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Scale 3409: "Katanimic"

Scale 3409: Katanimic, 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
Katanimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,4,6,8,10,11}
Forte Number6-22
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 343
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 3409 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 469
Scale 469: Katyrimic, Ian Ring Music TheoryKatyrimic
3rd mode:
Scale 1141
Scale 1141: Rynimic, Ian Ring Music TheoryRynimic
4th mode:
Scale 1309
Scale 1309: Pogimic, Ian Ring Music TheoryPogimic
5th mode:
Scale 1351
Scale 1351: Aeraptimic, Ian Ring Music TheoryAeraptimic
6th mode:
Scale 2723
Scale 2723: Raga Jivantika, Ian Ring Music TheoryRaga Jivantika

Prime

The prime form of this scale is Scale 343

Scale 343Scale 343: Ionorimic, Ian Ring Music TheoryIonorimic

Complement

The hexatonic modal family [3409, 469, 1141, 1309, 1351, 2723] (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 3409 is 343

Scale 343Scale 343: Ionorimic, Ian Ring Music TheoryIonorimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3409 is chiral, and its enantiomorph is scale 343

Scale 343Scale 343: Ionorimic, Ian Ring Music TheoryIonorimic

Transformations:

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

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 3411Scale 3411: Enigmatic, Ian Ring Music TheoryEnigmatic
Scale 3413Scale 3413: Leading Whole-tone, Ian Ring Music TheoryLeading Whole-tone
Scale 3417Scale 3417: Golian, Ian Ring Music TheoryGolian
Scale 3393Scale 3393, Ian Ring Music Theory
Scale 3401Scale 3401: Palimic, Ian Ring Music TheoryPalimic
Scale 3425Scale 3425, Ian Ring Music Theory
Scale 3441Scale 3441: Thacrian, Ian Ring Music TheoryThacrian
Scale 3345Scale 3345: Zylitonic, Ian Ring Music TheoryZylitonic
Scale 3377Scale 3377: Phralimic, Ian Ring Music TheoryPhralimic
Scale 3473Scale 3473: Lathimic, Ian Ring Music TheoryLathimic
Scale 3537Scale 3537: Katogian, Ian Ring Music TheoryKatogian
Scale 3153Scale 3153: Zathitonic, Ian Ring Music TheoryZathitonic
Scale 3281Scale 3281: Raga Vijayavasanta, Ian Ring Music TheoryRaga Vijayavasanta
Scale 3665Scale 3665: Stalimic, Ian Ring Music TheoryStalimic
Scale 3921Scale 3921: Pythian, Ian Ring Music TheoryPythian
Scale 2385Scale 2385: Aeolanitonic, Ian Ring Music TheoryAeolanitonic
Scale 2897Scale 2897: Rycrimic, Ian Ring Music TheoryRycrimic
Scale 1361Scale 1361: Bolitonic, Ian Ring Music TheoryBolitonic

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.