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Scale 2399: "Zanyllic"

Scale 2399: Zanyllic, 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
Zanyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,2,3,4,6,8,11}
Forte Number8-11
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3923
Hemitonia5 (multihemitonic)
Cohemitonia4 (multicohemitonic)
Imperfections3
Modes7
Prime?no
prime: 703
Deep Scaleno
Interval Vector565552
Interval Spectrump5m5n5s6d5t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {3,4,5,6,7}
<4> = {4,5,6,7,8}
<5> = {5,6,7,8,9}
<6> = {7,8,9,10}
<7> = {9,10,11}
Spectra Variation2.75
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 TriadsE{4,8,11}231.78
G♯{8,0,3}331.56
B{11,3,6}341.78
Minor Triadsc♯m{1,4,8}152.67
g♯m{8,11,3}431.44
bm{11,2,6}252.33
Augmented TriadsC+{0,4,8}341.89
Diminished Triads{0,3,6}231.89
g♯°{8,11,2}242
Parsimonious Voice Leading Between Common Triads of Scale 2399. Created by Ian Ring ©2019 G# G# c°->G# B B c°->B C+ C+ c#m c#m C+->c#m E E C+->E C+->G# g#m g#m E->g#m g#° g#° g#°->g#m bm bm g#°->bm g#m->G# g#m->B 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.

Diameter5
Radius3
Self-Centeredno
Central Verticesc°, E, g♯m, G♯
Peripheral Verticesc♯m, bm

Modes

Modes are the rotational transformation of this scale. Scale 2399 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3247
Scale 3247: Aeolonyllic, Ian Ring Music TheoryAeolonyllic
3rd mode:
Scale 3671
Scale 3671: Aeonyllic, Ian Ring Music TheoryAeonyllic
4th mode:
Scale 3883
Scale 3883: Kyryllic, Ian Ring Music TheoryKyryllic
5th mode:
Scale 3989
Scale 3989: Sythyllic, Ian Ring Music TheorySythyllic
6th mode:
Scale 2021
Scale 2021: Katycryllic, Ian Ring Music TheoryKatycryllic
7th mode:
Scale 1529
Scale 1529: Kataryllic, Ian Ring Music TheoryKataryllic
8th mode:
Scale 703
Scale 703: Aerocryllic, Ian Ring Music TheoryAerocryllicThis is the prime mode

Prime

The prime form of this scale is Scale 703

Scale 703Scale 703: Aerocryllic, Ian Ring Music TheoryAerocryllic

Complement

The octatonic modal family [2399, 3247, 3671, 3883, 3989, 2021, 1529, 703] (Forte: 8-11) is the complement of the tetratonic modal family [43, 1409, 1541, 2069] (Forte: 4-11)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2399 is 3923

Scale 3923Scale 3923: Stoptyllic, Ian Ring Music TheoryStoptyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2399 is chiral, and its enantiomorph is scale 3923

Scale 3923Scale 3923: Stoptyllic, Ian Ring Music TheoryStoptyllic

Transformations:

T0 2399  T0I 3923
T1 703  T1I 3751
T2 1406  T2I 3407
T3 2812  T3I 2719
T4 1529  T4I 1343
T5 3058  T5I 2686
T6 2021  T6I 1277
T7 4042  T7I 2554
T8 3989  T8I 1013
T9 3883  T9I 2026
T10 3671  T10I 4052
T11 3247  T11I 4009

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 2397Scale 2397: Stagian, Ian Ring Music TheoryStagian
Scale 2395Scale 2395: Zoptian, Ian Ring Music TheoryZoptian
Scale 2391Scale 2391: Molian, Ian Ring Music TheoryMolian
Scale 2383Scale 2383: Katorian, Ian Ring Music TheoryKatorian
Scale 2415Scale 2415: Lothyllic, Ian Ring Music TheoryLothyllic
Scale 2431Scale 2431: Gythygic, Ian Ring Music TheoryGythygic
Scale 2335Scale 2335: Epydian, Ian Ring Music TheoryEpydian
Scale 2367Scale 2367: Laryllic, Ian Ring Music TheoryLaryllic
Scale 2463Scale 2463: Ionathyllic, Ian Ring Music TheoryIonathyllic
Scale 2527Scale 2527: Phradygic, Ian Ring Music TheoryPhradygic
Scale 2143Scale 2143, Ian Ring Music Theory
Scale 2271Scale 2271: Poptyllic, Ian Ring Music TheoryPoptyllic
Scale 2655Scale 2655, Ian Ring Music Theory
Scale 2911Scale 2911: Katygic, Ian Ring Music TheoryKatygic
Scale 3423Scale 3423: Lothygic, Ian Ring Music TheoryLothygic
Scale 351Scale 351: Epanian, Ian Ring Music TheoryEpanian
Scale 1375Scale 1375: Bothyllic, Ian Ring Music TheoryBothyllic

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.