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Scale 3949: "Koptygic"

Scale 3949: Koptygic, 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
Koptygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,2,3,5,6,8,9,10,11}
Forte Number9-10
Rotational Symmetrynone
Reflection Axes4
Palindromicno
Chiralityno
Hemitonia6 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections3
Modes8
Prime?no
prime: 1759
Deep Scaleno
Interval Vector668664
Interval Spectrump6m6n8s6d6t4
Distribution Spectra<1> = {1,2}
<2> = {2,3}
<3> = {3,4,5}
<4> = {4,5,6}
<5> = {6,7,8}
<6> = {7,8,9}
<7> = {9,10}
<8> = {10,11}
Spectra Variation1.333
Maximally Evenno
Maximal Area Setyes
Interior Area2.799
Myhill Propertyno
Balancedno
Ridge Tones[8]
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}442.37
F{5,9,0}442.37
G♯{8,0,3}442.42
A♯{10,2,5}342.47
B{11,3,6}442.32
Minor Triadsdm{2,5,9}442.32
d♯m{3,6,10}342.47
fm{5,8,0}442.42
g♯m{8,11,3}442.37
bm{11,2,6}442.37
Augmented TriadsD+{2,6,10}442.32
Diminished Triads{0,3,6}242.58
{2,5,8}242.58
d♯°{3,6,9}242.74
{5,8,11}242.63
f♯°{6,9,0}242.63
g♯°{8,11,2}242.63
{9,0,3}242.63
{11,2,5}242.74
Parsimonious Voice Leading Between Common Triads of Scale 3949. Created by Ian Ring ©2019 G# G# c°->G# B B c°->B dm dm d°->dm fm fm d°->fm D D dm->D F F dm->F A# A# dm->A# D+ D+ D->D+ d#° d#° D->d#° f#° f#° D->f#° d#m d#m D+->d#m D+->A# bm bm D+->bm d#°->d#m d#m->B f°->fm g#m g#m f°->g#m fm->F fm->G# F->f#° F->a° g#° g#° g#°->g#m g#°->bm g#m->G# g#m->B G#->a° A#->b° b°->bm bm->B

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.

Diameter4
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 3949 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 2011
Scale 2011: Raphygic, Ian Ring Music TheoryRaphygic
3rd mode:
Scale 3053
Scale 3053: Zycrygic, Ian Ring Music TheoryZycrygic
4th mode:
Scale 1787
Scale 1787: Mycrygic, Ian Ring Music TheoryMycrygic
5th mode:
Scale 2941
Scale 2941: Laptygic, Ian Ring Music TheoryLaptygic
6th mode:
Scale 1759
Scale 1759: Pylygic, Ian Ring Music TheoryPylygicThis is the prime mode
7th mode:
Scale 2927
Scale 2927: Rodygic, Ian Ring Music TheoryRodygic
8th mode:
Scale 3511
Scale 3511: Epolygic, Ian Ring Music TheoryEpolygic
9th mode:
Scale 3803
Scale 3803: Epidygic, Ian Ring Music TheoryEpidygic

Prime

The prime form of this scale is Scale 1759

Scale 1759Scale 1759: Pylygic, Ian Ring Music TheoryPylygic

Complement

The nonatonic modal family [3949, 2011, 3053, 1787, 2941, 1759, 2927, 3511, 3803] (Forte: 9-10) is the complement of the tritonic modal family [73, 521, 577] (Forte: 3-10)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3949 is 1759

Scale 1759Scale 1759: Pylygic, Ian Ring Music TheoryPylygic

Transformations:

T0 3949  T0I 1759
T1 3803  T1I 3518
T2 3511  T2I 2941
T3 2927  T3I 1787
T4 1759  T4I 3574
T5 3518  T5I 3053
T6 2941  T6I 2011
T7 1787  T7I 4022
T8 3574  T8I 3949
T9 3053  T9I 3803
T10 2011  T10I 3511
T11 4022  T11I 2927

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 3951Scale 3951: Mathyllian, Ian Ring Music TheoryMathyllian
Scale 3945Scale 3945: Lydyllic, Ian Ring Music TheoryLydyllic
Scale 3947Scale 3947: Ryptygic, Ian Ring Music TheoryRyptygic
Scale 3941Scale 3941: Stathyllic, Ian Ring Music TheoryStathyllic
Scale 3957Scale 3957: Porygic, Ian Ring Music TheoryPorygic
Scale 3965Scale 3965: Messiaen Mode 7 Inverse, Ian Ring Music TheoryMessiaen Mode 7 Inverse
Scale 3917Scale 3917: Katoptyllic, Ian Ring Music TheoryKatoptyllic
Scale 3933Scale 3933: Ionidygic, Ian Ring Music TheoryIonidygic
Scale 3885Scale 3885: Styryllic, Ian Ring Music TheoryStyryllic
Scale 4013Scale 4013: Raga Pilu, Ian Ring Music TheoryRaga Pilu
Scale 4077Scale 4077: Gothyllian, Ian Ring Music TheoryGothyllian
Scale 3693Scale 3693: Stadyllic, Ian Ring Music TheoryStadyllic
Scale 3821Scale 3821: Epyrygic, Ian Ring Music TheoryEpyrygic
Scale 3437Scale 3437, Ian Ring Music Theory
Scale 2925Scale 2925: Diminished, Ian Ring Music TheoryDiminished
Scale 1901Scale 1901: Ionidyllic, Ian Ring Music TheoryIonidyllic

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.