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Scale 571: "Kynimic"

Scale 571: Kynimic, 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
Kynimic
Dozenal
Difian

Analysis

Cardinality

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

6 (hexatonic)

Pitch Class Set

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

{0,1,3,4,5,9}

Forte Number

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

6-15

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: 2953

Hemitonia

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

3 (trihemitonic)

Cohemitonia

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

1 (uncohemitonic)

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.

4

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.

5

Prime Form

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

no
prime: 311

Generator

Indicates if the scale can be constructed using a generator, and an origin.

none

Deep Scale

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

no

Interval Structure

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

[1, 2, 1, 1, 4, 3]

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.

<3, 2, 3, 4, 2, 1>

Interval Spectrum

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

p2m4n3s2d3t

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

Spectra Variation

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

3.333

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.

no

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.

2.116

Polygon Perimeter

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

5.699

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

Heteromorphic Profile

Defined by Norman Carey (2002), the heteromorphic profile is an ordered triple of (c, a, d) where c is the number of contradictions, a is the number of ambiguities, and d is the number of differences. When c is zero, the scale is Proper. When a is also zero, the scale is Strictly Proper.

(21, 18, 64)

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 TriadsF{5,9,0}221.2
A{9,1,4}221.2
Minor Triadsam{9,0,4}321
Augmented TriadsC♯+{1,5,9}231.4
Diminished Triads{9,0,3}131.6
Parsimonious Voice Leading Between Common Triads of Scale 571. Created by Ian Ring ©2019 C#+ C#+ F F C#+->F A A C#+->A am am F->am a°->am am->A

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.

Diameter3
Radius2
Self-Centeredno
Central VerticesF, am, A
Peripheral VerticesC♯+, a°

Modes

Modes are the rotational transformation of this scale. Scale 571 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 2333
Scale 2333: Stynimic, Ian Ring Music TheoryStynimic
3rd mode:
Scale 1607
Scale 1607: Epytimic, Ian Ring Music TheoryEpytimic
4th mode:
Scale 2851
Scale 2851: Katoptimic, Ian Ring Music TheoryKatoptimic
5th mode:
Scale 3473
Scale 3473: Lathimic, Ian Ring Music TheoryLathimic
6th mode:
Scale 473
Scale 473: Aeralimic, Ian Ring Music TheoryAeralimic

Prime

The prime form of this scale is Scale 311

Scale 311Scale 311: Stagimic, Ian Ring Music TheoryStagimic

Complement

The hexatonic modal family [571, 2333, 1607, 2851, 3473, 473] (Forte: 6-15) is the complement of the hexatonic modal family [311, 881, 1811, 2203, 2953, 3149] (Forte: 6-15)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 571 is 2953

Scale 2953Scale 2953: Ionylimic, Ian Ring Music TheoryIonylimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 571 is chiral, and its enantiomorph is scale 2953

Scale 2953Scale 2953: Ionylimic, Ian Ring Music TheoryIonylimic

Transformations:

In the abbreviation, the subscript number after "T" is the number of semitones of tranposition, "M" means the pitch class is multiplied by 5, and "I" means the result is inverted. Operation is an identical way to express the same thing; the syntax is <a,b> where each tone of the set x is transformed by the equation y = ax + b

Abbrev Operation Result Abbrev Operation Result
T0 <1,0> 571       T0I <11,0> 2953
T1 <1,1> 1142      T1I <11,1> 1811
T2 <1,2> 2284      T2I <11,2> 3622
T3 <1,3> 473      T3I <11,3> 3149
T4 <1,4> 946      T4I <11,4> 2203
T5 <1,5> 1892      T5I <11,5> 311
T6 <1,6> 3784      T6I <11,6> 622
T7 <1,7> 3473      T7I <11,7> 1244
T8 <1,8> 2851      T8I <11,8> 2488
T9 <1,9> 1607      T9I <11,9> 881
T10 <1,10> 3214      T10I <11,10> 1762
T11 <1,11> 2333      T11I <11,11> 3524
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 811      T0MI <7,0> 2713
T1M <5,1> 1622      T1MI <7,1> 1331
T2M <5,2> 3244      T2MI <7,2> 2662
T3M <5,3> 2393      T3MI <7,3> 1229
T4M <5,4> 691      T4MI <7,4> 2458
T5M <5,5> 1382      T5MI <7,5> 821
T6M <5,6> 2764      T6MI <7,6> 1642
T7M <5,7> 1433      T7MI <7,7> 3284
T8M <5,8> 2866      T8MI <7,8> 2473
T9M <5,9> 1637      T9MI <7,9> 851
T10M <5,10> 3274      T10MI <7,10> 1702
T11M <5,11> 2453      T11MI <7,11> 3404

The transformations that map this set to itself are: T0

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 569Scale 569: Mothitonic, Ian Ring Music TheoryMothitonic
Scale 573Scale 573: Saptimic, Ian Ring Music TheorySaptimic
Scale 575Scale 575: Ionydian, Ian Ring Music TheoryIonydian
Scale 563Scale 563: Thacritonic, Ian Ring Music TheoryThacritonic
Scale 567Scale 567: Aeoladimic, Ian Ring Music TheoryAeoladimic
Scale 555Scale 555: Aeolycritonic, Ian Ring Music TheoryAeolycritonic
Scale 539Scale 539: Delian, Ian Ring Music TheoryDelian
Scale 603Scale 603: Aeolygimic, Ian Ring Music TheoryAeolygimic
Scale 635Scale 635: Epolian, Ian Ring Music TheoryEpolian
Scale 699Scale 699: Aerothian, Ian Ring Music TheoryAerothian
Scale 827Scale 827: Mixolocrian, Ian Ring Music TheoryMixolocrian
Scale 59Scale 59: Ahuian, Ian Ring Music TheoryAhuian
Scale 315Scale 315: Stodimic, Ian Ring Music TheoryStodimic
Scale 1083Scale 1083: Goyian, Ian Ring Music TheoryGoyian
Scale 1595Scale 1595: Dacrian, Ian Ring Music TheoryDacrian
Scale 2619Scale 2619: Ionyrian, Ian Ring Music TheoryIonyrian

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. All other diagrams and visualizations are © Ian Ring. 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, and George Howlett for assistance with the Carnatic ragas.