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Scale 3999: "Dydyllian"

Scale 3999: Dydyllian, 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
Dydyllian

Analysis

Cardinality10 (decatonic)
Pitch Class Set{0,1,2,3,4,7,8,9,10,11}
Forte Number10-1
Rotational Symmetrynone
Reflection Axes5.5
Palindromicno
Chiralityno
Hemitonia9 (multihemitonic)
Cohemitonia8 (multicohemitonic)
Imperfections2
Modes9
Prime?no
prime: 1023
Deep Scaleno
Interval Vector988884
Interval Spectrump8m8n8s8d9t4
Distribution Spectra<1> = {1,3}
<2> = {2,4}
<3> = {3,5}
<4> = {4,6}
<5> = {5,7}
<6> = {6,8}
<7> = {7,9}
<8> = {8,10}
<9> = {9,11}
Spectra Variation1.8
Maximally Evenno
Maximal Area Setno
Interior Area2.75
Myhill Propertyyes
Balancedno
Ridge Tones[11]
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}452.4
D♯{3,7,10}352.7
E{4,8,11}352.4
G{7,11,2}352.7
G♯{8,0,3}452.4
A{9,1,4}352.9
Minor Triadscm{0,3,7}352.4
c♯m{1,4,8}352.7
em{4,7,11}452.4
gm{7,10,2}352.9
g♯m{8,11,3}452.4
am{9,0,4}352.7
Augmented TriadsC+{0,4,8}552.3
D♯+{3,7,11}552.3
Diminished Triadsc♯°{1,4,7}252.9
{4,7,10}252.9
{7,10,1}253.1
g♯°{8,11,2}252.9
{9,0,3}252.9
a♯°{10,1,4}253.1
Parsimonious Voice Leading Between Common Triads of Scale 3999. 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 C+->G# am am C+->am c#°->c#m A A c#m->A D# D# D#->D#+ D#->e° gm gm D#->gm D#+->em Parsimonious Voice Leading Between Common Triads of Scale 3999. Created by Ian Ring ©2019 G D#+->G g#m g#m D#+->g#m e°->em em->E E->g#m g°->gm a#° a#° g°->a#° gm->G g#° g#° G->g#° g#°->g#m g#m->G# G#->a° a°->am am->A A->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.

Diameter5
Radius5
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 3999 can be rotated to make 9 other scales. The 1st mode is itself.

2nd mode:
Scale 4047
Scale 4047: Thogyllian, Ian Ring Music TheoryThogyllian
3rd mode:
Scale 4071
Scale 4071: Rygyllian, Ian Ring Music TheoryRygyllian
4th mode:
Scale 4083
Scale 4083: Bathyllian, Ian Ring Music TheoryBathyllian
5th mode:
Scale 4089
Scale 4089: Katoryllian, Ian Ring Music TheoryKatoryllian
6th mode:
Scale 1023
Scale 1023: Dodyllian, Ian Ring Music TheoryDodyllianThis is the prime mode
7th mode:
Scale 2559
Scale 2559: Zogyllian, Ian Ring Music TheoryZogyllian
8th mode:
Scale 3327
Scale 3327: Madyllian, Ian Ring Music TheoryMadyllian
9th mode:
Scale 3711
Scale 3711: Dycryllian, Ian Ring Music TheoryDycryllian
10th mode:
Scale 3903
Scale 3903: Aeogyllian, Ian Ring Music TheoryAeogyllian

Prime

The prime form of this scale is Scale 1023

Scale 1023Scale 1023: Dodyllian, Ian Ring Music TheoryDodyllian

Complement

The decatonic modal family [3999, 4047, 4071, 4083, 4089, 1023, 2559, 3327, 3711, 3903] (Forte: 10-1) is the complement of the modal family [3, 2049] (Forte: 2-1)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3999 is 3903

Scale 3903Scale 3903: Aeogyllian, Ian Ring Music TheoryAeogyllian

Transformations:

T0 3999  T0I 3903
T1 3903  T1I 3711
T2 3711  T2I 3327
T3 3327  T3I 2559
T4 2559  T4I 1023
T5 1023  T5I 2046
T6 2046  T6I 4092
T7 4092  T7I 4089
T8 4089  T8I 4083
T9 4083  T9I 4071
T10 4071  T10I 4047
T11 4047  T11I 3999

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 3997Scale 3997: Dogygic, Ian Ring Music TheoryDogygic
Scale 3995Scale 3995: Ionygic, Ian Ring Music TheoryIonygic
Scale 3991Scale 3991: Badygic, Ian Ring Music TheoryBadygic
Scale 3983Scale 3983: Thyptygic, Ian Ring Music TheoryThyptygic
Scale 4015Scale 4015: Phradyllian, Ian Ring Music TheoryPhradyllian
Scale 4031Scale 4031: Godatic, Ian Ring Music TheoryGodatic
Scale 4063Scale 4063: Eptatic, Ian Ring Music TheoryEptatic
Scale 3871Scale 3871: Aerynygic, Ian Ring Music TheoryAerynygic
Scale 3935Scale 3935: Kataphyllian, Ian Ring Music TheoryKataphyllian
Scale 3743Scale 3743: Thadygic, Ian Ring Music TheoryThadygic
Scale 3487Scale 3487: Byptygic, Ian Ring Music TheoryByptygic
Scale 2975Scale 2975: Aeroptygic, Ian Ring Music TheoryAeroptygic
Scale 1951Scale 1951: Marygic, Ian Ring Music TheoryMarygic

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.