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Scale 3537: "Katogian"

Scale 3537: Katogian, 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

41161837294116105072918310504116183
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
Katogian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,4,6,7,8,10,11}
Forte Number7-13
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 375
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections4
Modes6
Prime?no
prime: 375
Deep Scaleno
Interval Vector443532
Interval Spectrump3m5n3s4d4t2
Distribution Spectra<1> = {1,2,4}
<2> = {2,3,5,6}
<3> = {4,6,7}
<4> = {5,6,8}
<5> = {6,7,9,10}
<6> = {8,10,11}
Spectra Variation2.857
Maximally Evenno
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicyes

Harmonic Chords

Modes

Modes are the rotational transformation of this scale. Scale 3537 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 477
Scale 477: Stacrian, Ian Ring Music TheoryStacrian
3rd mode:
Scale 1143
Scale 1143: Styrian, Ian Ring Music TheoryStyrian
4th mode:
Scale 2619
Scale 2619: Ionyrian, Ian Ring Music TheoryIonyrian
5th mode:
Scale 3357
Scale 3357: Phrodian, Ian Ring Music TheoryPhrodian
6th mode:
Scale 1863
Scale 1863: Pycrian, Ian Ring Music TheoryPycrian
7th mode:
Scale 2979
Scale 2979: Gyptian, Ian Ring Music TheoryGyptian

Prime

The prime form of this scale is Scale 375

Scale 375Scale 375: Sodian, Ian Ring Music TheorySodian

Complement

The heptatonic modal family [3537, 477, 1143, 2619, 3357, 1863, 2979] (Forte: 7-13) is the complement of the pentatonic modal family [279, 369, 1809, 2187, 3141] (Forte: 5-13)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3537 is 375

Scale 375Scale 375: Sodian, Ian Ring Music TheorySodian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3537 is chiral, and its enantiomorph is scale 375

Scale 375Scale 375: Sodian, Ian Ring Music TheorySodian

Transformations:

T0 3537  T0I 375
T1 2979  T1I 750
T2 1863  T2I 1500
T3 3726  T3I 3000
T4 3357  T4I 1905
T5 2619  T5I 3810
T6 1143  T6I 3525
T7 2286  T7I 2955
T8 477  T8I 1815
T9 954  T9I 3630
T10 1908  T10I 3165
T11 3816  T11I 2235

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 3539Scale 3539: Aeoryllic, Ian Ring Music TheoryAeoryllic
Scale 3541Scale 3541: Racryllic, Ian Ring Music TheoryRacryllic
Scale 3545Scale 3545: Thyptyllic, Ian Ring Music TheoryThyptyllic
Scale 3521Scale 3521, Ian Ring Music Theory
Scale 3529Scale 3529: Stalian, Ian Ring Music TheoryStalian
Scale 3553Scale 3553, Ian Ring Music Theory
Scale 3569Scale 3569: Aeoladyllic, Ian Ring Music TheoryAeoladyllic
Scale 3473Scale 3473: Lathimic, Ian Ring Music TheoryLathimic
Scale 3505Scale 3505: Stygian, Ian Ring Music TheoryStygian
Scale 3409Scale 3409: Katanimic, Ian Ring Music TheoryKatanimic
Scale 3281Scale 3281: Raga Vijayavasanta, Ian Ring Music TheoryRaga Vijayavasanta
Scale 3793Scale 3793: Aeopian, Ian Ring Music TheoryAeopian
Scale 4049Scale 4049: Stycryllic, Ian Ring Music TheoryStycryllic
Scale 2513Scale 2513: Aerycrimic, Ian Ring Music TheoryAerycrimic
Scale 3025Scale 3025: Epycrian, Ian Ring Music TheoryEpycrian
Scale 1489Scale 1489: Raga Jyoti, Ian Ring Music TheoryRaga Jyoti

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. Some scale names used on this and other pages are ©2005 William Zeitler (http://allthescales.org). Peruse this Bibliography.