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Scale 2203: "Dorimic"

Scale 2203: Dorimic, 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
Dorimic

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

{0,1,3,4,7,11}

Forte Number

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

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: 2851

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

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.

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

Interval Spectrum

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

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

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}321
Minor Triadscm{0,3,7}221.2
em{4,7,11}221.2
Augmented TriadsD♯+{3,7,11}231.4
Diminished Triadsc♯°{1,4,7}131.6
Parsimonious Voice Leading Between Common Triads of Scale 2203. Created by Ian Ring ©2019 cm cm C C cm->C D#+ D#+ cm->D#+ c#° c#° C->c#° em em C->em D#+->em

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 Verticescm, C, em
Peripheral Verticesc♯°, D♯+

Modes

Modes are the rotational transformation of this scale. Scale 2203 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 3149
Scale 3149: Phrycrimic, Ian Ring Music TheoryPhrycrimic
3rd mode:
Scale 1811
Scale 1811: Kyptimic, Ian Ring Music TheoryKyptimic
4th mode:
Scale 2953
Scale 2953: Ionylimic, Ian Ring Music TheoryIonylimic
5th mode:
Scale 881
Scale 881: Aerothimic, Ian Ring Music TheoryAerothimic
6th mode:
Scale 311
Scale 311: Stagimic, Ian Ring Music TheoryStagimicThis is the prime mode

Prime

The prime form of this scale is Scale 311

Scale 311Scale 311: Stagimic, Ian Ring Music TheoryStagimic

Complement

The hexatonic modal family [2203, 3149, 1811, 2953, 881, 311] (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 2203 is 2851

Scale 2851Scale 2851: Katoptimic, Ian Ring Music TheoryKatoptimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2203 is chiral, and its enantiomorph is scale 2851

Scale 2851Scale 2851: Katoptimic, Ian Ring Music TheoryKatoptimic

Transformations:

T0 2203  T0I 2851
T1 311  T1I 1607
T2 622  T2I 3214
T3 1244  T3I 2333
T4 2488  T4I 571
T5 881  T5I 1142
T6 1762  T6I 2284
T7 3524  T7I 473
T8 2953  T8I 946
T9 1811  T9I 1892
T10 3622  T10I 3784
T11 3149  T11I 3473

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 2201Scale 2201: Ionagitonic, Ian Ring Music TheoryIonagitonic
Scale 2205Scale 2205: Ionocrimic, Ian Ring Music TheoryIonocrimic
Scale 2207Scale 2207: Mygian, Ian Ring Music TheoryMygian
Scale 2195Scale 2195: Zalitonic, Ian Ring Music TheoryZalitonic
Scale 2199Scale 2199: Dyptimic, Ian Ring Music TheoryDyptimic
Scale 2187Scale 2187: Ionothitonic, Ian Ring Music TheoryIonothitonic
Scale 2219Scale 2219: Phrydimic, Ian Ring Music TheoryPhrydimic
Scale 2235Scale 2235: Bathian, Ian Ring Music TheoryBathian
Scale 2267Scale 2267: Padian, Ian Ring Music TheoryPadian
Scale 2075Scale 2075, Ian Ring Music Theory
Scale 2139Scale 2139, Ian Ring Music Theory
Scale 2331Scale 2331: Dylimic, Ian Ring Music TheoryDylimic
Scale 2459Scale 2459: Ionocrian, Ian Ring Music TheoryIonocrian
Scale 2715Scale 2715: Kynian, Ian Ring Music TheoryKynian
Scale 3227Scale 3227: Aeolocrian, Ian Ring Music TheoryAeolocrian
Scale 155Scale 155, Ian Ring Music Theory
Scale 1179Scale 1179: Sonimic, Ian Ring Music TheorySonimic

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.