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Scale 3939: "Dogyllic"

Scale 3939: Dogyllic, 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
Dogyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,5,6,8,9,10,11}
Forte Number8-4
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2271
Hemitonia6 (multihemitonic)
Cohemitonia4 (multicohemitonic)
Imperfections3
Modes7
Prime?no
prime: 447
Deep Scaleno
Interval Vector655552
Interval Spectrump5m5n5s5d6t2
Distribution Spectra<1> = {1,2,4}
<2> = {2,3,5}
<3> = {3,4,6,7}
<4> = {4,5,7,8}
<5> = {5,6,8,9}
<6> = {7,9,10}
<7> = {8,10,11}
Spectra Variation3
Maximally Evenno
Maximal Area Setno
Interior Area2.366
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 TriadsC♯{1,5,8}231.78
F{5,9,0}331.56
F♯{6,10,1}252.33
Minor Triadsfm{5,8,0}341.89
f♯m{6,9,1}341.78
a♯m{10,1,5}242
Augmented TriadsC♯+{1,5,9}431.44
Diminished Triads{5,8,11}152.67
f♯°{6,9,0}231.89
Parsimonious Voice Leading Between Common Triads of Scale 3939. Created by Ian Ring ©2019 C# C# C#+ C#+ C#->C#+ fm fm C#->fm F F C#+->F f#m f#m C#+->f#m a#m a#m C#+->a#m f°->fm fm->F f#° f#° F->f#° f#°->f#m F# F# f#m->F# F#->a#m

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♯, C♯+, F, f♯°
Peripheral Verticesf°, F♯

Modes

Modes are the rotational transformation of this scale. Scale 3939 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 4017
Scale 4017: Dolyllic, Ian Ring Music TheoryDolyllic
3rd mode:
Scale 507
Scale 507: Moryllic, Ian Ring Music TheoryMoryllic
4th mode:
Scale 2301
Scale 2301: Bydyllic, Ian Ring Music TheoryBydyllic
5th mode:
Scale 1599
Scale 1599: Pocryllic, Ian Ring Music TheoryPocryllic
6th mode:
Scale 2847
Scale 2847: Phracryllic, Ian Ring Music TheoryPhracryllic
7th mode:
Scale 3471
Scale 3471: Gyryllic, Ian Ring Music TheoryGyryllic
8th mode:
Scale 3783
Scale 3783: Phrygyllic, Ian Ring Music TheoryPhrygyllic

Prime

The prime form of this scale is Scale 447

Scale 447Scale 447: Thyphyllic, Ian Ring Music TheoryThyphyllic

Complement

The octatonic modal family [3939, 4017, 507, 2301, 1599, 2847, 3471, 3783] (Forte: 8-4) is the complement of the tetratonic modal family [39, 897, 2067, 3081] (Forte: 4-4)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3939 is 2271

Scale 2271Scale 2271: Poptyllic, Ian Ring Music TheoryPoptyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3939 is chiral, and its enantiomorph is scale 2271

Scale 2271Scale 2271: Poptyllic, Ian Ring Music TheoryPoptyllic

Transformations:

T0 3939  T0I 2271
T1 3783  T1I 447
T2 3471  T2I 894
T3 2847  T3I 1788
T4 1599  T4I 3576
T5 3198  T5I 3057
T6 2301  T6I 2019
T7 507  T7I 4038
T8 1014  T8I 3981
T9 2028  T9I 3867
T10 4056  T10I 3639
T11 4017  T11I 3183

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 3937Scale 3937, Ian Ring Music Theory
Scale 3941Scale 3941: Stathyllic, Ian Ring Music TheoryStathyllic
Scale 3943Scale 3943: Zynygic, Ian Ring Music TheoryZynygic
Scale 3947Scale 3947: Ryptygic, Ian Ring Music TheoryRyptygic
Scale 3955Scale 3955: Pothygic, Ian Ring Music TheoryPothygic
Scale 3907Scale 3907, Ian Ring Music Theory
Scale 3923Scale 3923: Stoptyllic, Ian Ring Music TheoryStoptyllic
Scale 3875Scale 3875: Aeryptian, Ian Ring Music TheoryAeryptian
Scale 4003Scale 4003: Sadyllic, Ian Ring Music TheorySadyllic
Scale 4067Scale 4067: Aeolarygic, Ian Ring Music TheoryAeolarygic
Scale 3683Scale 3683: Dycrian, Ian Ring Music TheoryDycrian
Scale 3811Scale 3811: Epogyllic, Ian Ring Music TheoryEpogyllic
Scale 3427Scale 3427: Zacrian, Ian Ring Music TheoryZacrian
Scale 2915Scale 2915: Aeolydian, Ian Ring Music TheoryAeolydian
Scale 1891Scale 1891: Thalian, Ian Ring Music TheoryThalian

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.