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Scale 2031: "Gadyllian"

Scale 2031: Gadyllian, 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
Gadyllian

Analysis

Cardinality10 (decatonic)
Pitch Class Set{0,1,2,3,5,6,7,8,9,10}
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♯{1,5,8}352.77
D{2,6,9}452.41
D♯{3,7,10}352.86
F{5,9,0}452.68
F♯{6,10,1}452.5
G♯{8,0,3}352.95
A♯{10,2,5}352.59
Minor Triadscm{0,3,7}352.95
dm{2,5,9}452.5
d♯m{3,6,10}452.68
fm{5,8,0}352.86
f♯m{6,9,1}452.41
gm{7,10,2}352.77
a♯m{10,1,5}352.59
Augmented TriadsC♯+{1,5,9}552.41
D+{2,6,10}552.41
Diminished Triads{0,3,6}253.05
{2,5,8}253.05
d♯°{3,6,9}252.86
f♯°{6,9,0}252.86
{7,10,1}253.05
{9,0,3}253.05
Parsimonious Voice Leading Between Common Triads of Scale 2031. Created by Ian Ring ©2019 cm cm c°->cm d#m d#m c°->d#m D# D# cm->D# G# G# cm->G# C# C# C#+ C#+ C#->C#+ C#->d° fm fm C#->fm dm dm C#+->dm F F C#+->F f#m f#m C#+->f#m a#m a#m C#+->a#m d°->dm D D dm->D A# A# dm->A# D+ D+ D->D+ d#° d#° D->d#° D->f#m D+->d#m F# F# D+->F# gm gm D+->gm D+->A# d#°->d#m d#m->D# D#->gm fm->F fm->G# f#° f#° F->f#° F->a° f#°->f#m f#m->F# F#->g° F#->a#m g°->gm G#->a° a#m->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.

Diameter5
Radius5
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 2031 can be rotated to make 9 other scales. The 1st mode is itself.

2nd mode:
Scale 3063
Scale 3063: Solyllian, Ian Ring Music TheorySolyllian
3rd mode:
Scale 3579
Scale 3579: Zyphyllian, Ian Ring Music TheoryZyphyllian
4th mode:
Scale 3837
Scale 3837: Minor Pentatonic With Leading Tones, Ian Ring Music TheoryMinor Pentatonic With Leading Tones
5th mode:
Scale 1983
Scale 1983: Soryllian, Ian Ring Music TheorySoryllianThis is the prime mode
6th mode:
Scale 3039
Scale 3039: Godyllian, Ian Ring Music TheoryGodyllian
7th mode:
Scale 3567
Scale 3567: Epityllian, Ian Ring Music TheoryEpityllian
8th mode:
Scale 3831
Scale 3831: Ionyllian, Ian Ring Music TheoryIonyllian
9th mode:
Scale 3963
Scale 3963: Aeoryllian, Ian Ring Music TheoryAeoryllian
10th mode:
Scale 4029
Scale 4029: Major/Minor Mixed, Ian Ring Music TheoryMajor/Minor Mixed

Prime

The prime form of this scale is Scale 1983

Scale 1983Scale 1983: Soryllian, Ian Ring Music TheorySoryllian

Complement

The decatonic modal family [2031, 3063, 3579, 3837, 1983, 3039, 3567, 3831, 3963, 4029] (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 2031 is 3837

Scale 3837Scale 3837: Minor Pentatonic With Leading Tones, Ian Ring Music TheoryMinor Pentatonic With Leading Tones

Transformations:

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

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 2029Scale 2029: Kiourdi, Ian Ring Music TheoryKiourdi
Scale 2027Scale 2027: Boptygic, Ian Ring Music TheoryBoptygic
Scale 2023Scale 2023: Zodygic, Ian Ring Music TheoryZodygic
Scale 2039Scale 2039: Danyllian, Ian Ring Music TheoryDanyllian
Scale 2047Scale 2047: Monatic, Ian Ring Music TheoryMonatic
Scale 1999Scale 1999: Zacrygic, Ian Ring Music TheoryZacrygic
Scale 2015Scale 2015: Messiaen Mode 7, Ian Ring Music TheoryMessiaen Mode 7
Scale 1967Scale 1967: Diatonic Dorian Mixed, Ian Ring Music TheoryDiatonic Dorian Mixed
Scale 1903Scale 1903: Rocrygic, Ian Ring Music TheoryRocrygic
Scale 1775Scale 1775: Lyrygic, Ian Ring Music TheoryLyrygic
Scale 1519Scale 1519: Locrian/Aeolian Mixed, Ian Ring Music TheoryLocrian/Aeolian Mixed
Scale 1007Scale 1007: Epitygic, Ian Ring Music TheoryEpitygic
Scale 3055Scale 3055: Messiaen Mode 7, Ian Ring Music TheoryMessiaen Mode 7
Scale 4079Scale 4079: Ionatic, Ian Ring Music TheoryIonatic

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.