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Scale 1267: "Katynian"

Scale 1267: Katynian, 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
Katynian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,4,5,6,7,10}
Forte Number7-19
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2533
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 1267 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 2681
Scale 2681: Aerycrian, Ian Ring Music TheoryAerycrian
3rd mode:
Scale 847
Scale 847: Ganian, Ian Ring Music TheoryGanian
4th mode:
Scale 2471
Scale 2471: Mela Ganamurti, Ian Ring Music TheoryMela Ganamurti
5th mode:
Scale 3283
Scale 3283: Mela Visvambhari, Ian Ring Music TheoryMela Visvambhari
6th mode:
Scale 3689
Scale 3689: Katocrian, Ian Ring Music TheoryKatocrian
7th mode:
Scale 973
Scale 973: Mela Syamalangi, Ian Ring Music TheoryMela Syamalangi

Prime

The prime form of this scale is Scale 719

Scale 719Scale 719: Kanian, Ian Ring Music TheoryKanian

Complement

The heptatonic modal family [1267, 2681, 847, 2471, 3283, 3689, 973] (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 1267 is 2533

Scale 2533Scale 2533: Podian, Ian Ring Music TheoryPodian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1267 is chiral, and its enantiomorph is scale 2533

Scale 2533Scale 2533: Podian, Ian Ring Music TheoryPodian

Transformations:

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

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 1265Scale 1265: Pynimic, Ian Ring Music TheoryPynimic
Scale 1269Scale 1269: Katythian, Ian Ring Music TheoryKatythian
Scale 1271Scale 1271: Kolyllic, Ian Ring Music TheoryKolyllic
Scale 1275Scale 1275: Stagyllic, Ian Ring Music TheoryStagyllic
Scale 1251Scale 1251: Sylimic, Ian Ring Music TheorySylimic
Scale 1259Scale 1259: Stadian, Ian Ring Music TheoryStadian
Scale 1235Scale 1235: Messiaen Truncated Mode 2, Ian Ring Music TheoryMessiaen Truncated Mode 2
Scale 1203Scale 1203: Pagimic, Ian Ring Music TheoryPagimic
Scale 1139Scale 1139: Aerygimic, Ian Ring Music TheoryAerygimic
Scale 1395Scale 1395: Asian (a), Ian Ring Music TheoryAsian (a)
Scale 1523Scale 1523: Zothyllic, Ian Ring Music TheoryZothyllic
Scale 1779Scale 1779: Zynyllic, Ian Ring Music TheoryZynyllic
Scale 243Scale 243, Ian Ring Music Theory
Scale 755Scale 755: Phrythian, Ian Ring Music TheoryPhrythian
Scale 2291Scale 2291: Zydian, Ian Ring Music TheoryZydian
Scale 3315Scale 3315: Tcherepnin Octatonic Mode 1, Ian Ring Music TheoryTcherepnin Octatonic Mode 1

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.