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Scale 2697: "Katagitonic"

Scale 2697: Katagitonic, 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

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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
Katagitonic

Analysis

Cardinality5 (pentatonic)
Pitch Class Set{0,3,7,9,11}
Forte Number5-26
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 555
Hemitonia1 (unhemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections4
Modes4
Prime?no
prime: 309
Deep Scaleno
Interval Vector122311
Interval Spectrumpm3n2s2dt
Distribution Spectra<1> = {1,2,3,4}
<2> = {3,4,6,7}
<3> = {5,6,8,9}
<4> = {8,9,10,11}
Spectra Variation2.8
Maximally Evenno
Maximal Area Setno
Interior Area2.049
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
Minor Triadscm{0,3,7}210.67
Augmented TriadsD♯+{3,7,11}121
Diminished Triads{9,0,3}121
Parsimonious Voice Leading Between Common Triads of Scale 2697. Created by Ian Ring ©2019 cm cm D#+ D#+ cm->D#+ cm->a°

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
Radius1
Self-Centeredno
Central Verticescm
Peripheral VerticesD♯+, a°

Modes

Modes are the rotational transformation of this scale. Scale 2697 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 849
Scale 849: Aerynitonic, Ian Ring Music TheoryAerynitonic
3rd mode:
Scale 309
Scale 309: Palitonic, Ian Ring Music TheoryPalitonicThis is the prime mode
4th mode:
Scale 1101
Scale 1101: Stothitonic, Ian Ring Music TheoryStothitonic
5th mode:
Scale 1299
Scale 1299: Aerophitonic, Ian Ring Music TheoryAerophitonic

Prime

The prime form of this scale is Scale 309

Scale 309Scale 309: Palitonic, Ian Ring Music TheoryPalitonic

Complement

The pentatonic modal family [2697, 849, 309, 1101, 1299] (Forte: 5-26) is the complement of the heptatonic modal family [699, 1497, 1623, 1893, 2397, 2859, 3477] (Forte: 7-26)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2697 is 555

Scale 555Scale 555: Aeolycritonic, Ian Ring Music TheoryAeolycritonic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2697 is chiral, and its enantiomorph is scale 555

Scale 555Scale 555: Aeolycritonic, Ian Ring Music TheoryAeolycritonic

Transformations:

T0 2697  T0I 555
T1 1299  T1I 1110
T2 2598  T2I 2220
T3 1101  T3I 345
T4 2202  T4I 690
T5 309  T5I 1380
T6 618  T6I 2760
T7 1236  T7I 1425
T8 2472  T8I 2850
T9 849  T9I 1605
T10 1698  T10I 3210
T11 3396  T11I 2325

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 2699Scale 2699: Sythimic, Ian Ring Music TheorySythimic
Scale 2701Scale 2701: Hawaiian, Ian Ring Music TheoryHawaiian
Scale 2689Scale 2689, Ian Ring Music Theory
Scale 2693Scale 2693, Ian Ring Music Theory
Scale 2705Scale 2705: Raga Mamata, Ian Ring Music TheoryRaga Mamata
Scale 2713Scale 2713: Porimic, Ian Ring Music TheoryPorimic
Scale 2729Scale 2729: Aeragimic, Ian Ring Music TheoryAeragimic
Scale 2761Scale 2761: Dagimic, Ian Ring Music TheoryDagimic
Scale 2569Scale 2569, Ian Ring Music Theory
Scale 2633Scale 2633: Bartók Beta Chord, Ian Ring Music TheoryBartók Beta Chord
Scale 2825Scale 2825, Ian Ring Music Theory
Scale 2953Scale 2953: Ionylimic, Ian Ring Music TheoryIonylimic
Scale 2185Scale 2185: Dygic, Ian Ring Music TheoryDygic
Scale 2441Scale 2441: Kyritonic, Ian Ring Music TheoryKyritonic
Scale 3209Scale 3209: Aeraphitonic, Ian Ring Music TheoryAeraphitonic
Scale 3721Scale 3721: Phragimic, Ian Ring Music TheoryPhragimic
Scale 649Scale 649: Byptic, Ian Ring Music TheoryByptic
Scale 1673Scale 1673: Thocritonic, Ian Ring Music TheoryThocritonic

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.