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Scale 2191: "Thydimic"

Scale 2191: Thydimic, 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
Thydimic

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

{0,1,2,3,7,11}

Forte Number

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

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.

[1]

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.

no
prime: 287

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.

[1, 1, 1, 4, 4, 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.

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

Interval Spectrum

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

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.

[2]

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{7,11,2}121
Minor Triadscm{0,3,7}121
Augmented TriadsD♯+{3,7,11}210.67

The following pitch classes are not present in any of the common triads: {1}

Parsimonious Voice Leading Between Common Triads of Scale 2191. Created by Ian Ring ©2019 cm cm D#+ D#+ cm->D#+ Parsimonious Voice Leading Between Common Triads of Scale 2191. Created by Ian Ring ©2019 G D#+->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 VerticesD♯+
Peripheral Verticescm, G

Modes

Modes are the rotational transformation of this scale. Scale 2191 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 3143
Scale 3143: Polimic, Ian Ring Music TheoryPolimic
3rd mode:
Scale 3619
Scale 3619: Thanimic, Ian Ring Music TheoryThanimic
4th mode:
Scale 3857
Scale 3857: Ponimic, Ian Ring Music TheoryPonimic
5th mode:
Scale 497
Scale 497: Kadimic, Ian Ring Music TheoryKadimic
6th mode:
Scale 287
Scale 287: Gynimic, Ian Ring Music TheoryGynimicThis is the prime mode

Prime

The prime form of this scale is Scale 287

Scale 287Scale 287: Gynimic, Ian Ring Music TheoryGynimic

Complement

The hexatonic modal family [2191, 3143, 3619, 3857, 497, 287] (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 2191 is 3619

Scale 3619Scale 3619: Thanimic, Ian Ring Music TheoryThanimic

Transformations:

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

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 2189Scale 2189: Zagitonic, Ian Ring Music TheoryZagitonic
Scale 2187Scale 2187: Ionothitonic, Ian Ring Music TheoryIonothitonic
Scale 2183Scale 2183, Ian Ring Music Theory
Scale 2199Scale 2199: Dyptimic, Ian Ring Music TheoryDyptimic
Scale 2207Scale 2207: Mygian, Ian Ring Music TheoryMygian
Scale 2223Scale 2223: Konian, Ian Ring Music TheoryKonian
Scale 2255Scale 2255: Dylian, Ian Ring Music TheoryDylian
Scale 2063Scale 2063: Pentatonic Chromatic 2, Ian Ring Music TheoryPentatonic Chromatic 2
Scale 2127Scale 2127, Ian Ring Music Theory
Scale 2319Scale 2319, Ian Ring Music Theory
Scale 2447Scale 2447: Thagian, Ian Ring Music TheoryThagian
Scale 2703Scale 2703: Galian, Ian Ring Music TheoryGalian
Scale 3215Scale 3215: Katydian, Ian Ring Music TheoryKatydian
Scale 143Scale 143, Ian Ring Music Theory
Scale 1167Scale 1167: Aerodimic, Ian Ring Music TheoryAerodimic

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.