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Scale 3959: "Katagyllian"

Scale 3959: Katagyllian, 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
Katagyllian

Analysis

Cardinality10 (decatonic)
Pitch Class Set{0,1,2,4,5,6,8,9,10,11}
Forte Number10-4
Rotational Symmetrynone
Reflection Axes5
Palindromicno
Chiralityno
Hemitonia8 (multihemitonic)
Cohemitonia6 (multicohemitonic)
Imperfections2
Modes9
Prime?no
prime: 1919
Deep Scaleno
Interval Vector888984
Interval Spectrump8m9n8s8d8t4
Distribution Spectra<1> = {1,2}
<2> = {2,3}
<3> = {3,4}
<4> = {4,5,6}
<5> = {5,6,7}
<6> = {6,7,8}
<7> = {8,9}
<8> = {9,10}
<9> = {10,11}
Spectra Variation1.2
Maximally Evenno
Maximal Area Setyes
Interior Area2.866
Myhill Propertyno
Balancedno
Ridge Tones[10]
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 TriadsC♯{1,5,8}452.43
D{2,6,9}352.74
E{4,8,11}353
F{5,9,0}452.43
F♯{6,10,1}352.74
A{9,1,4}452.52
A♯{10,2,5}452.65
Minor Triadsc♯m{1,4,8}352.74
dm{2,5,9}452.43
fm{5,8,0}452.65
f♯m{6,9,1}452.52
am{9,0,4}352.74
a♯m{10,1,5}452.43
bm{11,2,6}353
Augmented TriadsC+{0,4,8}452.78
C♯+{1,5,9}652.13
D+{2,6,10}452.78
Diminished Triads{2,5,8}252.83
{5,8,11}253.13
f♯°{6,9,0}252.91
g♯°{8,11,2}253.13
a♯°{10,1,4}252.91
{11,2,5}253.13
Parsimonious Voice Leading Between Common Triads of Scale 3959. Created by Ian Ring ©2019 C+ C+ c#m c#m C+->c#m E E C+->E fm fm C+->fm am am C+->am C# C# c#m->C# A A c#m->A C#+ C#+ C#->C#+ C#->d° C#->fm dm dm C#+->dm F F C#+->F f#m f#m C#+->f#m C#+->A a#m a#m C#+->a#m d°->dm D D dm->D A# A# dm->A# D+ D+ D->D+ D->f#m F# F# D+->F# D+->A# bm bm D+->bm E->f° g#° g#° E->g#° f°->fm fm->F f#° f#° F->f#° F->am f#°->f#m f#m->F# F#->a#m g#°->bm am->A a#° a#° A->a#° a#°->a#m a#m->A# A#->b° b°->bm

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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.

Diameter5
Radius5
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 3959 can be rotated to make 9 other scales. The 1st mode is itself.

2nd mode:
Scale 4027
Scale 4027: Ragyllian, Ian Ring Music TheoryRagyllian
3rd mode:
Scale 4061
Scale 4061: Staptyllian, Ian Ring Music TheoryStaptyllian
4th mode:
Scale 2039
Scale 2039: Danyllian, Ian Ring Music TheoryDanyllian
5th mode:
Scale 3067
Scale 3067: Goptyllian, Ian Ring Music TheoryGoptyllian
6th mode:
Scale 3581
Scale 3581: Epocryllian, Ian Ring Music TheoryEpocryllian
7th mode:
Scale 1919
Scale 1919: Rocryllian, Ian Ring Music TheoryRocryllianThis is the prime mode
8th mode:
Scale 3007
Scale 3007: Zyryllian, Ian Ring Music TheoryZyryllian
9th mode:
Scale 3551
Scale 3551: Sagyllian, Ian Ring Music TheorySagyllian
10th mode:
Scale 3823
Scale 3823: Epinyllian, Ian Ring Music TheoryEpinyllian

Prime

The prime form of this scale is Scale 1919

Scale 1919Scale 1919: Rocryllian, Ian Ring Music TheoryRocryllian

Complement

The decatonic modal family [3959, 4027, 4061, 2039, 3067, 3581, 1919, 3007, 3551, 3823] (Forte: 10-4) is the complement of the modal family [17, 257] (Forte: 2-4)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3959 is 3551

Scale 3551Scale 3551: Sagyllian, Ian Ring Music TheorySagyllian

Transformations:

T0 3959  T0I 3551
T1 3823  T1I 3007
T2 3551  T2I 1919
T3 3007  T3I 3838
T4 1919  T4I 3581
T5 3838  T5I 3067
T6 3581  T6I 2039
T7 3067  T7I 4078
T8 2039  T8I 4061
T9 4078  T9I 4027
T10 4061  T10I 3959
T11 4027  T11I 3823

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 3957Scale 3957: Porygic, Ian Ring Music TheoryPorygic
Scale 3955Scale 3955: Pothygic, Ian Ring Music TheoryPothygic
Scale 3963Scale 3963: Aeoryllian, Ian Ring Music TheoryAeoryllian
Scale 3967Scale 3967: Soratic, Ian Ring Music TheorySoratic
Scale 3943Scale 3943: Zynygic, Ian Ring Music TheoryZynygic
Scale 3951Scale 3951: Mathyllian, Ian Ring Music TheoryMathyllian
Scale 3927Scale 3927: Monygic, Ian Ring Music TheoryMonygic
Scale 3895Scale 3895: Eparygic, Ian Ring Music TheoryEparygic
Scale 4023Scale 4023: Styptyllian, Ian Ring Music TheoryStyptyllian
Scale 4087Scale 4087: Aeolatic, Ian Ring Music TheoryAeolatic
Scale 3703Scale 3703: Katalygic, Ian Ring Music TheoryKatalygic
Scale 3831Scale 3831: Ionyllian, Ian Ring Music TheoryIonyllian
Scale 3447Scale 3447: Kynygic, Ian Ring Music TheoryKynygic
Scale 2935Scale 2935: Modygic, Ian Ring Music TheoryModygic
Scale 1911Scale 1911: Messiaen Mode 3, Ian Ring Music TheoryMessiaen Mode 3

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.