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Scale 4041: "Zaryllic"

Scale 4041: Zaryllic, 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

41161837294116105072918310504116183
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
Zaryllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,3,6,7,8,9,10,11}
Forte Number8-3
Rotational Symmetrynone
Reflection Axes3
Palindromicno
Chiralityno
Hemitonia6 (multihemitonic)
Cohemitonia5 (multicohemitonic)
Imperfections4
Modes7
Prime?no
prime: 639
Deep Scaleno
Interval Vector656542
Interval Spectrump4m5n6s5d6t2
Distribution Spectra<1> = {1,3}
<2> = {2,4,6}
<3> = {3,5,7}
<4> = {4,6,8}
<5> = {5,7,9}
<6> = {6,8,10}
<7> = {9,11}
Spectra Variation3
Maximally Evenno
Maximal Area Setno
Interior Area2.5
Myhill Propertyno
Balancedno
Ridge Tones[6]
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}242.09
G♯{8,0,3}342
B{11,3,6}341.91
Minor Triadscm{0,3,7}341.91
d♯m{3,6,10}342
g♯m{8,11,3}242.09
Augmented TriadsD♯+{3,7,11}441.82
Diminished Triads{0,3,6}242.18
d♯°{3,6,9}242.27
f♯°{6,9,0}242.36
{9,0,3}242.27
Parsimonious Voice Leading Between Common Triads of Scale 4041. Created by Ian Ring ©2019 cm cm c°->cm B B c°->B D#+ D#+ cm->D#+ G# G# cm->G# d#° d#° d#m d#m d#°->d#m f#° f#° d#°->f#° D# D# d#m->D# d#m->B D#->D#+ g#m g#m D#+->g#m D#+->B f#°->a° g#m->G# G#->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.

Diameter4
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 4041 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 1017
Scale 1017: Dythyllic, Ian Ring Music TheoryDythyllic
3rd mode:
Scale 639
Scale 639: Ionaryllic, Ian Ring Music TheoryIonaryllicThis is the prime mode
4th mode:
Scale 2367
Scale 2367: Laryllic, Ian Ring Music TheoryLaryllic
5th mode:
Scale 3231
Scale 3231: Kataptyllic, Ian Ring Music TheoryKataptyllic
6th mode:
Scale 3663
Scale 3663: Sonyllic, Ian Ring Music TheorySonyllic
7th mode:
Scale 3879
Scale 3879: Pathyllic, Ian Ring Music TheoryPathyllic
8th mode:
Scale 3987
Scale 3987: Loryllic, Ian Ring Music TheoryLoryllic

Prime

The prime form of this scale is Scale 639

Scale 639Scale 639: Ionaryllic, Ian Ring Music TheoryIonaryllic

Complement

The octatonic modal family [4041, 1017, 639, 2367, 3231, 3663, 3879, 3987] (Forte: 8-3) is the complement of the tetratonic modal family [27, 1539, 2061, 2817] (Forte: 4-3)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 4041 is 639

Scale 639Scale 639: Ionaryllic, Ian Ring Music TheoryIonaryllic

Transformations:

T0 4041  T0I 639
T1 3987  T1I 1278
T2 3879  T2I 2556
T3 3663  T3I 1017
T4 3231  T4I 2034
T5 2367  T5I 4068
T6 639  T6I 4041
T7 1278  T7I 3987
T8 2556  T8I 3879
T9 1017  T9I 3663
T10 2034  T10I 3231
T11 4068  T11I 2367

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 4043Scale 4043: Phrocrygic, Ian Ring Music TheoryPhrocrygic
Scale 4045Scale 4045: Gyptygic, Ian Ring Music TheoryGyptygic
Scale 4033Scale 4033, Ian Ring Music Theory
Scale 4037Scale 4037: Ionyllic, Ian Ring Music TheoryIonyllic
Scale 4049Scale 4049: Stycryllic, Ian Ring Music TheoryStycryllic
Scale 4057Scale 4057: Phrygic, Ian Ring Music TheoryPhrygic
Scale 4073Scale 4073: Sathygic, Ian Ring Music TheorySathygic
Scale 3977Scale 3977: Kythian, Ian Ring Music TheoryKythian
Scale 4009Scale 4009: Phranyllic, Ian Ring Music TheoryPhranyllic
Scale 3913Scale 3913: Bonian, Ian Ring Music TheoryBonian
Scale 3785Scale 3785: Epagian, Ian Ring Music TheoryEpagian
Scale 3529Scale 3529: Stalian, Ian Ring Music TheoryStalian
Scale 3017Scale 3017: Gacrian, Ian Ring Music TheoryGacrian
Scale 1993Scale 1993: Katoptian, Ian Ring Music TheoryKatoptian

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.