯°{1,4,7}252.91
{2,5,8}253.13
{5,8,11}252.83
g♯°{8,11,2}253.13
{9,0,3}252.91
{11,2,5}253.13
Parsimonious Voice Leading Between Common Triads of Scale 3007. Created by Ian Ring ©2019 cm cm 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 fm fm C+->fm C+->G# am am C+->am c#°->c#m C# C# c#m->C# A A c#m->A C#+ C#+ C#->C#+ C#->d° C#->fm dm dm C#+->dm F F C#+->F C#+->A d°->dm dm->b° D#+->em Parsimonious Voice Leading Between Common Triads of Scale 3007. Created by Ian Ring ©2019 G D#+->G g#m g#m D#+->g#m em->E E->f° E->g#m f°->fm fm->F F->am g#° g#° G->g#° G->b° g#°->g#m g#m->G# G#->a° a°->am am->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 3007 can be rotated to make 9 other scales. The 1st mode is itself.

2nd mode:
Scale 3551
Scale 3551: Sagyllian, Ian Ring Music TheorySagyllian
3rd mode:
Scale 3823
Scale 3823: Epinyllian, Ian Ring Music TheoryEpinyllian
4th mode:
Scale 3959
Scale 3959: Katagyllian, Ian Ring Music TheoryKatagyllian
5th mode:
Scale 4027
Scale 4027: Ragyllian, Ian Ring Music TheoryRagyllian
6th mode:
Scale 4061
Scale 4061: Staptyllian, Ian Ring Music TheoryStaptyllian
7th mode:
Scale 2039
Scale 2039: Danyllian, Ian Ring Music TheoryDanyllian
8th mode:
Scale 3067
Scale 3067: Goptyllian, Ian Ring Music TheoryGoptyllian
9th mode:
Scale 3581
Scale 3581: Epocryllian, Ian Ring Music TheoryEpocryllian
10th mode:
Scale 1919
Scale 1919: Rocryllian, Ian Ring Music TheoryRocryllianThis is the prime mode

Prime

The prime form of this scale is Scale 1919

Scale 1919Scale 1919: Rocryllian, Ian Ring Music TheoryRocryllian

Complement

The decatonic modal family [3007, 3551, 3823, 3959, 4027, 4061, 2039, 3067, 3581, 1919] (Forte: 10-4) is the complement of the modal family [17, 257] (Forte: 2-4)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3007 is 4027

Scale 4027Scale 4027: Ragyllian, Ian Ring Music TheoryRagyllian

Transformations:

T0 3007  T0I 4027
T1 1919  T1I 3959
T2 3838  T2I 3823
T3 3581  T3I 3551
T4 3067  T4I 3007
T5 2039  T5I 1919
T6 4078  T6I 3838
T7 4061  T7I 3581
T8 4027  T8I 3067
T9 3959  T9I 2039
T10 3823  T10I 4078
T11 3551  T11I 4061

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 3005Scale 3005: Gycrygic, Ian Ring Music TheoryGycrygic
Scale 3003Scale 3003: Genus Chromaticum, Ian Ring Music TheoryGenus Chromaticum
Scale 2999Scale 2999: Chromatic and Permuted Diatonic Dorian Mixed, Ian Ring Music TheoryChromatic and Permuted Diatonic Dorian Mixed
Scale 2991Scale 2991: Zanygic, Ian Ring Music TheoryZanygic
Scale 2975Scale 2975: Aeroptygic, Ian Ring Music TheoryAeroptygic
Scale 3039Scale 3039: Godyllian, Ian Ring Music TheoryGodyllian
Scale 3071Scale 3071: Solatic, Ian Ring Music TheorySolatic
Scale 2879Scale 2879: Stadygic, Ian Ring Music TheoryStadygic
Scale 2943Scale 2943: Dathyllian, Ian Ring Music TheoryDathyllian
Scale 2751Scale 2751: Sylygic, Ian Ring Music TheorySylygic
Scale 2495Scale 2495: Aeolocrygic, Ian Ring Music TheoryAeolocrygic
Scale 3519Scale 3519: Raga Sindhi-Bhairavi, Ian Ring Music TheoryRaga Sindhi-Bhairavi
Scale 4031Scale 4031: Godatic, Ian Ring Music TheoryGodatic
Scale 959Scale 959: Katylygic, Ian Ring Music TheoryKatylygic
Scale 1983Scale 1983: Soryllian, Ian Ring Music TheorySoryllian

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.