The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 797: "Katocrimic"

Scale 797: Katocrimic, 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
Katocrimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,2,3,4,8,9}
Forte Number6-Z17
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1817
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes5
Prime?no
prime: 407
Deep Scaleno
Interval Vector322332
Interval Spectrump3m3n2s2d3t2
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 Variation2.667
Maximally Evenno
Maximal Area Setno
Interior Area2.116
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicno

Common Triads

These are the common triads (major, minor, augmented and diminished) that you can create from members of this scale.

* Pitches are shown with C as the root

Triad TypeTriad*Pitch ClassesDegreeEccentricityCloseness Centrality
Major TriadsG♯{8,0,3}221
Minor Triadsam{9,0,4}221
Augmented TriadsC+{0,4,8}221
Diminished Triadsa°{9,0,3}221
Parsimonious Voice Leading Between Common Triads of Scale 797. Created by Ian Ring ©2019 C+ C+ G# G# C+->G# am am C+->am a° a° G#->a° a°->am

Above is a graph showing opportunities for parsimonious voice leading between triads*. Each line connects two triads that have two common tones, while the third tone changes by one generic scale step.

Diameter2
Radius2
Self-Centeredyes

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		Scale 1223: Phryptimic, Ian Ring Music TheoryPhryptimic
3rd mode:
Scale 2659		Scale 2659: Katynimic, Ian Ring Music TheoryKatynimic
4th mode:
Scale 3377		Scale 3377: Phralimic, Ian Ring Music TheoryPhralimic
5th mode:
Scale 467		Scale 467: Raga Dhavalangam, Ian Ring Music TheoryRaga Dhavalangam
6th mode:
Scale 2281		Scale 2281: Rathimic, Ian Ring Music TheoryRathimic

Prime

The prime form of this scale is Scale 407

Scale 407Scale 407: Zylimic, Ian Ring Music TheoryZylimic

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 1817Scale 1817: Phrythimic, Ian Ring Music TheoryPhrythimic

Enantiomorph

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

Scale 1817Scale 1817: Phrythimic, Ian Ring Music TheoryPhrythimic

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 799Scale 799: Lolian, Ian Ring Music TheoryLolian
Scale 793Scale 793: Mocritonic, Ian Ring Music TheoryMocritonic
Scale 795Scale 795: Aeologimic, Ian Ring Music TheoryAeologimic
Scale 789Scale 789: Zogitonic, Ian Ring Music TheoryZogitonic
Scale 781Scale 781, Ian Ring Music Theory
Scale 813Scale 813: Larimic, Ian Ring Music TheoryLarimic
Scale 829Scale 829: Lygian, Ian Ring Music TheoryLygian
Scale 861Scale 861: Rylian, Ian Ring Music TheoryRylian
Scale 925Scale 925: Chromatic Hypodorian, Ian Ring Music TheoryChromatic Hypodorian
Scale 541Scale 541, Ian Ring Music Theory
Scale 669Scale 669: Gycrimic, Ian Ring Music TheoryGycrimic
Scale 285Scale 285: Zaritonic, Ian Ring Music TheoryZaritonic
Scale 1309Scale 1309: Pogimic, Ian Ring Music TheoryPogimic
Scale 1821Scale 1821: Aeradian, Ian Ring Music TheoryAeradian
Scale 2845Scale 2845: Baptian, Ian Ring Music TheoryBaptian

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, graph visualization by Graphviz, and MIDI playback by MIDI.js. Some scale names used on this and other pages are ©2005 William Zeitler (http://allthescales.org) used with permission.

Pitch spelling algorithm employed here is adapted from a method by Uzay Bora, Baris Tekin Tezel, and Alper Vahaplar. (An algorithm for spelling the pitches of any musical scale) Contact authors Patent owner: Dokuz Eylül University, Used with Permission. Contact TTO

Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography. Special thanks to Richard Repp for helping with technical accuracy.