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Scale 1303: "Epolimic"

Scale 1303: Epolimic, 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
Epolimic

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

{0,1,2,4,8,10}

Forte Number

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

6-21

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: 3349

Hemitonia

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

2 (dihemitonic)

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.

5

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: 349

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, 2, 4, 2, 2]

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.

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

Interval Spectrum

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

pm4n2s4d2t2

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

Spectra Variation

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

3

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.

2.232

Polygon Perimeter

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

5.767

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
Minor Triadsc♯m{1,4,8}210.67
Augmented TriadsC+{0,4,8}121
Diminished Triadsa♯°{10,1,4}121

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

Parsimonious Voice Leading Between Common Triads of Scale 1303. Created by Ian Ring ©2019 C+ C+ c#m c#m C+->c#m a#° a#° c#m->a#°

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♯m
Peripheral VerticesC+, a♯°

Modes

Modes are the rotational transformation of this scale. Scale 1303 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 2699
Scale 2699: Sythimic, Ian Ring Music TheorySythimic
3rd mode:
Scale 3397
Scale 3397: Sydimic, Ian Ring Music TheorySydimic
4th mode:
Scale 1873
Scale 1873: Dathimic, Ian Ring Music TheoryDathimic
5th mode:
Scale 373
Scale 373: Epagimic, Ian Ring Music TheoryEpagimic
6th mode:
Scale 1117
Scale 1117: Raptimic, Ian Ring Music TheoryRaptimic

Prime

The prime form of this scale is Scale 349

Scale 349Scale 349: Borimic, Ian Ring Music TheoryBorimic

Complement

The hexatonic modal family [1303, 2699, 3397, 1873, 373, 1117] (Forte: 6-21) is the complement of the hexatonic modal family [349, 1111, 1489, 1861, 2603, 3349] (Forte: 6-21)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1303 is 3349

Scale 3349Scale 3349: Aeolocrimic, Ian Ring Music TheoryAeolocrimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1303 is chiral, and its enantiomorph is scale 3349

Scale 3349Scale 3349: Aeolocrimic, Ian Ring Music TheoryAeolocrimic

Transformations:

T0 1303  T0I 3349
T1 2606  T1I 2603
T2 1117  T2I 1111
T3 2234  T3I 2222
T4 373  T4I 349
T5 746  T5I 698
T6 1492  T6I 1396
T7 2984  T7I 2792
T8 1873  T8I 1489
T9 3746  T9I 2978
T10 3397  T10I 1861
T11 2699  T11I 3722

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 1301Scale 1301: Koditonic, Ian Ring Music TheoryKoditonic
Scale 1299Scale 1299: Aerophitonic, Ian Ring Music TheoryAerophitonic
Scale 1307Scale 1307: Katorimic, Ian Ring Music TheoryKatorimic
Scale 1311Scale 1311: Bynian, Ian Ring Music TheoryBynian
Scale 1287Scale 1287, Ian Ring Music Theory
Scale 1295Scale 1295, Ian Ring Music Theory
Scale 1319Scale 1319: Phronimic, Ian Ring Music TheoryPhronimic
Scale 1335Scale 1335: Elephant Scale, Ian Ring Music TheoryElephant Scale
Scale 1367Scale 1367: Leading Whole-Tone Inverse, Ian Ring Music TheoryLeading Whole-Tone Inverse
Scale 1431Scale 1431: Phragian, Ian Ring Music TheoryPhragian
Scale 1047Scale 1047, Ian Ring Music Theory
Scale 1175Scale 1175: Epycrimic, Ian Ring Music TheoryEpycrimic
Scale 1559Scale 1559, Ian Ring Music Theory
Scale 1815Scale 1815: Godian, Ian Ring Music TheoryGodian
Scale 279Scale 279: Poditonic, Ian Ring Music TheoryPoditonic
Scale 791Scale 791: Aeoloptimic, Ian Ring Music TheoryAeoloptimic
Scale 2327Scale 2327: Epalimic, Ian Ring Music TheoryEpalimic
Scale 3351Scale 3351: Crater Scale, Ian Ring Music TheoryCrater Scale

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.