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Scale 4075: "Katyllian"

Scale 4075: Katyllian, Ian Ring Music Theory

Common Names

Zeitler
Katyllian

Analysis

Cardinality10 (decatonic)
Pitch Class Set{0,1,3,5,6,7,8,9,10,11}
Forte Number10-2
Rotational Symmetrynone
Reflection Axes3
Palindromicno
Chiralityno
Hemitonia8 (multihemitonic)
Cohemitonia7 (multicohemitonic)
Imperfections2
Modes9
Prime?no
prime: 1535
Deep Scaleno
Interval Vector898884
Interval Spectrump8m8n8s9d8t4
Distribution Spectra<1> = {1,2}
<2> = {2,3,4}
<3> = {3,4,5}
<4> = {4,5,6}
<5> = {5,6,7}
<6> = {6,7,8}
<7> = {7,8,9}
<8> = {8,9,10}
<9> = {10,11}
Spectra Variation1.6
Maximally Evenno
Myhill Propertyno
Balancedno
Ridge Tones[6]
Coherenceno
Heliotonicno

Modes

Modes are the rotational transformation of this scale. Scale 4075 can be rotated to make 9 other scales. The 1st mode is itself.

2nd mode:
Scale 4085
Scale 4085: Sydyllian, Ian Ring Music TheorySydyllian
3rd mode:
Scale 2045
Scale 2045: Katogyllian, Ian Ring Music TheoryKatogyllian
4th mode:
Scale 1535
Scale 1535: Mixodyllian, Ian Ring Music TheoryMixodyllianThis is the prime mode
5th mode:
Scale 2815
Scale 2815: Aeradyllian, Ian Ring Music TheoryAeradyllian
6th mode:
Scale 3455
Scale 3455: Ryptyllian, Ian Ring Music TheoryRyptyllian
7th mode:
Scale 3775
Scale 3775: Loptyllian, Ian Ring Music TheoryLoptyllian
8th mode:
Scale 3935
Scale 3935: Kataphyllian, Ian Ring Music TheoryKataphyllian
9th mode:
Scale 4015
Scale 4015: Phradyllian, Ian Ring Music TheoryPhradyllian
10th mode:
Scale 4055
Scale 4055: Dagyllian, Ian Ring Music TheoryDagyllian

Prime

The prime form of this scale is Scale 1535

Scale 1535Scale 1535: Mixodyllian, Ian Ring Music TheoryMixodyllian

Complement

The decatonic modal family [4075, 4085, 2045, 1535, 2815, 3455, 3775, 3935, 4015, 4055] (Forte: 10-2) is the complement of the modal family [5, 1025] (Forte: 2-2)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 4075 is 2815

Scale 2815Scale 2815: Aeradyllian, Ian Ring Music TheoryAeradyllian

Transformations:

T0 4075  T0I 2815
T1 4055  T1I 1535
T2 4015  T2I 3070
T3 3935  T3I 2045
T4 3775  T4I 4090
T5 3455  T5I 4085
T6 2815  T6I 4075
T7 1535  T7I 4055
T8 3070  T8I 4015
T9 2045  T9I 3935
T10 4090  T10I 3775
T11 4085  T11I 3455

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 4073Scale 4073: Sathygic, Ian Ring Music TheorySathygic
Scale 4077Scale 4077: Gothyllian, Ian Ring Music TheoryGothyllian
Scale 4079Scale 4079: Ionatic, Ian Ring Music TheoryIonatic
Scale 4067Scale 4067: Aeolarygic, Ian Ring Music TheoryAeolarygic
Scale 4071Scale 4071: Rygyllian, Ian Ring Music TheoryRygyllian
Scale 4083Scale 4083: Bathyllian, Ian Ring Music TheoryBathyllian
Scale 4091Scale 4091: Thydatic, Ian Ring Music TheoryThydatic
Scale 4043Scale 4043: Phrocrygic, Ian Ring Music TheoryPhrocrygic
Scale 4059Scale 4059: Zolyllian, Ian Ring Music TheoryZolyllian
Scale 4011Scale 4011: Styrygic, Ian Ring Music TheoryStyrygic
Scale 3947Scale 3947: Ryptygic, Ian Ring Music TheoryRyptygic
Scale 3819Scale 3819: Aeolanygic, Ian Ring Music TheoryAeolanygic
Scale 3563Scale 3563: Ionoptygic, Ian Ring Music TheoryIonoptygic
Scale 3051Scale 3051: Stalygic, Ian Ring Music TheoryStalygic
Scale 2027Scale 2027: Boptygic, Ian Ring Music TheoryBoptygic

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