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Scale 3447: "Kynygic"

Scale 3447: Kynygic, 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
Kynygic

Analysis

Cardinality

Cardinality is the count of how many pitches are in the scale.

9 (nonatonic)

Pitch Class Set

The tones in this scale, expressed as numbers from 0 to 11

{0,1,2,4,5,6,8,10,11}

Forte Number

A code assigned by theorist Alan Forte, for this pitch class set and all of its transpositional (rotation) and inversional (reflection) transformations.

9-8

Rotational Symmetry

Some scales have rotational symmetry, sometimes known as "limited transposition". If there are any rotational symmetries, these are the intervals of periodicity.

none

Reflection Axes

If a scale has an axis of reflective symmetry, then it can transform into itself by inversion. It also implies that the scale has Ridge Tones. Notably an axis of reflection can occur directly on a tone or half way between two tones.

none

Palindromicity

A palindromic scale has the same pattern of intervals both ascending and descending.

no

Chirality

A chiral scale can not be transformed into its inverse by rotation. If a scale is chiral, then it has an enantiomorph.

yes
enantiomorph: 3543

Hemitonia

A hemitone is two tones separated by a semitone interval. Hemitonia describes how many such hemitones exist.

6 (multihemitonic)

Cohemitonia

A cohemitone is an instance of two adjacent hemitones. Cohemitonia describes how many such cohemitones exist.

4 (multicohemitonic)

Imperfections

An imperfection is a tone which does not have a perfect fifth above it in the scale. This value is the quantity of imperfections in this scale.

3

Modes

Modes are the rotational transformations of this scale. This number does not include the scale itself, so the number is usually one less than its cardinality; unless there are rotational symmetries then there are even fewer modes.

8

Prime Form

Describes if this scale is in prime form, using the Rahn/Ring formula.

no
prime: 1503

Deep Scale

A deep scale is one where the interval vector has 6 different digits.

no

Interval Vector

Describes the intervallic content of the scale, read from left to right as the number of occurences of each interval size from semitone, up to six semitones.

[6, 7, 6, 7, 6, 4]

Interval Spectrum

The same as the Interval Vector, but expressed in a syntax used by Howard Hansen.

p6m7n6s7d6t4

Distribution Spectra

Describes the specific interval sizes that exist for each generic interval size. Each generic <g> has a spectrum {n,...}. The Spectrum Width is the difference between the highest and lowest values in each spectrum.

<1> = {1,2}
<2> = {2,3,4}
<3> = {3,4,5}
<4> = {4,5,6}
<5> = {6,7,8}
<6> = {7,8,9}
<7> = {8,9,10}
<8> = {10,11}

Spectra Variation

Determined by the Distribution Spectra; this is the sum of all spectrum widths divided by the scale cardinality.

1.556

Maximally Even

A scale is maximally even if the tones are optimally spaced apart from each other.

no

Maximal Area Set

A scale is a maximal area set if a polygon described by vertices dodecimetrically placed around a circle produces the maximal interior area for scales of the same cardinality. All maximally even sets have maximal area, but not all maximal area sets are maximally even.

yes

Interior Area

Area of the polygon described by vertices placed for each tone of the scale dodecimetrically around a unit circle, ie a circle with radius of 1.

2.799

Polygon Perimeter

Perimeter of the polygon described by vertices placed for each tone of the scale dodecimetrically around a unit circle.

6.106

Myhill Property

A scale has Myhill Property if the Interval Spectra has exactly two specific intervals for every generic interval.

no

Balanced

A scale is balanced if the distribution of its tones would satisfy the "centrifuge problem", ie are placed such that it would balance on its centre point.

no

Ridge Tones

Ridge Tones are those that appear in all transpositions of a scale upon the members of that scale. Ridge Tones correspond directly with axes of reflective symmetry.

none

Propriety

Also known as Rothenberg Propriety, named after its inventor. Propriety describes whether every specific interval is uniquely mapped to a generic interval. A scale is either "Proper", "Strictly Proper", or "Improper".

Improper

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}442.07
E{4,8,11}342.47
F♯{6,10,1}242.47
A♯{10,2,5}442.2
Minor Triadsc♯m{1,4,8}342.33
fm{5,8,0}342.33
a♯m{10,1,5}442.07
bm{11,2,6}342.47
Augmented TriadsC+{0,4,8}342.4
D+{2,6,10}342.4
Diminished Triads{2,5,8}242.33
{5,8,11}242.67
g♯°{8,11,2}242.53
a♯°{10,1,4}242.47
{11,2,5}242.53
Parsimonious Voice Leading Between Common Triads of Scale 3447. Created by Ian Ring ©2019 C+ C+ c#m c#m C+->c#m E E C+->E fm fm C+->fm C# C# c#m->C# a#° a#° c#m->a#° C#->d° C#->fm a#m a#m C#->a#m A# A# d°->A# D+ D+ F# F# D+->F# D+->A# bm bm D+->bm E->f° g#° g#° E->g#° f°->fm F#->a#m g#°->bm a#°->a#m a#m->A# A#->b° b°->bm

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 3447 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 3771
Scale 3771: Stophygic, Ian Ring Music TheoryStophygic
3rd mode:
Scale 3933
Scale 3933: Ionidygic, Ian Ring Music TheoryIonidygic
4th mode:
Scale 2007
Scale 2007: Stonygic, Ian Ring Music TheoryStonygic
5th mode:
Scale 3051
Scale 3051: Stalygic, Ian Ring Music TheoryStalygic
6th mode:
Scale 3573
Scale 3573: Kaptygic, Ian Ring Music TheoryKaptygic
7th mode:
Scale 1917
Scale 1917: Sacrygic, Ian Ring Music TheorySacrygic
8th mode:
Scale 1503
Scale 1503: Padygic, Ian Ring Music TheoryPadygicThis is the prime mode
9th mode:
Scale 2799
Scale 2799: Epilygic, Ian Ring Music TheoryEpilygic

Prime

The prime form of this scale is Scale 1503

Scale 1503Scale 1503: Padygic, Ian Ring Music TheoryPadygic

Complement

The nonatonic modal family [3447, 3771, 3933, 2007, 3051, 3573, 1917, 1503, 2799] (Forte: 9-8) is the complement of the tritonic modal family [69, 321, 1041] (Forte: 3-8)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3447 is 3543

Scale 3543Scale 3543: Aeolonygic, Ian Ring Music TheoryAeolonygic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3447 is chiral, and its enantiomorph is scale 3543

Scale 3543Scale 3543: Aeolonygic, Ian Ring Music TheoryAeolonygic

Transformations:

T0 3447  T0I 3543
T1 2799  T1I 2991
T2 1503  T2I 1887
T3 3006  T3I 3774
T4 1917  T4I 3453
T5 3834  T5I 2811
T6 3573  T6I 1527
T7 3051  T7I 3054
T8 2007  T8I 2013
T9 4014  T9I 4026
T10 3933  T10I 3957
T11 3771  T11I 3819

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 3445Scale 3445: Messiaen Mode 6 Inverse, Ian Ring Music TheoryMessiaen Mode 6 Inverse
Scale 3443Scale 3443: Verdi's Scala Enigmatica, Ian Ring Music TheoryVerdi's Scala Enigmatica
Scale 3451Scale 3451: Garygic, Ian Ring Music TheoryGarygic
Scale 3455Scale 3455: Ryptyllian, Ian Ring Music TheoryRyptyllian
Scale 3431Scale 3431: Zyptyllic, Ian Ring Music TheoryZyptyllic
Scale 3439Scale 3439: Lythygic, Ian Ring Music TheoryLythygic
Scale 3415Scale 3415: Ionaptyllic, Ian Ring Music TheoryIonaptyllic
Scale 3383Scale 3383: Zoptyllic, Ian Ring Music TheoryZoptyllic
Scale 3511Scale 3511: Epolygic, Ian Ring Music TheoryEpolygic
Scale 3575Scale 3575: Symmetrical Decatonic, Ian Ring Music TheorySymmetrical Decatonic
Scale 3191Scale 3191: Bynyllic, Ian Ring Music TheoryBynyllic
Scale 3319Scale 3319: Tholygic, Ian Ring Music TheoryTholygic
Scale 3703Scale 3703: Katalygic, Ian Ring Music TheoryKatalygic
Scale 3959Scale 3959: Katagyllian, Ian Ring Music TheoryKatagyllian
Scale 2423Scale 2423, Ian Ring Music Theory
Scale 2935Scale 2935: Modygic, Ian Ring Music TheoryModygic
Scale 1399Scale 1399: Syryllic, Ian Ring Music TheorySyryllic

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.