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Scale 3917: "Katoptyllic"

Scale 3917: Katoptyllic, 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
Katoptyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,2,3,6,8,9,10,11}
Forte Number8-12
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1631
Hemitonia5 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections4
Modes7
Prime?no
prime: 763
Deep Scaleno
Interval Vector556543
Interval Spectrump4m5n6s5d5t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {3,4,6}
<4> = {4,5,7,8}
<5> = {6,8,9}
<6> = {7,8,9,10}
<7> = {9,10,11}
Spectra Variation2.5
Maximally Evenno
Maximal Area Setno
Interior Area2.616
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 TriadsD{2,6,9}342.17
G♯{8,0,3}342.17
B{11,3,6}441.83
Minor Triadsd♯m{3,6,10}342
g♯m{8,11,3}342
bm{11,2,6}342
Augmented TriadsD+{2,6,10}342
Diminished Triads{0,3,6}242.17
d♯°{3,6,9}242.33
f♯°{6,9,0}242.33
g♯°{8,11,2}242.33
{9,0,3}242.33
Parsimonious Voice Leading Between Common Triads of Scale 3917. Created by Ian Ring ©2019 G# G# c°->G# B B c°->B D D D+ D+ D->D+ d#° d#° D->d#° f#° f#° D->f#° d#m d#m D+->d#m bm bm D+->bm d#°->d#m d#m->B f#°->a° g#° g#° g#m g#m g#°->g#m g#°->bm g#m->G# g#m->B G#->a° bm->B

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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.

Diameter4
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 3917 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 2003
Scale 2003: Podyllic, Ian Ring Music TheoryPodyllic
3rd mode:
Scale 3049
Scale 3049: Phrydyllic, Ian Ring Music TheoryPhrydyllic
4th mode:
Scale 893
Scale 893: Dadyllic, Ian Ring Music TheoryDadyllic
5th mode:
Scale 1247
Scale 1247: Aeodyllic, Ian Ring Music TheoryAeodyllic
6th mode:
Scale 2671
Scale 2671: Aerolyllic, Ian Ring Music TheoryAerolyllic
7th mode:
Scale 3383
Scale 3383: Zoptyllic, Ian Ring Music TheoryZoptyllic
8th mode:
Scale 3739
Scale 3739: Epanyllic, Ian Ring Music TheoryEpanyllic

Prime

The prime form of this scale is Scale 763

Scale 763Scale 763: Doryllic, Ian Ring Music TheoryDoryllic

Complement

The octatonic modal family [3917, 2003, 3049, 893, 1247, 2671, 3383, 3739] (Forte: 8-12) is the complement of the tetratonic modal family [77, 833, 1043, 2569] (Forte: 4-12)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3917 is 1631

Scale 1631Scale 1631: Rynyllic, Ian Ring Music TheoryRynyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3917 is chiral, and its enantiomorph is scale 1631

Scale 1631Scale 1631: Rynyllic, Ian Ring Music TheoryRynyllic

Transformations:

T0 3917  T0I 1631
T1 3739  T1I 3262
T2 3383  T2I 2429
T3 2671  T3I 763
T4 1247  T4I 1526
T5 2494  T5I 3052
T6 893  T6I 2009
T7 1786  T7I 4018
T8 3572  T8I 3941
T9 3049  T9I 3787
T10 2003  T10I 3479
T11 4006  T11I 2863

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 3919Scale 3919: Lynygic, Ian Ring Music TheoryLynygic
Scale 3913Scale 3913: Bonian, Ian Ring Music TheoryBonian
Scale 3915Scale 3915, Ian Ring Music Theory
Scale 3909Scale 3909: Rydian, Ian Ring Music TheoryRydian
Scale 3925Scale 3925: Thyryllic, Ian Ring Music TheoryThyryllic
Scale 3933Scale 3933: Ionidygic, Ian Ring Music TheoryIonidygic
Scale 3949Scale 3949: Koptygic, Ian Ring Music TheoryKoptygic
Scale 3853Scale 3853, Ian Ring Music Theory
Scale 3885Scale 3885: Styryllic, Ian Ring Music TheoryStyryllic
Scale 3981Scale 3981: Phrycryllic, Ian Ring Music TheoryPhrycryllic
Scale 4045Scale 4045: Gyptygic, Ian Ring Music TheoryGyptygic
Scale 3661Scale 3661: Mixodorian, Ian Ring Music TheoryMixodorian
Scale 3789Scale 3789: Eporyllic, Ian Ring Music TheoryEporyllic
Scale 3405Scale 3405: Stynian, Ian Ring Music TheoryStynian
Scale 2893Scale 2893: Lylian, Ian Ring Music TheoryLylian
Scale 1869Scale 1869: Katyrian, Ian Ring Music TheoryKatyrian

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.