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Scale 317: "Korimic"

Scale 317: Korimic, 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
Korimic
Dozenal
Cafian

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

{0,2,3,4,5,8}

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-Z39

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: 1937

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.

2 (dicohemitonic)

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

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.

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

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, 3, 3, 3, 2, 1>

Interval Spectrum

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

p2m3n3s3d3t

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

3.667

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.

(29, 19, 67)

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}131.5
Minor Triadsfm{5,8,0}221
Augmented TriadsC+{0,4,8}221
Diminished Triads{2,5,8}131.5
Parsimonious Voice Leading Between Common Triads of Scale 317. Created by Ian Ring ©2019 C+ C+ fm fm C+->fm G# G# C+->G# d°->fm

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 VerticesC+, fm
Peripheral Verticesd°, G♯

Modes

Modes are the rotational transformation of this scale. Scale 317 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 1103
Scale 1103: Lynimic, Ian Ring Music TheoryLynimic
3rd mode:
Scale 2599
Scale 2599: Malimic, Ian Ring Music TheoryMalimic
4th mode:
Scale 3347
Scale 3347: Synimic, Ian Ring Music TheorySynimic
5th mode:
Scale 3721
Scale 3721: Phragimic, Ian Ring Music TheoryPhragimic
6th mode:
Scale 977
Scale 977: Kocrimic, Ian Ring Music TheoryKocrimic

Prime

This is the prime form of this scale.

Complement

The hexatonic modal family [317, 1103, 2599, 3347, 3721, 977] (Forte: 6-Z39) is the complement of the hexatonic modal family [187, 1559, 1889, 2141, 2827, 3461] (Forte: 6-Z10)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 317 is 1937

Scale 1937Scale 1937: Galimic, Ian Ring Music TheoryGalimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 317 is chiral, and its enantiomorph is scale 1937

Scale 1937Scale 1937: Galimic, Ian Ring Music TheoryGalimic

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> 317       T0I <11,0> 1937
T1 <1,1> 634      T1I <11,1> 3874
T2 <1,2> 1268      T2I <11,2> 3653
T3 <1,3> 2536      T3I <11,3> 3211
T4 <1,4> 977      T4I <11,4> 2327
T5 <1,5> 1954      T5I <11,5> 559
T6 <1,6> 3908      T6I <11,6> 1118
T7 <1,7> 3721      T7I <11,7> 2236
T8 <1,8> 3347      T8I <11,8> 377
T9 <1,9> 2599      T9I <11,9> 754
T10 <1,10> 1103      T10I <11,10> 1508
T11 <1,11> 2206      T11I <11,11> 3016
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 1307      T0MI <7,0> 2837
T1M <5,1> 2614      T1MI <7,1> 1579
T2M <5,2> 1133      T2MI <7,2> 3158
T3M <5,3> 2266      T3MI <7,3> 2221
T4M <5,4> 437      T4MI <7,4> 347
T5M <5,5> 874      T5MI <7,5> 694
T6M <5,6> 1748      T6MI <7,6> 1388
T7M <5,7> 3496      T7MI <7,7> 2776
T8M <5,8> 2897      T8MI <7,8> 1457
T9M <5,9> 1699      T9MI <7,9> 2914
T10M <5,10> 3398      T10MI <7,10> 1733
T11M <5,11> 2701      T11MI <7,11> 3466

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 319Scale 319: Epodian, Ian Ring Music TheoryEpodian
Scale 313Scale 313: Goritonic, Ian Ring Music TheoryGoritonic
Scale 315Scale 315: Stodimic, Ian Ring Music TheoryStodimic
Scale 309Scale 309: Palitonic, Ian Ring Music TheoryPalitonic
Scale 301Scale 301: Raga Audav Tukhari, Ian Ring Music TheoryRaga Audav Tukhari
Scale 285Scale 285: Zaritonic, Ian Ring Music TheoryZaritonic
Scale 349Scale 349: Borimic, Ian Ring Music TheoryBorimic
Scale 381Scale 381: Kogian, Ian Ring Music TheoryKogian
Scale 445Scale 445: Gocrian, Ian Ring Music TheoryGocrian
Scale 61Scale 61: Ajuian, Ian Ring Music TheoryAjuian
Scale 189Scale 189: Befian, Ian Ring Music TheoryBefian
Scale 573Scale 573: Saptimic, Ian Ring Music TheorySaptimic
Scale 829Scale 829: Lygian, Ian Ring Music TheoryLygian
Scale 1341Scale 1341: Madian, Ian Ring Music TheoryMadian
Scale 2365Scale 2365: Sythian, Ian Ring Music TheorySythian

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.