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Scale 287: "Gynimic"

Scale 287: Gynimic, 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
Gynimic

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

{0,1,2,3,4,8}

Forte Number

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

6-Z37

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.

[2]

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.

no

Hemitonia

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

4 (multihemitonic)

Cohemitonia

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

3 (tricohemitonic)

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.

yes

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.

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

Interval Spectrum

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

p2m3n2s3d4t

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

Spectra Variation

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

4

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.

1.866

Polygon Perimeter

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

5.535

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.

[4]

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 TriadsG♯{8,0,3}121
Minor Triadsc♯m{1,4,8}121
Augmented TriadsC+{0,4,8}210.67

The following pitch classes are not present in any of the common triads: {2}

Parsimonious Voice Leading Between Common Triads of Scale 287. Created by Ian Ring ©2019 C+ C+ c#m c#m C+->c#m G# G# C+->G#

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.

Diameter2
Radius1
Self-Centeredno
Central VerticesC+
Peripheral Verticesc♯m, G♯

Modes

Modes are the rotational transformation of this scale. Scale 287 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 2191
Scale 2191: Thydimic, Ian Ring Music TheoryThydimic
3rd mode:
Scale 3143
Scale 3143: Polimic, Ian Ring Music TheoryPolimic
4th mode:
Scale 3619
Scale 3619: Thanimic, Ian Ring Music TheoryThanimic
5th mode:
Scale 3857
Scale 3857: Ponimic, Ian Ring Music TheoryPonimic
6th mode:
Scale 497
Scale 497: Kadimic, Ian Ring Music TheoryKadimic

Prime

This is the prime form of this scale.

Complement

The hexatonic modal family [287, 2191, 3143, 3619, 3857, 497] (Forte: 6-Z37) is the complement of the hexatonic modal family [119, 1799, 2107, 2947, 3101, 3521] (Forte: 6-Z4)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 287 is 3857

Scale 3857Scale 3857: Ponimic, Ian Ring Music TheoryPonimic

Transformations:

T0 287  T0I 3857
T1 574  T1I 3619
T2 1148  T2I 3143
T3 2296  T3I 2191
T4 497  T4I 287
T5 994  T5I 574
T6 1988  T6I 1148
T7 3976  T7I 2296
T8 3857  T8I 497
T9 3619  T9I 994
T10 3143  T10I 1988
T11 2191  T11I 3976

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 285Scale 285: Zaritonic, Ian Ring Music TheoryZaritonic
Scale 283Scale 283: Aerylitonic, Ian Ring Music TheoryAerylitonic
Scale 279Scale 279: Poditonic, Ian Ring Music TheoryPoditonic
Scale 271Scale 271, Ian Ring Music Theory
Scale 303Scale 303: Golimic, Ian Ring Music TheoryGolimic
Scale 319Scale 319: Epodian, Ian Ring Music TheoryEpodian
Scale 351Scale 351: Epanian, Ian Ring Music TheoryEpanian
Scale 415Scale 415: Aeoladian, Ian Ring Music TheoryAeoladian
Scale 31Scale 31, Ian Ring Music Theory
Scale 159Scale 159, Ian Ring Music Theory
Scale 543Scale 543, Ian Ring Music Theory
Scale 799Scale 799: Lolian, Ian Ring Music TheoryLolian
Scale 1311Scale 1311: Bynian, Ian Ring Music TheoryBynian
Scale 2335Scale 2335: Epydian, Ian Ring Music TheoryEpydian

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.