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Scale 2013: "Mocrygic"

Scale 2013: Mocrygic, 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
Mocrygic
Dozenal
MENIAN

Analysis

Cardinality

Cardinality is the count of how many pitches are in the scale.

9 (nonatonic)

Pitch Class Set

The tones in this scale, expressed as numbers from 0 to 11

{0,2,3,4,6,7,8,9,10}

Forte Number

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

9-8

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: 1917

Hemitonia

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

6 (multihemitonic)

Cohemitonia

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

4 (multicohemitonic)

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.

3

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.

8

Prime Form

Describes if this scale is in prime form, using the Rahn/Ring formula.

no
prime: 1503

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.

[6, 7, 6, 7, 6, 4]

Interval Spectrum

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

p6m7n6s7d6t4

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

Spectra Variation

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

1.556

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.

yes

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.

2.799

Polygon Perimeter

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

6.106

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}342.33
D{2,6,9}342.47
D♯{3,7,10}442.07
G♯{8,0,3}342.33
Minor Triadscm{0,3,7}442.07
d♯m{3,6,10}442.2
gm{7,10,2}242.47
am{9,0,4}342.47
Augmented TriadsC+{0,4,8}342.4
D+{2,6,10}342.4
Diminished Triads{0,3,6}242.33
d♯°{3,6,9}242.53
{4,7,10}242.47
f♯°{6,9,0}242.53
{9,0,3}242.67
Parsimonious Voice Leading Between Common Triads of Scale 2013. Created by Ian Ring ©2019 cm cm c°->cm d#m d#m c°->d#m C C cm->C D# D# cm->D# G# G# cm->G# C+ C+ C->C+ C->e° C+->G# am am C+->am D D D+ D+ D->D+ d#° d#° D->d#° f#° f#° D->f#° D+->d#m gm gm D+->gm d#°->d#m d#m->D# D#->e° D#->gm f#°->am G#->a° a°->am

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.

Diameter4
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 2013 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 1527
Scale 1527: Aeolyrygic, Ian Ring Music TheoryAeolyrygic
3rd mode:
Scale 2811
Scale 2811: Barygic, Ian Ring Music TheoryBarygic
4th mode:
Scale 3453
Scale 3453: Katarygic, Ian Ring Music TheoryKatarygic
5th mode:
Scale 1887
Scale 1887: Rechberger’s Decamode V, Ian Ring Music TheoryRechberger’s Decamode V
6th mode:
Scale 2991
Scale 2991: Zanygic, Ian Ring Music TheoryZanygic
7th mode:
Scale 3543
Scale 3543: Aeolonygic, Ian Ring Music TheoryAeolonygic
8th mode:
Scale 3819
Scale 3819: Aeolanygic, Ian Ring Music TheoryAeolanygic
9th mode:
Scale 3957
Scale 3957: Porygic, Ian Ring Music TheoryPorygic

Prime

The prime form of this scale is Scale 1503

Scale 1503Scale 1503: Padygic, Ian Ring Music TheoryPadygic

Complement

The nonatonic modal family [2013, 1527, 2811, 3453, 1887, 2991, 3543, 3819, 3957] (Forte: 9-8) is the complement of the tritonic modal family [69, 321, 1041] (Forte: 3-8)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2013 is 1917

Scale 1917Scale 1917: Sacrygic, Ian Ring Music TheorySacrygic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2013 is chiral, and its enantiomorph is scale 1917

Scale 1917Scale 1917: Sacrygic, Ian Ring Music TheorySacrygic

Transformations:

T0 2013  T0I 1917
T1 4026  T1I 3834
T2 3957  T2I 3573
T3 3819  T3I 3051
T4 3543  T4I 2007
T5 2991  T5I 4014
T6 1887  T6I 3933
T7 3774  T7I 3771
T8 3453  T8I 3447
T9 2811  T9I 2799
T10 1527  T10I 1503
T11 3054  T11I 3006

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 2015Scale 2015: Messiaen Mode 7, Ian Ring Music TheoryMessiaen Mode 7
Scale 2009Scale 2009: Stacryllic, Ian Ring Music TheoryStacryllic
Scale 2011Scale 2011: Raphygic, Ian Ring Music TheoryRaphygic
Scale 2005Scale 2005: Gygyllic, Ian Ring Music TheoryGygyllic
Scale 1997Scale 1997: Raga Cintamani, Ian Ring Music TheoryRaga Cintamani
Scale 2029Scale 2029: Kiourdi, Ian Ring Music TheoryKiourdi
Scale 2045Scale 2045: Katogyllian, Ian Ring Music TheoryKatogyllian
Scale 1949Scale 1949: Mathyllic, Ian Ring Music TheoryMathyllic
Scale 1981Scale 1981: Houseini, Ian Ring Music TheoryHouseini
Scale 1885Scale 1885: Epotyllic, Ian Ring Music TheoryEpotyllic
Scale 1757Scale 1757: Ionyphyllic, Ian Ring Music TheoryIonyphyllic
Scale 1501Scale 1501: Messiaen 3rd Mode, Ian Ring Music TheoryMessiaen 3rd Mode
Scale 989Scale 989: Phrolyllic, Ian Ring Music TheoryPhrolyllic
Scale 3037Scale 3037: Nine Tone Scale, Ian Ring Music TheoryNine Tone Scale
Scale 4061Scale 4061: Staptyllian, Ian Ring Music TheoryStaptyllian

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.