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Scale 3817: "Zoryllic"

Scale 3817: Zoryllic, 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
Zoryllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,3,5,6,7,9,10,11}
Forte Number8-Z29
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 751
Hemitonia5 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections3
Modes7
Prime?no
prime: 751
Deep Scaleno
Interval Vector555553
Interval Spectrump5m5n5s5d5t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {3,4,5,6}
<4> = {5,6,7}
<5> = {6,7,8,9}
<6> = {7,8,9,10}
<7> = {9,10,11}
Spectra Variation2.25
Maximally Evenno
Maximal Area Setno
Interior Area2.616
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 TriadsD♯{3,7,10}242.1
F{5,9,0}242.3
B{11,3,6}341.9
Minor Triadscm{0,3,7}341.9
d♯m{3,6,10}341.9
Augmented TriadsD♯+{3,7,11}341.9
Diminished Triads{0,3,6}242.1
d♯°{3,6,9}242.1
f♯°{6,9,0}242.3
{9,0,3}242.1
Parsimonious Voice Leading Between Common Triads of Scale 3817. Created by Ian Ring ©2019 cm cm c°->cm B B c°->B D#+ D#+ cm->D#+ cm->a° d#° d#° d#m d#m d#°->d#m f#° f#° d#°->f#° D# D# d#m->D# d#m->B D#->D#+ D#+->B F F F->f#° F->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 3817 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 989
Scale 989: Phrolyllic, Ian Ring Music TheoryPhrolyllic
3rd mode:
Scale 1271
Scale 1271: Kolyllic, Ian Ring Music TheoryKolyllic
4th mode:
Scale 2683
Scale 2683: Thodyllic, Ian Ring Music TheoryThodyllic
5th mode:
Scale 3389
Scale 3389: Socryllic, Ian Ring Music TheorySocryllic
6th mode:
Scale 1871
Scale 1871: Aeolyllic, Ian Ring Music TheoryAeolyllic
7th mode:
Scale 2983
Scale 2983: Zythyllic, Ian Ring Music TheoryZythyllic
8th mode:
Scale 3539
Scale 3539: Aeoryllic, Ian Ring Music TheoryAeoryllic

Prime

The prime form of this scale is Scale 751

Scale 751Scale 751, Ian Ring Music Theory

Complement

The octatonic modal family [3817, 989, 1271, 2683, 3389, 1871, 2983, 3539] (Forte: 8-Z29) is the complement of the tetratonic modal family [139, 353, 1553, 2117] (Forte: 4-Z29)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3817 is 751

Scale 751Scale 751, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3817 is chiral, and its enantiomorph is scale 751

Scale 751Scale 751, Ian Ring Music Theory

Transformations:

T0 3817  T0I 751
T1 3539  T1I 1502
T2 2983  T2I 3004
T3 1871  T3I 1913
T4 3742  T4I 3826
T5 3389  T5I 3557
T6 2683  T6I 3019
T7 1271  T7I 1943
T8 2542  T8I 3886
T9 989  T9I 3677
T10 1978  T10I 3259
T11 3956  T11I 2423

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 3819Scale 3819: Aeolanygic, Ian Ring Music TheoryAeolanygic
Scale 3821Scale 3821: Epyrygic, Ian Ring Music TheoryEpyrygic
Scale 3809Scale 3809, Ian Ring Music Theory
Scale 3813Scale 3813: Aeologyllic, Ian Ring Music TheoryAeologyllic
Scale 3825Scale 3825: Pynyllic, Ian Ring Music TheoryPynyllic
Scale 3833Scale 3833: Dycrygic, Ian Ring Music TheoryDycrygic
Scale 3785Scale 3785: Epagian, Ian Ring Music TheoryEpagian
Scale 3801Scale 3801: Maptyllic, Ian Ring Music TheoryMaptyllic
Scale 3753Scale 3753: Phraptian, Ian Ring Music TheoryPhraptian
Scale 3689Scale 3689: Katocrian, Ian Ring Music TheoryKatocrian
Scale 3945Scale 3945: Lydyllic, Ian Ring Music TheoryLydyllic
Scale 4073Scale 4073: Sathygic, Ian Ring Music TheorySathygic
Scale 3305Scale 3305: Chromatic Hypophrygian, Ian Ring Music TheoryChromatic Hypophrygian
Scale 3561Scale 3561: Pothyllic, Ian Ring Music TheoryPothyllic
Scale 2793Scale 2793: Eporian, Ian Ring Music TheoryEporian
Scale 1769Scale 1769: Blues Heptatonic II, Ian Ring Music TheoryBlues Heptatonic 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.