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Scale 1813: "Katothimic"

Scale 1813: Katothimic, 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
Katothimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,2,4,8,9,10}
Forte Number6-22
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1309
Hemitonia2 (dihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections4
Modes5
Prime?no
prime: 343
Deep Scaleno
Interval Vector241422
Interval Spectrump2m4ns4d2t2
Distribution Spectra<1> = {1,2,4}
<2> = {2,3,4,5,6}
<3> = {4,5,6,7,8}
<4> = {6,7,8,9,10}
<5> = {8,10,11}
Spectra Variation3
Maximally Evenno
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicno

Modes

Modes are the rotational transformation of this scale. Scale 1813 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 1477
Scale 1477: Raga Jaganmohanam, Ian Ring Music TheoryRaga Jaganmohanam
3rd mode:
Scale 1393
Scale 1393: Mycrimic, Ian Ring Music TheoryMycrimic
4th mode:
Scale 343
Scale 343: Ionorimic, Ian Ring Music TheoryIonorimicThis is the prime mode
5th mode:
Scale 2219
Scale 2219: Phrydimic, Ian Ring Music TheoryPhrydimic
6th mode:
Scale 3157
Scale 3157: Zyptimic, Ian Ring Music TheoryZyptimic

Prime

The prime form of this scale is Scale 343

Scale 343Scale 343: Ionorimic, Ian Ring Music TheoryIonorimic

Complement

The hexatonic modal family [1813, 1477, 1393, 343, 2219, 3157] (Forte: 6-22) is the complement of the hexatonic modal family [343, 1393, 1477, 1813, 2219, 3157] (Forte: 6-22)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1813 is 1309

Scale 1309Scale 1309: Pogimic, Ian Ring Music TheoryPogimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1813 is chiral, and its enantiomorph is scale 1309

Scale 1309Scale 1309: Pogimic, Ian Ring Music TheoryPogimic

Transformations:

T0 1813  T0I 1309
T1 3626  T1I 2618
T2 3157  T2I 1141
T3 2219  T3I 2282
T4 343  T4I 469
T5 686  T5I 938
T6 1372  T6I 1876
T7 2744  T7I 3752
T8 1393  T8I 3409
T9 2786  T9I 2723
T10 1477  T10I 1351
T11 2954  T11I 2702

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 1815Scale 1815: Godian, Ian Ring Music TheoryGodian
Scale 1809Scale 1809: Ranitonic, Ian Ring Music TheoryRanitonic
Scale 1811Scale 1811: Kyptimic, Ian Ring Music TheoryKyptimic
Scale 1817Scale 1817: Phrythimic, Ian Ring Music TheoryPhrythimic
Scale 1821Scale 1821: Aeradian, Ian Ring Music TheoryAeradian
Scale 1797Scale 1797, Ian Ring Music Theory
Scale 1805Scale 1805, Ian Ring Music Theory
Scale 1829Scale 1829: Pathimic, Ian Ring Music TheoryPathimic
Scale 1845Scale 1845: Lagian, Ian Ring Music TheoryLagian
Scale 1877Scale 1877: Aeroptian, Ian Ring Music TheoryAeroptian
Scale 1941Scale 1941: Aeranian, Ian Ring Music TheoryAeranian
Scale 1557Scale 1557, Ian Ring Music Theory
Scale 1685Scale 1685: Zeracrimic, Ian Ring Music TheoryZeracrimic
Scale 1301Scale 1301: Koditonic, Ian Ring Music TheoryKoditonic
Scale 789Scale 789: Zogitonic, Ian Ring Music TheoryZogitonic
Scale 2837Scale 2837: Aelothimic, Ian Ring Music TheoryAelothimic
Scale 3861Scale 3861: Phroptian, Ian Ring Music TheoryPhroptian

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.