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Scale 1935: "Mycryllic"

Scale 1935: Mycryllic, 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
Mycryllic

Analysis

Cardinality

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

8 (octatonic)

Pitch Class Set

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

{0,1,2,3,7,8,9,10}

Forte Number

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

8-6

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.

[5]

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.

no

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.

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.

7

Prime Form

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

no
prime: 495

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, 5, 4, 4, 6, 3]

Interval Spectrum

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

p6m4n4s5d6t3

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

Spectra Variation

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

2.5

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.

2.366

Polygon Perimeter

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

5.838

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.

[10]

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}231.5
G♯{8,0,3}241.83
Minor Triadscm{0,3,7}231.5
gm{7,10,2}241.83
Diminished Triads{7,10,1}152.5
{9,0,3}152.5
Parsimonious Voice Leading Between Common Triads of Scale 1935. Created by Ian Ring ©2019 cm cm D# D# cm->D# G# G# cm->G# gm gm D#->gm g°->gm G#->a°

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.

Diameter5
Radius3
Self-Centeredno
Central Verticescm, D♯
Peripheral Verticesg°, a°

Modes

Modes are the rotational transformation of this scale. Scale 1935 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3015
Scale 3015: Laptyllic, Ian Ring Music TheoryLaptyllic
3rd mode:
Scale 3555
Scale 3555: Pylyllic, Ian Ring Music TheoryPylyllic
4th mode:
Scale 3825
Scale 3825: Pynyllic, Ian Ring Music TheoryPynyllic
5th mode:
Scale 495
Scale 495: Bocryllic, Ian Ring Music TheoryBocryllicThis is the prime mode
6th mode:
Scale 2295
Scale 2295: Kogyllic, Ian Ring Music TheoryKogyllic
7th mode:
Scale 3195
Scale 3195: Raryllic, Ian Ring Music TheoryRaryllic
8th mode:
Scale 3645
Scale 3645: Zycryllic, Ian Ring Music TheoryZycryllic

Prime

The prime form of this scale is Scale 495

Scale 495Scale 495: Bocryllic, Ian Ring Music TheoryBocryllic

Complement

The octatonic modal family [1935, 3015, 3555, 3825, 495, 2295, 3195, 3645] (Forte: 8-6) is the complement of the tetratonic modal family [135, 225, 2115, 3105] (Forte: 4-6)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1935 is 3645

Scale 3645Scale 3645: Zycryllic, Ian Ring Music TheoryZycryllic

Transformations:

T0 1935  T0I 3645
T1 3870  T1I 3195
T2 3645  T2I 2295
T3 3195  T3I 495
T4 2295  T4I 990
T5 495  T5I 1980
T6 990  T6I 3960
T7 1980  T7I 3825
T8 3960  T8I 3555
T9 3825  T9I 3015
T10 3555  T10I 1935
T11 3015  T11I 3870

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 1933Scale 1933: Mocrian, Ian Ring Music TheoryMocrian
Scale 1931Scale 1931: Stogian, Ian Ring Music TheoryStogian
Scale 1927Scale 1927, Ian Ring Music Theory
Scale 1943Scale 1943, Ian Ring Music Theory
Scale 1951Scale 1951: Marygic, Ian Ring Music TheoryMarygic
Scale 1967Scale 1967: Diatonic Dorian Mixed, Ian Ring Music TheoryDiatonic Dorian Mixed
Scale 1999Scale 1999: Zacrygic, Ian Ring Music TheoryZacrygic
Scale 1807Scale 1807, Ian Ring Music Theory
Scale 1871Scale 1871: Aeolyllic, Ian Ring Music TheoryAeolyllic
Scale 1679Scale 1679: Kydian, Ian Ring Music TheoryKydian
Scale 1423Scale 1423: Doptian, Ian Ring Music TheoryDoptian
Scale 911Scale 911: Radian, Ian Ring Music TheoryRadian
Scale 2959Scale 2959: Dygyllic, Ian Ring Music TheoryDygyllic
Scale 3983Scale 3983: Thyptygic, Ian Ring Music TheoryThyptygic

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.