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Scale 2031: "Gadyllian"

Scale 2031: Gadyllian, Ian Ring Music Theory

Common Names



Cardinality10 (decatonic)
Pitch Class Set{0,1,2,3,5,6,7,8,9,10}
Forte Number10-5
Rotational Symmetrynone
Reflection Axes1.5
Hemitonia8 (multihemitonic)
Cohemitonia6 (multicohemitonic)
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
Myhill Propertyno
Ridge Tones[3]


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


The prime form of this scale is Scale 1983

Scale 1983Scale 1983: Soryllian, Ian Ring Music TheorySoryllian


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)


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


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, and MIDI playback by MIDI.js. Bibliography