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Scale 3787: "Kagyllic"

Scale 3787: Kagyllic, 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
Kagyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,3,6,7,9,10,11}
Forte Number8-12
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2671
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♯{3,7,10}342
F♯{6,10,1}342
B{11,3,6}342
Minor Triadscm{0,3,7}342.17
d♯m{3,6,10}441.83
f♯m{6,9,1}342.17
Augmented TriadsD♯+{3,7,11}342
Diminished Triads{0,3,6}242.33
d♯°{3,6,9}242.17
f♯°{6,9,0}242.33
{7,10,1}242.33
{9,0,3}242.33
Parsimonious Voice Leading Between Common Triads of Scale 3787. Created by Ian Ring ©2019 cm cm c°->cm B B c°->B D#+ D#+ cm->D#+ cm->a° d#° d#° d#m d#m d#°->d#m f#m f#m d#°->f#m D# D# d#m->D# F# F# d#m->F# d#m->B D#->D#+ D#->g° D#+->B f#° f#° f#°->f#m f#°->a° f#m->F# F#->g°

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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 3787 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3941
Scale 3941: Stathyllic, Ian Ring Music TheoryStathyllic
3rd mode:
Scale 2009
Scale 2009: Stacryllic, Ian Ring Music TheoryStacryllic
4th mode:
Scale 763
Scale 763: Doryllic, Ian Ring Music TheoryDoryllicThis is the prime mode
5th mode:
Scale 2429
Scale 2429: Kadyllic, Ian Ring Music TheoryKadyllic
6th mode:
Scale 1631
Scale 1631: Rynyllic, Ian Ring Music TheoryRynyllic
7th mode:
Scale 2863
Scale 2863: Aerogyllic, Ian Ring Music TheoryAerogyllic
8th mode:
Scale 3479
Scale 3479: Rothyllic, Ian Ring Music TheoryRothyllic

Prime

The prime form of this scale is Scale 763

Scale 763Scale 763: Doryllic, Ian Ring Music TheoryDoryllic

Complement

The octatonic modal family [3787, 3941, 2009, 763, 2429, 1631, 2863, 3479] (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 3787 is 2671

Scale 2671Scale 2671: Aerolyllic, Ian Ring Music TheoryAerolyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3787 is chiral, and its enantiomorph is scale 2671

Scale 2671Scale 2671: Aerolyllic, Ian Ring Music TheoryAerolyllic

Transformations:

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

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 3785Scale 3785: Epagian, Ian Ring Music TheoryEpagian
Scale 3789Scale 3789: Eporyllic, Ian Ring Music TheoryEporyllic
Scale 3791Scale 3791: Stodygic, Ian Ring Music TheoryStodygic
Scale 3779Scale 3779, Ian Ring Music Theory
Scale 3783Scale 3783: Phrygyllic, Ian Ring Music TheoryPhrygyllic
Scale 3795Scale 3795: Epothyllic, Ian Ring Music TheoryEpothyllic
Scale 3803Scale 3803: Epidygic, Ian Ring Music TheoryEpidygic
Scale 3819Scale 3819: Aeolanygic, Ian Ring Music TheoryAeolanygic
Scale 3723Scale 3723: Myptian, Ian Ring Music TheoryMyptian
Scale 3755Scale 3755: Phryryllic, Ian Ring Music TheoryPhryryllic
Scale 3659Scale 3659: Polian, Ian Ring Music TheoryPolian
Scale 3915Scale 3915, Ian Ring Music Theory
Scale 4043Scale 4043: Phrocrygic, Ian Ring Music TheoryPhrocrygic
Scale 3275Scale 3275: Mela Divyamani, Ian Ring Music TheoryMela Divyamani
Scale 3531Scale 3531: Neveseri, Ian Ring Music TheoryNeveseri
Scale 2763Scale 2763: Mela Suvarnangi, Ian Ring Music TheoryMela Suvarnangi
Scale 1739Scale 1739: Mela Sadvidhamargini, Ian Ring Music TheoryMela Sadvidhamargini

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.