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Scale 3039: "Godyllian"

Scale 3039: Godyllian, 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
Godyllian

Analysis

Cardinality10 (decatonic)
Pitch Class Set{0,1,2,3,4,6,7,8,9,11}
Forte Number10-5
Rotational Symmetrynone
Reflection Axes1.5
Palindromicno
Chiralityno
Hemitonia8 (multihemitonic)
Cohemitonia6 (multicohemitonic)
Imperfections1
Modes9
Prime?no
prime: 1983
Deep Scaleno
Interval Vector888894
Interval Spectrump9m8n8s8d8t4
Distribution Spectra<1> = {1,2}
<2> = {2,3}
<3> = {3,4}
<4> = {4,5}
<5> = {5,6,7}
<6> = {7,8}
<7> = {8,9}
<8> = {9,10}
<9> = {10,11}
Spectra Variation1
Maximally Evenno
Maximal Area Setyes
Interior Area2.866
Myhill Propertyno
Balancedno
Ridge Tones[3]
ProprietyProper
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}452.5
D{2,6,9}352.95
E{4,8,11}352.59
G{7,11,2}352.77
G♯{8,0,3}452.41
A{9,1,4}352.86
B{11,3,6}452.68
Minor Triadscm{0,3,7}452.41
c♯m{1,4,8}352.77
em{4,7,11}352.59
f♯m{6,9,1}352.95
g♯m{8,11,3}452.5
am{9,0,4}452.68
bm{11,2,6}352.86
Augmented TriadsC+{0,4,8}552.41
D♯+{3,7,11}552.41
Diminished Triads{0,3,6}252.86
c♯°{1,4,7}253.05
d♯°{3,6,9}253.05
f♯°{6,9,0}253.05
g♯°{8,11,2}253.05
{9,0,3}252.86
Parsimonious Voice Leading Between Common Triads of Scale 3039. Created by Ian Ring ©2019 cm cm c°->cm B B c°->B 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->d#° f#m f#m D->f#m bm bm D->bm d#°->B D#+->em Parsimonious Voice Leading Between Common Triads of Scale 3039. Created by Ian Ring ©2019 G D#+->G g#m g#m D#+->g#m D#+->B em->E E->g#m f#° f#° f#°->f#m f#°->am f#m->A g#° g#° G->g#° G->bm g#°->g#m g#m->G# G#->a° a°->am am->A 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
Radius5
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 3039 can be rotated to make 9 other scales. The 1st mode is itself.

2nd mode:
Scale 3567
Scale 3567: Epityllian, Ian Ring Music TheoryEpityllian
3rd mode:
Scale 3831
Scale 3831: Ionyllian, Ian Ring Music TheoryIonyllian
4th mode:
Scale 3963
Scale 3963: Aeoryllian, Ian Ring Music TheoryAeoryllian
5th mode:
Scale 4029
Scale 4029: Major/Minor Mixed, Ian Ring Music TheoryMajor/Minor Mixed
6th mode:
Scale 2031
Scale 2031: Gadyllian, Ian Ring Music TheoryGadyllian
7th mode:
Scale 3063
Scale 3063: Solyllian, Ian Ring Music TheorySolyllian
8th mode:
Scale 3579
Scale 3579: Zyphyllian, Ian Ring Music TheoryZyphyllian
9th mode:
Scale 3837
Scale 3837: Minor Pentatonic With Leading Tones, Ian Ring Music TheoryMinor Pentatonic With Leading Tones
10th mode:
Scale 1983
Scale 1983: Soryllian, Ian Ring Music TheorySoryllianThis is the prime mode

Prime

The prime form of this scale is Scale 1983

Scale 1983Scale 1983: Soryllian, Ian Ring Music TheorySoryllian

Complement

The decatonic modal family [3039, 3567, 3831, 3963, 4029, 2031, 3063, 3579, 3837, 1983] (Forte: 10-5) is the complement of the modal family [33, 129] (Forte: 2-5)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3039 is 3963

Scale 3963Scale 3963: Aeoryllian, Ian Ring Music TheoryAeoryllian

Transformations:

T0 3039  T0I 3963
T1 1983  T1I 3831
T2 3966  T2I 3567
T3 3837  T3I 3039
T4 3579  T4I 1983
T5 3063  T5I 3966
T6 2031  T6I 3837
T7 4062  T7I 3579
T8 4029  T8I 3063
T9 3963  T9I 2031
T10 3831  T10I 4062
T11 3567  T11I 4029

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 3037Scale 3037: Nine Tone Scale, Ian Ring Music TheoryNine Tone Scale
Scale 3035Scale 3035: Gocrygic, Ian Ring Music TheoryGocrygic
Scale 3031Scale 3031: Epithygic, Ian Ring Music TheoryEpithygic
Scale 3023Scale 3023: Mothygic, Ian Ring Music TheoryMothygic
Scale 3055Scale 3055: Messiaen Mode 7, Ian Ring Music TheoryMessiaen Mode 7
Scale 3071Scale 3071: Solatic, Ian Ring Music TheorySolatic
Scale 2975Scale 2975: Aeroptygic, Ian Ring Music TheoryAeroptygic
Scale 3007Scale 3007: Zyryllian, Ian Ring Music TheoryZyryllian
Scale 2911Scale 2911: Katygic, Ian Ring Music TheoryKatygic
Scale 2783Scale 2783: Gothygic, Ian Ring Music TheoryGothygic
Scale 2527Scale 2527: Phradygic, Ian Ring Music TheoryPhradygic
Scale 3551Scale 3551: Sagyllian, Ian Ring Music TheorySagyllian
Scale 4063Scale 4063: Eptatic, Ian Ring Music TheoryEptatic
Scale 991Scale 991: Aeolygic, Ian Ring Music TheoryAeolygic
Scale 2015Scale 2015: Messiaen Mode 7, Ian Ring Music TheoryMessiaen Mode 7

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. Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography.