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Scale 1879: "Mixoryllic"

Scale 1879: Mixoryllic, 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
Mixoryllic
Dozenal
Likian

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

{0,1,2,4,6,8,9,10}

Forte Number

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

8-24

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.

4 (multihemitonic)

Cohemitonia

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

2 (dicohemitonic)

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.

4

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: 1399

Generator

Indicates if the scale can be constructed using a generator, and an origin.

none

Deep Scale

A deep scale is one where the interval vector has 6 different digits.

no

Interval Structure

Defines the scale as the sequence of intervals between one tone and the next.

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

<4, 6, 4, 7, 4, 3>

Interval Spectrum

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

p4m7n4s6d4t3

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

Spectra Variation

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

1.5

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.

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.

2.732

Polygon Perimeter

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

6.071

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

Heteromorphic Profile

Defined by Norman Carey (2002), the heteromorphic profile is an ordered triple of (c, a, d) where c is the number of contradictions, a is the number of ambiguities, and d is the number of differences. When c is zero, the scale is Proper. When a is also zero, the scale is Strictly Proper.

(4, 53, 126)

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}242.1
F♯{6,10,1}341.9
A{9,1,4}431.5
Minor Triadsc♯m{1,4,8}242.1
f♯m{6,9,1}431.5
am{9,0,4}341.9
Augmented TriadsC+{0,4,8}252.5
D+{2,6,10}252.5
Diminished Triadsf♯°{6,9,0}231.9
a♯°{10,1,4}231.9
Parsimonious Voice Leading Between Common Triads of Scale 1879. Created by Ian Ring ©2019 C+ C+ c#m c#m C+->c#m am am C+->am A A c#m->A D D D+ D+ D->D+ f#m f#m D->f#m F# F# D+->F# f#° f#° f#°->f#m f#°->am f#m->F# f#m->A a#° a#° F#->a#° am->A A->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 Verticesf♯°, f♯m, A, a♯°
Peripheral VerticesC+, D+

Modes

Modes are the rotational transformation of this scale. Scale 1879 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 2987
Scale 2987: Neapolitan Major and Minor Mixed, Ian Ring Music TheoryNeapolitan Major and Minor Mixed
3rd mode:
Scale 3541
Scale 3541: Racryllic, Ian Ring Music TheoryRacryllic
4th mode:
Scale 1909
Scale 1909: Epicryllic, Ian Ring Music TheoryEpicryllic
5th mode:
Scale 1501
Scale 1501: Stygyllic, Ian Ring Music TheoryStygyllic
6th mode:
Scale 1399
Scale 1399: Syryllic, Ian Ring Music TheorySyryllicThis is the prime mode
7th mode:
Scale 2747
Scale 2747: Stythyllic, Ian Ring Music TheoryStythyllic
8th mode:
Scale 3421
Scale 3421: Aerothyllic, Ian Ring Music TheoryAerothyllic

Prime

The prime form of this scale is Scale 1399

Scale 1399Scale 1399: Syryllic, Ian Ring Music TheorySyryllic

Complement

The octatonic modal family [1879, 2987, 3541, 1909, 1501, 1399, 2747, 3421] (Forte: 8-24) is the complement of the tetratonic modal family [277, 337, 1093, 1297] (Forte: 4-24)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1879 is 3421

Scale 3421Scale 3421: Aerothyllic, Ian Ring Music TheoryAerothyllic

Transformations:

In the abbreviation, the subscript number after "T" is the number of semitones of tranposition, "M" means the pitch class is multiplied by 5, and "I" means the result is inverted. Operation is an identical way to express the same thing; the syntax is <a,b> where each tone of the set x is transformed by the equation y = ax + b

Abbrev Operation Result Abbrev Operation Result
T0 <1,0> 1879       T0I <11,0> 3421
T1 <1,1> 3758      T1I <11,1> 2747
T2 <1,2> 3421      T2I <11,2> 1399
T3 <1,3> 2747      T3I <11,3> 2798
T4 <1,4> 1399      T4I <11,4> 1501
T5 <1,5> 2798      T5I <11,5> 3002
T6 <1,6> 1501      T6I <11,6> 1909
T7 <1,7> 3002      T7I <11,7> 3818
T8 <1,8> 1909      T8I <11,8> 3541
T9 <1,9> 3818      T9I <11,9> 2987
T10 <1,10> 3541      T10I <11,10> 1879
T11 <1,11> 2987      T11I <11,11> 3758
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 1909      T0MI <7,0> 1501
T1M <5,1> 3818      T1MI <7,1> 3002
T2M <5,2> 3541      T2MI <7,2> 1909
T3M <5,3> 2987      T3MI <7,3> 3818
T4M <5,4> 1879       T4MI <7,4> 3541
T5M <5,5> 3758      T5MI <7,5> 2987
T6M <5,6> 3421      T6MI <7,6> 1879
T7M <5,7> 2747      T7MI <7,7> 3758
T8M <5,8> 1399      T8MI <7,8> 3421
T9M <5,9> 2798      T9MI <7,9> 2747
T10M <5,10> 1501      T10MI <7,10> 1399
T11M <5,11> 3002      T11MI <7,11> 2798

The transformations that map this set to itself are: T0, T10I, T4M, T6MI

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 1877Scale 1877: Aeroptian, Ian Ring Music TheoryAeroptian
Scale 1875Scale 1875: Persichetti Scale, Ian Ring Music TheoryPersichetti Scale
Scale 1883Scale 1883: Lomian, Ian Ring Music TheoryLomian
Scale 1887Scale 1887: Aerocrygic, Ian Ring Music TheoryAerocrygic
Scale 1863Scale 1863: Pycrian, Ian Ring Music TheoryPycrian
Scale 1871Scale 1871: Aeolyllic, Ian Ring Music TheoryAeolyllic
Scale 1895Scale 1895: Salyllic, Ian Ring Music TheorySalyllic
Scale 1911Scale 1911: Messiaen Mode 3, Ian Ring Music TheoryMessiaen Mode 3
Scale 1815Scale 1815: Godian, Ian Ring Music TheoryGodian
Scale 1847Scale 1847: Thacryllic, Ian Ring Music TheoryThacryllic
Scale 1943Scale 1943: Luxian, Ian Ring Music TheoryLuxian
Scale 2007Scale 2007: Stonygic, Ian Ring Music TheoryStonygic
Scale 1623Scale 1623: Lothian, Ian Ring Music TheoryLothian
Scale 1751Scale 1751: Aeolyryllic, Ian Ring Music TheoryAeolyryllic
Scale 1367Scale 1367: Leading Whole-Tone Inverse, Ian Ring Music TheoryLeading Whole-Tone Inverse
Scale 855Scale 855: Porian, Ian Ring Music TheoryPorian
Scale 2903Scale 2903: Gothyllic, Ian Ring Music TheoryGothyllic
Scale 3927Scale 3927: Monygic, Ian Ring Music TheoryMonygic

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. All other diagrams and visualizations are © Ian Ring. 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, and George Howlett for assistance with the Carnatic ragas.