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Scale 2791: "Mixothyllic"

Scale 2791: Mixothyllic, 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
Mixothyllic

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

{0,1,2,5,6,7,9,11}

Forte Number

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

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: 3307

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.

[1, 1, 3, 1, 1, 2, 2, 1] 9

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 TriadsD{2,6,9}331.56
F{5,9,0}252.33
G{7,11,2}152.67
Minor Triadsdm{2,5,9}331.67
f♯m{6,9,1}331.67
bm{11,2,6}341.89
Augmented TriadsC♯+{1,5,9}341.78
Diminished Triadsf♯°{6,9,0}242.22
{11,2,5}242
Parsimonious Voice Leading Between Common Triads of Scale 2791. Created by Ian Ring ©2019 C#+ C#+ dm dm C#+->dm F F C#+->F f#m f#m C#+->f#m D D dm->D dm->b° D->f#m bm bm D->bm f#° f#° F->f#° f#°->f#m Parsimonious Voice Leading Between Common Triads of Scale 2791. Created by Ian Ring ©2019 G G->bm b°->bm

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 Verticesdm, D, f♯m
Peripheral VerticesF, G

Modes

Modes are the rotational transformation of this scale. Scale 2791 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3443
Scale 3443: Verdi's Scala Enigmatica, Ian Ring Music TheoryVerdi's Scala Enigmatica
3rd mode:
Scale 3769
Scale 3769: Eponyllic, Ian Ring Music TheoryEponyllic
4th mode:
Scale 983
Scale 983: Thocryllic, Ian Ring Music TheoryThocryllic
5th mode:
Scale 2539
Scale 2539: Half-Diminished Bebop, Ian Ring Music TheoryHalf-Diminished Bebop
6th mode:
Scale 3317
Scale 3317: Katynyllic, Ian Ring Music TheoryKatynyllic
7th mode:
Scale 1853
Scale 1853: Maryllic, Ian Ring Music TheoryMaryllic
8th mode:
Scale 1487
Scale 1487: Mothyllic, Ian Ring Music TheoryMothyllic

Prime

The prime form of this scale is Scale 943

Scale 943Scale 943: Aerygyllic, Ian Ring Music TheoryAerygyllic

Complement

The octatonic modal family [2791, 3443, 3769, 983, 2539, 3317, 1853, 1487] (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 2791 is 3307

Scale 3307Scale 3307: Boptyllic, Ian Ring Music TheoryBoptyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2791 is chiral, and its enantiomorph is scale 3307

Scale 3307Scale 3307: Boptyllic, Ian Ring Music TheoryBoptyllic

Transformations:

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

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 2789Scale 2789: Zolian, Ian Ring Music TheoryZolian
Scale 2787Scale 2787: Zyrian, Ian Ring Music TheoryZyrian
Scale 2795Scale 2795: Van der Horst Octatonic, Ian Ring Music TheoryVan der Horst Octatonic
Scale 2799Scale 2799: Epilygic, Ian Ring Music TheoryEpilygic
Scale 2807Scale 2807: Zylygic, Ian Ring Music TheoryZylygic
Scale 2759Scale 2759: Mela Pavani, Ian Ring Music TheoryMela Pavani
Scale 2775Scale 2775: Godyllic, Ian Ring Music TheoryGodyllic
Scale 2727Scale 2727: Mela Manavati, Ian Ring Music TheoryMela Manavati
Scale 2663Scale 2663: Lalian, Ian Ring Music TheoryLalian
Scale 2919Scale 2919: Molyllic, Ian Ring Music TheoryMolyllic
Scale 3047Scale 3047: Panygic, Ian Ring Music TheoryPanygic
Scale 2279Scale 2279: Dyrian, Ian Ring Music TheoryDyrian
Scale 2535Scale 2535: Messiaen Mode 4, Ian Ring Music TheoryMessiaen Mode 4
Scale 3303Scale 3303: Mylyllic, Ian Ring Music TheoryMylyllic
Scale 3815Scale 3815: Galygic, Ian Ring Music TheoryGalygic
Scale 743Scale 743: Chromatic Hypophrygian Inverse, Ian Ring Music TheoryChromatic Hypophrygian Inverse
Scale 1767Scale 1767: Dyryllic, Ian Ring Music TheoryDyryllic

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.