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Scale 3573: "Kaptygic"

Scale 3573: Kaptygic, 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

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
Kaptygic

Analysis

Cardinality

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

9 (enneatonic)

Pitch Class Set

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

{0,2,4,5,6,7,8,10,11}

Forte Number

A code assigned by theorist Allen 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: 1527

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 Formula

Defines the scale as the sequence of intervals between one tone and the next.

[2, 2, 1, 1, 1, 1, 2, 1, 1]

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 Hanson.

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{0,4,7}242.47
E{4,8,11}442.2
G{7,11,2}442.07
A♯{10,2,5}342.47
Minor Triadsem{4,7,11}442.07
fm{5,8,0}342.47
gm{7,10,2}342.33
bm{11,2,6}342.33
Augmented TriadsC+{0,4,8}342.4
D+{2,6,10}342.4
Diminished Triads{2,5,8}242.53
{4,7,10}242.47
{5,8,11}242.53
g♯°{8,11,2}242.33
{11,2,5}242.67
Parsimonious Voice Leading Between Common Triads of Scale 3573. Created by Ian Ring ©2019 C C C+ C+ C->C+ em em C->em E E C+->E fm fm C+->fm d°->fm A# A# d°->A# D+ D+ gm gm D+->gm D+->A# bm bm D+->bm e°->em e°->gm em->E Parsimonious Voice Leading Between Common Triads of Scale 3573. Created by Ian Ring ©2019 G em->G E->f° g#° g#° E->g#° f°->fm gm->G G->g#° G->bm 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.

Diameter4
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 3573 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 1917
Scale 1917: Sacrygic, Ian Ring Music TheorySacrygic
3rd mode:
Scale 1503
Scale 1503: Padygic, Ian Ring Music TheoryPadygicThis is the prime mode
4th mode:
Scale 2799
Scale 2799: Epilygic, Ian Ring Music TheoryEpilygic
5th mode:
Scale 3447
Scale 3447: Kynygic, Ian Ring Music TheoryKynygic
6th mode:
Scale 3771
Scale 3771: Stophygic, Ian Ring Music TheoryStophygic
7th mode:
Scale 3933
Scale 3933: Ionidygic, Ian Ring Music TheoryIonidygic
8th mode:
Scale 2007
Scale 2007: Stonygic, Ian Ring Music TheoryStonygic
9th mode:
Scale 3051
Scale 3051: Stalygic, Ian Ring Music TheoryStalygic

Prime

The prime form of this scale is Scale 1503

Scale 1503Scale 1503: Padygic, Ian Ring Music TheoryPadygic

Complement

The enneatonic modal family [3573, 1917, 1503, 2799, 3447, 3771, 3933, 2007, 3051] (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 3573 is 1527

Scale 1527Scale 1527: Aeolyrigic, Ian Ring Music TheoryAeolyrigic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3573 is chiral, and its enantiomorph is scale 1527

Scale 1527Scale 1527: Aeolyrigic, Ian Ring Music TheoryAeolyrigic

Transformations:

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

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 3575Scale 3575: Symmetrical Decatonic, Ian Ring Music TheorySymmetrical Decatonic
Scale 3569Scale 3569: Aeoladyllic, Ian Ring Music TheoryAeoladyllic
Scale 3571Scale 3571: Dyrygic, Ian Ring Music TheoryDyrygic
Scale 3577Scale 3577: Loptygic, Ian Ring Music TheoryLoptygic
Scale 3581Scale 3581: Epocryllian, Ian Ring Music TheoryEpocryllian
Scale 3557Scale 3557, Ian Ring Music Theory
Scale 3565Scale 3565: Aeolorygic, Ian Ring Music TheoryAeolorygic
Scale 3541Scale 3541: Racryllic, Ian Ring Music TheoryRacryllic
Scale 3509Scale 3509: Stogyllic, Ian Ring Music TheoryStogyllic
Scale 3445Scale 3445: Messiaen Mode 6 Inverse, Ian Ring Music TheoryMessiaen Mode 6 Inverse
Scale 3317Scale 3317: Katynyllic, Ian Ring Music TheoryKatynyllic
Scale 3829Scale 3829: Taishikicho, Ian Ring Music TheoryTaishikicho
Scale 4085Scale 4085: Rechberger's Decamode, Ian Ring Music TheoryRechberger's Decamode
Scale 2549Scale 2549: Rydyllic, Ian Ring Music TheoryRydyllic
Scale 3061Scale 3061: Apinygic, Ian Ring Music TheoryApinygic
Scale 1525Scale 1525: Sodyllic, Ian Ring Music TheorySodyllic

This scale analysis was created by Ian Ring, Canadian Composer of works for Piano, and total music theory nerd. 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.