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Scale 1655: "Katygyllic"

Scale 1655: Katygyllic, 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
Katygyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,2,4,5,6,9,10}
Forte Number8-19
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3533
Hemitonia5 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections3
Modes7
Prime?no
prime: 887
Deep Scaleno
Interval Vector545752
Interval Spectrump5m7n5s4d5t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4}
<3> = {4,5,6}
<4> = {5,6,7}
<5> = {6,7,8}
<6> = {8,9,10}
<7> = {9,10,11}
Spectra Variation1.75
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}342.15
F{5,9,0}342.08
F♯{6,10,1}342
A{9,1,4}342.08
A♯{10,2,5}342.15
Minor Triadsdm{2,5,9}331.92
f♯m{6,9,1}431.77
am{9,0,4}252.62
a♯m{10,1,5}431.77
Augmented TriadsC♯+{1,5,9}531.54
D+{2,6,10}352.38
Diminished Triadsf♯°{6,9,0}242.31
a♯°{10,1,4}242.31
Parsimonious Voice Leading Between Common Triads of Scale 1655. Created by Ian Ring ©2019 C#+ C#+ dm dm C#+->dm F F C#+->F f#m f#m C#+->f#m A A C#+->A a#m a#m C#+->a#m D D dm->D A# A# dm->A# D+ D+ D->D+ D->f#m F# F# D+->F# D+->A# f#° f#° F->f#° am am F->am f#°->f#m f#m->F# F#->a#m am->A a#° a#° A->a#° a#°->a#m a#m->A#

view full size

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.

Diameter5
Radius3
Self-Centeredno
Central VerticesC♯+, dm, f♯m, a♯m
Peripheral VerticesD+, am

Modes

Modes are the rotational transformation of this scale. Scale 1655 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 2875		Scale 2875: Ganyllic, Ian Ring Music TheoryGanyllic
3rd mode:
Scale 3485		Scale 3485: Sabach, Ian Ring Music TheorySabach
4th mode:
Scale 1895		Scale 1895: Salyllic, Ian Ring Music TheorySalyllic
5th mode:
Scale 2995		Scale 2995: Raga Saurashtra, Ian Ring Music TheoryRaga Saurashtra
6th mode:
Scale 3545		Scale 3545: Thyptyllic, Ian Ring Music TheoryThyptyllic
7th mode:
Scale 955		Scale 955: Ionogyllic, Ian Ring Music TheoryIonogyllic
8th mode:
Scale 2525		Scale 2525: Aeolaryllic, Ian Ring Music TheoryAeolaryllic

Prime

The prime form of this scale is Scale 887

Scale 887Scale 887: Sathyllic, Ian Ring Music TheorySathyllic

Complement

The octatonic modal family [1655, 2875, 3485, 1895, 2995, 3545, 955, 2525] (Forte: 8-19) is the complement of the tetratonic modal family [275, 305, 785, 2185] (Forte: 4-19)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1655 is 3533

Scale 3533Scale 3533: Thadyllic, Ian Ring Music TheoryThadyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1655 is chiral, and its enantiomorph is scale 3533

Scale 3533Scale 3533: Thadyllic, Ian Ring Music TheoryThadyllic

Transformations:

T0 1655  T0I 3533
T1 3310  T1I 2971
T2 2525  T2I 1847
T3 955  T3I 3694
T4 1910  T4I 3293
T5 3820  T5I 2491
T6 3545  T6I 887
T7 2995  T7I 1774
T8 1895  T8I 3548
T9 3790  T9I 3001
T10 3485  T10I 1907
T11 2875  T11I 3814

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 1653Scale 1653: Minor Romani Inverse, Ian Ring Music TheoryMinor Romani Inverse
Scale 1651Scale 1651: Asian, Ian Ring Music TheoryAsian
Scale 1659Scale 1659: Maqam Shadd'araban, Ian Ring Music TheoryMaqam Shadd'araban
Scale 1663Scale 1663: Lydygic, Ian Ring Music TheoryLydygic
Scale 1639Scale 1639: Aeolothian, Ian Ring Music TheoryAeolothian
Scale 1647Scale 1647: Polyllic, Ian Ring Music TheoryPolyllic
Scale 1623Scale 1623: Lothian, Ian Ring Music TheoryLothian
Scale 1591Scale 1591: Rodian, Ian Ring Music TheoryRodian
Scale 1719Scale 1719: Lyryllic, Ian Ring Music TheoryLyryllic
Scale 1783Scale 1783: Youlan Scale, Ian Ring Music TheoryYoulan Scale
Scale 1911Scale 1911: Messiaen Mode 3, Ian Ring Music TheoryMessiaen Mode 3
Scale 1143Scale 1143: Styrian, Ian Ring Music TheoryStyrian
Scale 1399Scale 1399: Syryllic, Ian Ring Music TheorySyryllic
Scale 631Scale 631: Zygian, Ian Ring Music TheoryZygian
Scale 2679Scale 2679: Rathyllic, Ian Ring Music TheoryRathyllic
Scale 3703Scale 3703: Katalygic, Ian Ring Music TheoryKatalygic

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.