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Scale 1869: "Katyrian"

Scale 1869: Katyrian, 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
Katyrian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,2,3,6,8,9,10}
Forte Number7-28
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1629
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections4
Modes6
Prime?no
prime: 747
Deep Scaleno
Interval Vector344433
Interval Spectrump3m4n4s4d3t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {4,5,6}
<4> = {6,7,8}
<5> = {7,8,9,10}
<6> = {9,10,11}
Spectra Variation2
Maximally Evenno
Maximal Area Setno
Interior Area2.549
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicyes

Harmonic Chords

Modes

Modes are the rotational transformation of this scale. Scale 1869 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 1491
Scale 1491: Mela Namanarayani, Ian Ring Music TheoryMela Namanarayani
3rd mode:
Scale 2793
Scale 2793: Eporian, Ian Ring Music TheoryEporian
4th mode:
Scale 861
Scale 861: Rylian, Ian Ring Music TheoryRylian
5th mode:
Scale 1239
Scale 1239: Epaptian, Ian Ring Music TheoryEpaptian
6th mode:
Scale 2667
Scale 2667: Byrian, Ian Ring Music TheoryByrian
7th mode:
Scale 3381
Scale 3381: Katanian, Ian Ring Music TheoryKatanian

Prime

The prime form of this scale is Scale 747

Scale 747Scale 747: Lynian, Ian Ring Music TheoryLynian

Complement

The heptatonic modal family [1869, 1491, 2793, 861, 1239, 2667, 3381] (Forte: 7-28) is the complement of the pentatonic modal family [333, 837, 1107, 1233, 2601] (Forte: 5-28)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1869 is 1629

Scale 1629Scale 1629: Synian, Ian Ring Music TheorySynian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1869 is chiral, and its enantiomorph is scale 1629

Scale 1629Scale 1629: Synian, Ian Ring Music TheorySynian

Transformations:

T0 1869  T0I 1629
T1 3738  T1I 3258
T2 3381  T2I 2421
T3 2667  T3I 747
T4 1239  T4I 1494
T5 2478  T5I 2988
T6 861  T6I 1881
T7 1722  T7I 3762
T8 3444  T8I 3429
T9 2793  T9I 2763
T10 1491  T10I 1431
T11 2982  T11I 2862

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 1871Scale 1871: Aeolyllic, Ian Ring Music TheoryAeolyllic
Scale 1865Scale 1865: Thagimic, Ian Ring Music TheoryThagimic
Scale 1867Scale 1867: Solian, Ian Ring Music TheorySolian
Scale 1861Scale 1861: Phrygimic, Ian Ring Music TheoryPhrygimic
Scale 1877Scale 1877: Aeroptian, Ian Ring Music TheoryAeroptian
Scale 1885Scale 1885: Saptyllic, Ian Ring Music TheorySaptyllic
Scale 1901Scale 1901: Ionidyllic, Ian Ring Music TheoryIonidyllic
Scale 1805Scale 1805, Ian Ring Music Theory
Scale 1837Scale 1837: Dalian, Ian Ring Music TheoryDalian
Scale 1933Scale 1933: Mocrian, Ian Ring Music TheoryMocrian
Scale 1997Scale 1997: Raga Cintamani, Ian Ring Music TheoryRaga Cintamani
Scale 1613Scale 1613: Thylimic, Ian Ring Music TheoryThylimic
Scale 1741Scale 1741: Lydian Diminished, Ian Ring Music TheoryLydian Diminished
Scale 1357Scale 1357: Takemitsu Linea Mode 2, Ian Ring Music TheoryTakemitsu Linea Mode 2
Scale 845Scale 845: Raga Neelangi, Ian Ring Music TheoryRaga Neelangi
Scale 2893Scale 2893: Lylian, Ian Ring Music TheoryLylian
Scale 3917Scale 3917: Katoptyllic, Ian Ring Music TheoryKatoptyllic

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.