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Scale 3689: "Katocrian"

Scale 3689: Katocrian, 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
Katocrian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,3,5,6,9,10,11}
Forte Number7-19
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 719
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections3
Modes6
Prime?no
prime: 719
Deep Scaleno
Interval Vector434343
Interval Spectrump4m3n4s3d4t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {3,5,6}
<4> = {6,7,9}
<5> = {7,8,9,10}
<6> = {9,10,11}
Spectra Variation2.286
Maximally Evenno
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicyes

Harmonic Chords

Modes

Modes are the rotational transformation of this scale. Scale 3689 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 973
Scale 973: Mela Syamalangi, Ian Ring Music TheoryMela Syamalangi
3rd mode:
Scale 1267
Scale 1267: Katynian, Ian Ring Music TheoryKatynian
4th mode:
Scale 2681
Scale 2681: Aerycrian, Ian Ring Music TheoryAerycrian
5th mode:
Scale 847
Scale 847: Ganian, Ian Ring Music TheoryGanian
6th mode:
Scale 2471
Scale 2471: Mela Ganamurti, Ian Ring Music TheoryMela Ganamurti
7th mode:
Scale 3283
Scale 3283: Mela Visvambhari, Ian Ring Music TheoryMela Visvambhari

Prime

The prime form of this scale is Scale 719

Scale 719Scale 719: Kanian, Ian Ring Music TheoryKanian

Complement

The heptatonic modal family [3689, 973, 1267, 2681, 847, 2471, 3283] (Forte: 7-19) is the complement of the pentatonic modal family [203, 707, 1561, 2149, 2401] (Forte: 5-19)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3689 is 719

Scale 719Scale 719: Kanian, Ian Ring Music TheoryKanian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3689 is chiral, and its enantiomorph is scale 719

Scale 719Scale 719: Kanian, Ian Ring Music TheoryKanian

Transformations:

T0 3689  T0I 719
T1 3283  T1I 1438
T2 2471  T2I 2876
T3 847  T3I 1657
T4 1694  T4I 3314
T5 3388  T5I 2533
T6 2681  T6I 971
T7 1267  T7I 1942
T8 2534  T8I 3884
T9 973  T9I 3673
T10 1946  T10I 3251
T11 3892  T11I 2407

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 3691Scale 3691: Badyllic, Ian Ring Music TheoryBadyllic
Scale 3693Scale 3693: Stadyllic, Ian Ring Music TheoryStadyllic
Scale 3681Scale 3681, Ian Ring Music Theory
Scale 3685Scale 3685: Kodian, Ian Ring Music TheoryKodian
Scale 3697Scale 3697: Ionarian, Ian Ring Music TheoryIonarian
Scale 3705Scale 3705: Messiaen Mode 4 Inverse, Ian Ring Music TheoryMessiaen Mode 4 Inverse
Scale 3657Scale 3657: Epynimic, Ian Ring Music TheoryEpynimic
Scale 3673Scale 3673: Ranian, Ian Ring Music TheoryRanian
Scale 3625Scale 3625: Podimic, Ian Ring Music TheoryPodimic
Scale 3753Scale 3753: Phraptian, Ian Ring Music TheoryPhraptian
Scale 3817Scale 3817: Zoryllic, Ian Ring Music TheoryZoryllic
Scale 3945Scale 3945: Lydyllic, Ian Ring Music TheoryLydyllic
Scale 3177Scale 3177: Rothimic, Ian Ring Music TheoryRothimic
Scale 3433Scale 3433: Thonian, Ian Ring Music TheoryThonian
Scale 2665Scale 2665: Aeradimic, Ian Ring Music TheoryAeradimic
Scale 1641Scale 1641: Bocrimic, Ian Ring Music TheoryBocrimic

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.