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Scale 1881: "Katorian"

Scale 1881: Katorian, 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
Katorian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,3,4,6,8,9,10}
Forte Number7-28
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 861
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 1881 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 747
Scale 747: Lynian, Ian Ring Music TheoryLynianThis is the prime mode
3rd mode:
Scale 2421
Scale 2421: Malian, Ian Ring Music TheoryMalian
4th mode:
Scale 1629
Scale 1629: Synian, Ian Ring Music TheorySynian
5th mode:
Scale 1431
Scale 1431: Phragian, Ian Ring Music TheoryPhragian
6th mode:
Scale 2763
Scale 2763: Mela Suvarnangi, Ian Ring Music TheoryMela Suvarnangi
7th mode:
Scale 3429
Scale 3429: Marian, Ian Ring Music TheoryMarian

Prime

The prime form of this scale is Scale 747

Scale 747Scale 747: Lynian, Ian Ring Music TheoryLynian

Complement

The heptatonic modal family [1881, 747, 2421, 1629, 1431, 2763, 3429] (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 1881 is 861

Scale 861Scale 861: Rylian, Ian Ring Music TheoryRylian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1881 is chiral, and its enantiomorph is scale 861

Scale 861Scale 861: Rylian, Ian Ring Music TheoryRylian

Transformations:

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

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 1883Scale 1883, Ian Ring Music Theory
Scale 1885Scale 1885: Saptyllic, Ian Ring Music TheorySaptyllic
Scale 1873Scale 1873: Dathimic, Ian Ring Music TheoryDathimic
Scale 1877Scale 1877: Aeroptian, Ian Ring Music TheoryAeroptian
Scale 1865Scale 1865: Thagimic, Ian Ring Music TheoryThagimic
Scale 1897Scale 1897: Ionopian, Ian Ring Music TheoryIonopian
Scale 1913Scale 1913, Ian Ring Music Theory
Scale 1817Scale 1817: Phrythimic, Ian Ring Music TheoryPhrythimic
Scale 1849Scale 1849: Chromatic Hypodorian Inverse, Ian Ring Music TheoryChromatic Hypodorian Inverse
Scale 1945Scale 1945: Zarian, Ian Ring Music TheoryZarian
Scale 2009Scale 2009: Stacryllic, Ian Ring Music TheoryStacryllic
Scale 1625Scale 1625: Lythimic, Ian Ring Music TheoryLythimic
Scale 1753Scale 1753: Hungarian Major, Ian Ring Music TheoryHungarian Major
Scale 1369Scale 1369: Boptimic, Ian Ring Music TheoryBoptimic
Scale 857Scale 857: Aeolydimic, Ian Ring Music TheoryAeolydimic
Scale 2905Scale 2905: Aeolian Flat 1, Ian Ring Music TheoryAeolian Flat 1
Scale 3929Scale 3929: Aeolothyllic, Ian Ring Music TheoryAeolothyllic

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.