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Scale 1949: "Mathyllic"

Scale 1949: Mathyllic, 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
Mathyllic

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

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

Forte Number

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

8-16

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: 1853

Hemitonia

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

5 (multihemitonic)

Cohemitonia

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

3 (tricohemitonic)

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: 943

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.

[2, 1, 1, 3, 1, 1, 1, 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.

<5, 5, 4, 5, 6, 3>

Interval Spectrum

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

p6m5n4s5d5t3

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

Spectra Variation

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

1.75

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.

2.616

Polygon Perimeter

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

6.002

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}331.67
D♯{3,7,10}341.89
G♯{8,0,3}331.67
Minor Triadscm{0,3,7}331.56
gm{7,10,2}152.67
am{9,0,4}252.33
Augmented TriadsC+{0,4,8}341.78
Diminished Triads{4,7,10}242
{9,0,3}242.22
Parsimonious Voice Leading Between Common Triads of Scale 1949. Created by Ian Ring ©2019 cm cm 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#->e° gm gm D#->gm 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.

Diameter5
Radius3
Self-Centeredno
Central Verticescm, C, G♯
Peripheral Verticesgm, am

Modes

Modes are the rotational transformation of this scale. Scale 1949 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 1511
Scale 1511: Styptyllic, Ian Ring Music TheoryStyptyllic
3rd mode:
Scale 2803
Scale 2803: Raga Bhatiyar, Ian Ring Music TheoryRaga Bhatiyar
4th mode:
Scale 3449
Scale 3449: Bacryllic, Ian Ring Music TheoryBacryllic
5th mode:
Scale 943
Scale 943: Aerygyllic, Ian Ring Music TheoryAerygyllicThis is the prime mode
6th mode:
Scale 2519
Scale 2519: Dathyllic, Ian Ring Music TheoryDathyllic
7th mode:
Scale 3307
Scale 3307: Boptyllic, Ian Ring Music TheoryBoptyllic
8th mode:
Scale 3701
Scale 3701: Bagyllic, Ian Ring Music TheoryBagyllic

Prime

The prime form of this scale is Scale 943

Scale 943Scale 943: Aerygyllic, Ian Ring Music TheoryAerygyllic

Complement

The octatonic modal family [1949, 1511, 2803, 3449, 943, 2519, 3307, 3701] (Forte: 8-16) is the complement of the tetratonic modal family [163, 389, 1121, 2129] (Forte: 4-16)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1949 is 1853

Scale 1853Scale 1853: Maryllic, Ian Ring Music TheoryMaryllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1949 is chiral, and its enantiomorph is scale 1853

Scale 1853Scale 1853: Maryllic, Ian Ring Music TheoryMaryllic

Transformations:

T0 1949  T0I 1853
T1 3898  T1I 3706
T2 3701  T2I 3317
T3 3307  T3I 2539
T4 2519  T4I 983
T5 943  T5I 1966
T6 1886  T6I 3932
T7 3772  T7I 3769
T8 3449  T8I 3443
T9 2803  T9I 2791
T10 1511  T10I 1487
T11 3022  T11I 2974

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 1951Scale 1951: Marygic, Ian Ring Music TheoryMarygic
Scale 1945Scale 1945: Zarian, Ian Ring Music TheoryZarian
Scale 1947Scale 1947: Byptyllic, Ian Ring Music TheoryByptyllic
Scale 1941Scale 1941: Aeranian, Ian Ring Music TheoryAeranian
Scale 1933Scale 1933: Mocrian, Ian Ring Music TheoryMocrian
Scale 1965Scale 1965: Raga Mukhari, Ian Ring Music TheoryRaga Mukhari
Scale 1981Scale 1981: Houseini, Ian Ring Music TheoryHouseini
Scale 2013Scale 2013: Mocrygic, Ian Ring Music TheoryMocrygic
Scale 1821Scale 1821: Aeradian, Ian Ring Music TheoryAeradian
Scale 1885Scale 1885: Saptyllic, Ian Ring Music TheorySaptyllic
Scale 1693Scale 1693: Dogian, Ian Ring Music TheoryDogian
Scale 1437Scale 1437: Sabach ascending, Ian Ring Music TheorySabach ascending
Scale 925Scale 925: Chromatic Hypodorian, Ian Ring Music TheoryChromatic Hypodorian
Scale 2973Scale 2973: Panyllic, Ian Ring Music TheoryPanyllic
Scale 3997Scale 3997: Dogygic, Ian Ring Music TheoryDogygic

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.