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Scale 3535: "Mylygic"

Scale 3535: Mylygic, 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
Mylygic

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

{0,1,2,3,6,7,8,10,11}

Forte Number

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

9-4

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: 3703

Hemitonia

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

7 (multihemitonic)

Cohemitonia

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

5 (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.

2

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: 959

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.

[7, 6, 6, 7, 7, 3]

Interval Spectrum

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

p7m7n6s6d7t3

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

Spectra Variation

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

2

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.

2.683

Polygon Perimeter

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

6.038

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 TriadsD♯{3,7,10}332
F♯{6,10,1}263
G{7,11,2}431.87
G♯{8,0,3}263
B{11,3,6}442
Minor Triadscm{0,3,7}352.4
d♯m{3,6,10}342.2
gm{7,10,2}442.07
g♯m{8,11,3}352.4
bm{11,2,6}342.07
Augmented TriadsD+{2,6,10}452.27
D♯+{3,7,11}541.8
Diminished Triads{0,3,6}252.6
{7,10,1}252.8
g♯°{8,11,2}242.47
Parsimonious Voice Leading Between Common Triads of Scale 3535. Created by Ian Ring ©2019 cm cm c°->cm B B c°->B D#+ D#+ cm->D#+ G# G# cm->G# D+ D+ d#m d#m D+->d#m F# F# D+->F# gm gm D+->gm bm bm D+->bm D# D# d#m->D# d#m->B D#->D#+ D#->gm Parsimonious Voice Leading Between Common Triads of Scale 3535. Created by Ian Ring ©2019 G D#+->G g#m g#m D#+->g#m D#+->B F#->g° g°->gm gm->G g#° g#° G->g#° G->bm g#°->g#m g#m->G# bm->B

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.

Diameter6
Radius3
Self-Centeredno
Central VerticesD♯, G
Peripheral VerticesF♯, G♯

Modes

Modes are the rotational transformation of this scale. Scale 3535 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 3815
Scale 3815: Galygic, Ian Ring Music TheoryGalygic
3rd mode:
Scale 3955
Scale 3955: Pothygic, Ian Ring Music TheoryPothygic
4th mode:
Scale 4025
Scale 4025: Kalygic, Ian Ring Music TheoryKalygic
5th mode:
Scale 1015
Scale 1015: Ionodygic, Ian Ring Music TheoryIonodygic
6th mode:
Scale 2555
Scale 2555: Bythygic, Ian Ring Music TheoryBythygic
7th mode:
Scale 3325
Scale 3325: Mixolygic, Ian Ring Music TheoryMixolygic
8th mode:
Scale 1855
Scale 1855: Gaptygic, Ian Ring Music TheoryGaptygic
9th mode:
Scale 2975
Scale 2975: Aeroptygic, Ian Ring Music TheoryAeroptygic

Prime

The prime form of this scale is Scale 959

Scale 959Scale 959: Katylygic, Ian Ring Music TheoryKatylygic

Complement

The nonatonic modal family [3535, 3815, 3955, 4025, 1015, 2555, 3325, 1855, 2975] (Forte: 9-4) is the complement of the tritonic modal family [35, 385, 2065] (Forte: 3-4)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3535 is 3703

Scale 3703Scale 3703: Katalygic, Ian Ring Music TheoryKatalygic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3535 is chiral, and its enantiomorph is scale 3703

Scale 3703Scale 3703: Katalygic, Ian Ring Music TheoryKatalygic

Transformations:

T0 3535  T0I 3703
T1 2975  T1I 3311
T2 1855  T2I 2527
T3 3710  T3I 959
T4 3325  T4I 1918
T5 2555  T5I 3836
T6 1015  T6I 3577
T7 2030  T7I 3059
T8 4060  T8I 2023
T9 4025  T9I 4046
T10 3955  T10I 3997
T11 3815  T11I 3899

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 3533Scale 3533: Thadyllic, Ian Ring Music TheoryThadyllic
Scale 3531Scale 3531: Neveseri, Ian Ring Music TheoryNeveseri
Scale 3527Scale 3527: Ronyllic, Ian Ring Music TheoryRonyllic
Scale 3543Scale 3543: Aeolonygic, Ian Ring Music TheoryAeolonygic
Scale 3551Scale 3551: Sagyllian, Ian Ring Music TheorySagyllian
Scale 3567Scale 3567: Epityllian, Ian Ring Music TheoryEpityllian
Scale 3471Scale 3471: Gyryllic, Ian Ring Music TheoryGyryllic
Scale 3503Scale 3503: Zyphygic, Ian Ring Music TheoryZyphygic
Scale 3407Scale 3407: Katocryllic, Ian Ring Music TheoryKatocryllic
Scale 3279Scale 3279: Pythyllic, Ian Ring Music TheoryPythyllic
Scale 3791Scale 3791: Stodygic, Ian Ring Music TheoryStodygic
Scale 4047Scale 4047: Thogyllian, Ian Ring Music TheoryThogyllian
Scale 2511Scale 2511: Aeroptyllic, Ian Ring Music TheoryAeroptyllic
Scale 3023Scale 3023: Mothygic, Ian Ring Music TheoryMothygic
Scale 1487Scale 1487: Mothyllic, Ian Ring Music TheoryMothyllic

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.