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Scale 4089: "Katoryllian"

Scale 4089: Katoryllian, Ian Ring Music Theory

Common Names

Zeitler
Katoryllian

Analysis

Cardinality10 (decatonic)
Pitch Class Set{0,3,4,5,6,7,8,9,10,11}
Forte Number10-1
Rotational Symmetrynone
Reflection Axes1.5
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
Myhill Propertyyes
Balancedno
Ridge Tones[3]
Coherenceno
Heliotonicno

Modes

Modes are the rotational transformation of this scale. Scale 4089 can be rotated to make 9 other scales. The 1st mode is itself.

2nd mode:
Scale 1023
Scale 1023: Dodyllian, Ian Ring Music TheoryDodyllianThis is the prime mode
3rd mode:
Scale 2559
Scale 2559: Zogyllian, Ian Ring Music TheoryZogyllian
4th mode:
Scale 3327
Scale 3327: Madyllian, Ian Ring Music TheoryMadyllian
5th mode:
Scale 3711
Scale 3711: Dycryllian, Ian Ring Music TheoryDycryllian
6th mode:
Scale 3903
Scale 3903: Aeogyllian, Ian Ring Music TheoryAeogyllian
7th mode:
Scale 3999
Scale 3999: Dydyllian, Ian Ring Music TheoryDydyllian
8th mode:
Scale 4047
Scale 4047: Thogyllian, Ian Ring Music TheoryThogyllian
9th mode:
Scale 4071
Scale 4071: Rygyllian, Ian Ring Music TheoryRygyllian
10th mode:
Scale 4083
Scale 4083: Bathyllian, Ian Ring Music TheoryBathyllian

Prime

The prime form of this scale is Scale 1023

Scale 1023Scale 1023: Dodyllian, Ian Ring Music TheoryDodyllian

Complement

The decatonic modal family [4089, 1023, 2559, 3327, 3711, 3903, 3999, 4047, 4071, 4083] (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 4089 is 1023

Scale 1023Scale 1023: Dodyllian, Ian Ring Music TheoryDodyllian

Transformations:

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

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 4091Scale 4091: Thydatic, Ian Ring Music TheoryThydatic
Scale 4093Scale 4093: Aerycratic, Ian Ring Music TheoryAerycratic
Scale 4081Scale 4081: Manygic, Ian Ring Music TheoryManygic
Scale 4085Scale 4085: Sydyllian, Ian Ring Music TheorySydyllian
Scale 4073Scale 4073: Sathygic, Ian Ring Music TheorySathygic
Scale 4057Scale 4057: Phrygic, Ian Ring Music TheoryPhrygic
Scale 4025Scale 4025: Kalygic, Ian Ring Music TheoryKalygic
Scale 3961Scale 3961: Zathygic, Ian Ring Music TheoryZathygic
Scale 3833Scale 3833: Dycrygic, Ian Ring Music TheoryDycrygic
Scale 3577Scale 3577: Loptygic, Ian Ring Music TheoryLoptygic
Scale 3065Scale 3065: Zothygic, Ian Ring Music TheoryZothygic
Scale 2041Scale 2041: Aeolacrygic, Ian Ring Music TheoryAeolacrygic

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