Scale 797: "Katocrimic"

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

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: Katocrimic

Analysis

Cardinality	6 (hexatonic)
Pitch Class Set	{0,2,3,4,8,9}
Forte Number	6-Z17
Rotational Symmetry	none
Reflection Axes	none
Palindromic	no
Chirality	yes enantiomorph: 1817
Hemitonia	3 (trihemitonic)
Cohemitonia	1 (uncohemitonic)
Imperfections	3
Modes	5
Prime?	no prime: 407
Deep Scale	no
Interval Vector	322332
Interval Spectrum	p³m³n²s²d³t²
Distribution Spectra	<1> = {1,2,3,4} <2> = {2,3,4,5} <3> = {4,6,8} <4> = {7,8,9,10} <5> = {8,9,10,11}
Spectra Variation	2.667
Maximally Even	no
Maximal Area Set	no
Interior Area	2.116
Myhill Property	no
Balanced	no
Ridge Tones	none
Propriety	Improper
Heliotonic	no

Modes

Modes are the rotational transformation of this scale. Scale 797 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode: Scale 1223				Phryptimic
3rd mode: Scale 2659				Katynimic
4th mode: Scale 3377				Phralimic
5th mode: Scale 467				Raga Dhavalangam
6th mode: Scale 2281				Rathimic

Prime

The prime form of this scale is Scale 407

Scale 407

Zylimic

Complement

The hexatonic modal family [797, 1223, 2659, 3377, 467, 2281] (Forte: 6-Z17) is the complement of the hexatonic modal family [359, 907, 1649, 2227, 2501, 3161] (Forte: 6-Z43)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 797 is 1817

Scale 1817

Phrythimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 797 is chiral, and its enantiomorph is scale 1817

Scale 1817

Phrythimic

Transformations:

T₀	797	T₀I	1817
T₁	1594	T₁I	3634
T₂	3188	T₂I	3173
T₃	2281	T₃I	2251
T₄	467	T₄I	407
T₅	934	T₅I	814
T₆	1868	T₆I	1628
T₇	3736	T₇I	3256
T₈	3377	T₈I	2417
T₉	2659	T₉I	739
T₁₀	1223	T₁₀I	1478
T₁₁	2446	T₁₁I	2956

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 799				Lolian
Scale 793				Mocritonic
Scale 795				Aeologimic
Scale 789				Zogitonic
Scale 781
Scale 813				Larimic
Scale 829				Lygian
Scale 861				Rylian
Scale 925				Chromatic Hypodorian
Scale 541
Scale 669				Gycrimic
Scale 285				Zaritonic
Scale 1309				Pogimic
Scale 1821				Aeradian
Scale 2845				Baptian

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.