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Scale 3467: "Katonian"

Scale 3467: Katonian, 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
Katonian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,3,7,8,10,11}
Forte Number7-11
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2615
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections3
Modes6
Prime?no
prime: 379
Deep Scaleno
Interval Vector444441
Interval Spectrump4m4n4s4d4t
Distribution Spectra<1> = {1,2,4}
<2> = {2,3,5,6}
<3> = {3,4,7}
<4> = {5,8,9}
<5> = {6,7,9,10}
<6> = {8,10,11}
Spectra Variation3.143
Maximally Evenno
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicyes

Harmonic Chords

Modes

Modes are the rotational transformation of this scale. Scale 3467 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 3781
Scale 3781: Gyphian, Ian Ring Music TheoryGyphian
3rd mode:
Scale 1969
Scale 1969: Stylian, Ian Ring Music TheoryStylian
4th mode:
Scale 379
Scale 379: Aeragian, Ian Ring Music TheoryAeragianThis is the prime mode
5th mode:
Scale 2237
Scale 2237: Epothian, Ian Ring Music TheoryEpothian
6th mode:
Scale 1583
Scale 1583: Salian, Ian Ring Music TheorySalian
7th mode:
Scale 2839
Scale 2839: Lyptian, Ian Ring Music TheoryLyptian

Prime

The prime form of this scale is Scale 379

Scale 379Scale 379: Aeragian, Ian Ring Music TheoryAeragian

Complement

The heptatonic modal family [3467, 3781, 1969, 379, 2237, 1583, 2839] (Forte: 7-11) is the complement of the pentatonic modal family [157, 929, 1063, 2579, 3337] (Forte: 5-11)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3467 is 2615

Scale 2615Scale 2615: Thoptian, Ian Ring Music TheoryThoptian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3467 is chiral, and its enantiomorph is scale 2615

Scale 2615Scale 2615: Thoptian, Ian Ring Music TheoryThoptian

Transformations:

T0 3467  T0I 2615
T1 2839  T1I 1135
T2 1583  T2I 2270
T3 3166  T3I 445
T4 2237  T4I 890
T5 379  T5I 1780
T6 758  T6I 3560
T7 1516  T7I 3025
T8 3032  T8I 1955
T9 1969  T9I 3910
T10 3938  T10I 3725
T11 3781  T11I 3355

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 3465Scale 3465: Katathimic, Ian Ring Music TheoryKatathimic
Scale 3469Scale 3469: Monian, Ian Ring Music TheoryMonian
Scale 3471Scale 3471: Gyryllic, Ian Ring Music TheoryGyryllic
Scale 3459Scale 3459, Ian Ring Music Theory
Scale 3463Scale 3463, Ian Ring Music Theory
Scale 3475Scale 3475: Kylian, Ian Ring Music TheoryKylian
Scale 3483Scale 3483: Mixotharyllic, Ian Ring Music TheoryMixotharyllic
Scale 3499Scale 3499: Hamel, Ian Ring Music TheoryHamel
Scale 3531Scale 3531: Neveseri, Ian Ring Music TheoryNeveseri
Scale 3339Scale 3339, Ian Ring Music Theory
Scale 3403Scale 3403: Bylian, Ian Ring Music TheoryBylian
Scale 3211Scale 3211: Epacrimic, Ian Ring Music TheoryEpacrimic
Scale 3723Scale 3723: Myptian, Ian Ring Music TheoryMyptian
Scale 3979Scale 3979: Dynyllic, Ian Ring Music TheoryDynyllic
Scale 2443Scale 2443: Panimic, Ian Ring Music TheoryPanimic
Scale 2955Scale 2955: Thorian, Ian Ring Music TheoryThorian
Scale 1419Scale 1419: Raga Kashyapi, Ian Ring Music TheoryRaga Kashyapi

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.