The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 2861: "Katothian"

Scale 2861: Katothian, 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
Katothian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,2,3,5,8,9,11}
Forte Number7-31
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1691
Hemitonia3 (trihemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections4
Modes6
Prime?no
prime: 731
Deep Scaleno
Interval Vector336333
Interval Spectrump3m3n6s3d3t3
Distribution Spectra<1> = {1,2,3}
<2> = {3,4,5}
<3> = {4,5,6}
<4> = {6,7,8}
<5> = {7,8,9}
<6> = {9,10,11}
Spectra Variation1.714
Maximally Evenno
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicyes

Harmonic Chords

Modes

Modes are the rotational transformation of this scale. Scale 2861 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 1739
Scale 1739: Mela Sadvidhamargini, Ian Ring Music TheoryMela Sadvidhamargini
3rd mode:
Scale 2917
Scale 2917: Nohkan Flute Scale, Ian Ring Music TheoryNohkan Flute Scale
4th mode:
Scale 1753
Scale 1753: Hungarian Major, Ian Ring Music TheoryHungarian Major
5th mode:
Scale 731
Scale 731: Ionorian, Ian Ring Music TheoryIonorianThis is the prime mode
6th mode:
Scale 2413
Scale 2413: Locrian Natural 2, Ian Ring Music TheoryLocrian Natural 2
7th mode:
Scale 1627
Scale 1627: Zyptian, Ian Ring Music TheoryZyptian

Prime

The prime form of this scale is Scale 731

Scale 731Scale 731: Ionorian, Ian Ring Music TheoryIonorian

Complement

The heptatonic modal family [2861, 1739, 2917, 1753, 731, 2413, 1627] (Forte: 7-31) is the complement of the pentatonic modal family [587, 601, 713, 1609, 2341] (Forte: 5-31)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2861 is 1691

Scale 1691Scale 1691: Kathian, Ian Ring Music TheoryKathian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2861 is chiral, and its enantiomorph is scale 1691

Scale 1691Scale 1691: Kathian, Ian Ring Music TheoryKathian

Transformations:

T0 2861  T0I 1691
T1 1627  T1I 3382
T2 3254  T2I 2669
T3 2413  T3I 1243
T4 731  T4I 2486
T5 1462  T5I 877
T6 2924  T6I 1754
T7 1753  T7I 3508
T8 3506  T8I 2921
T9 2917  T9I 1747
T10 1739  T10I 3494
T11 3478  T11I 2893

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 2863Scale 2863: Aerogyllic, Ian Ring Music TheoryAerogyllic
Scale 2857Scale 2857: Stythimic, Ian Ring Music TheoryStythimic
Scale 2859Scale 2859: Phrycrian, Ian Ring Music TheoryPhrycrian
Scale 2853Scale 2853: Baptimic, Ian Ring Music TheoryBaptimic
Scale 2869Scale 2869: Ionian Augmented, Ian Ring Music TheoryIonian Augmented
Scale 2877Scale 2877: Phrylyllic, Ian Ring Music TheoryPhrylyllic
Scale 2829Scale 2829, Ian Ring Music Theory
Scale 2845Scale 2845: Baptian, Ian Ring Music TheoryBaptian
Scale 2893Scale 2893: Lylian, Ian Ring Music TheoryLylian
Scale 2925Scale 2925: Diminished, Ian Ring Music TheoryDiminished
Scale 2989Scale 2989: Bebop Minor, Ian Ring Music TheoryBebop Minor
Scale 2605Scale 2605: Rylimic, Ian Ring Music TheoryRylimic
Scale 2733Scale 2733: Melodic Minor Ascending, Ian Ring Music TheoryMelodic Minor Ascending
Scale 2349Scale 2349: Raga Ghantana, Ian Ring Music TheoryRaga Ghantana
Scale 3373Scale 3373: Lodian, Ian Ring Music TheoryLodian
Scale 3885Scale 3885: Styryllic, Ian Ring Music TheoryStyryllic
Scale 813Scale 813: Larimic, Ian Ring Music TheoryLarimic
Scale 1837Scale 1837: Dalian, Ian Ring Music TheoryDalian

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.