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Scale 1911: "Messiaen Mode 3"

Scale 1911: Messiaen Mode 3, 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

Messiaen
Messiaen Mode 3
Named After Composers
Tcherepnin Nonatonic Mode 3
Zeitler
Stynygic

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

{0,1,2,4,5,6,8,9,10}

Forte Number

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

9-12

Rotational Symmetry

Some scales have rotational symmetry, sometimes known as "limited transposition". If there are any rotational symmetries, these are the intervals of periodicity.

[4, 8]

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.

[1, 3, 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.

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.

3

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.

2

Prime Form

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

yes

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, 6, 6, 9, 6, 3]

Interval Spectrum

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

p6m9n6s6d6t3

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

Spectra Variation

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

0.667

Maximally Even

A scale is maximally even if the tones are optimally spaced apart from each other.

yes

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.

2.799

Polygon Perimeter

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

6.106

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.

yes

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.

[2,6,10]

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".

Proper

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♯{1,5,8}442.11
D{2,6,9}352.56
F{5,9,0}442.11
F♯{6,10,1}352.56
A{9,1,4}442.11
A♯{10,2,5}352.56
Minor Triadsc♯m{1,4,8}352.56
dm{2,5,9}442.11
fm{5,8,0}352.56
f♯m{6,9,1}442.11
am{9,0,4}352.56
a♯m{10,1,5}442.11
Augmented TriadsC+{0,4,8}363
C♯+{1,5,9}631.67
D+{2,6,10}363
Diminished Triads{2,5,8}242.56
f♯°{6,9,0}242.56
a♯°{10,1,4}242.56
Parsimonious Voice Leading Between Common Triads of Scale 1911. Created by Ian Ring ©2019 C+ C+ c#m c#m C+->c#m fm fm C+->fm am am C+->am C# C# c#m->C# A A c#m->A C#+ C#+ C#->C#+ C#->d° C#->fm dm dm C#+->dm F F C#+->F f#m f#m C#+->f#m C#+->A a#m a#m C#+->a#m d°->dm D D dm->D A# A# dm->A# D+ D+ D->D+ D->f#m F# F# D+->F# D+->A# fm->F f#° f#° F->f#° F->am f#°->f#m f#m->F# F#->a#m am->A a#° a#° A->a#° a#°->a#m a#m->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.

Diameter6
Radius3
Self-Centeredno
Central VerticesC♯+
Peripheral VerticesC+, D+

Modes

Modes are the rotational transformation of this scale. Scale 1911 can be rotated to make 2 other scales. The 1st mode is itself.

2nd mode:
Scale 3003
Scale 3003: Genus Chromaticum, Ian Ring Music TheoryGenus Chromaticum
3rd mode:
Scale 3549
Scale 3549: Messiaen Mode 3 Inverse, Ian Ring Music TheoryMessiaen Mode 3 Inverse

Prime

This is the prime form of this scale.

Complement

The nonatonic modal family [1911, 3003, 3549] (Forte: 9-12) is the complement of the tritonic modal family [273] (Forte: 3-12)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1911 is 3549

Scale 3549Scale 3549: Messiaen Mode 3 Inverse, Ian Ring Music TheoryMessiaen Mode 3 Inverse

Transformations:

T0 1911  T0I 3549
T1 3822  T1I 3003
T2 3549  T2I 1911
T3 3003  T3I 3822
T4 1911  T4I 3549
T5 3822  T5I 3003
T6 3549  T6I 1911
T7 3003  T7I 3822
T8 1911  T8I 3549
T9 3822  T9I 3003
T10 3549  T10I 1911
T11 3003  T11I 3822

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 1909Scale 1909: Epicryllic, Ian Ring Music TheoryEpicryllic
Scale 1907Scale 1907: Lynyllic, Ian Ring Music TheoryLynyllic
Scale 1915Scale 1915: Thydygic, Ian Ring Music TheoryThydygic
Scale 1919Scale 1919: Rocryllian, Ian Ring Music TheoryRocryllian
Scale 1895Scale 1895: Salyllic, Ian Ring Music TheorySalyllic
Scale 1903Scale 1903: Rocrygic, Ian Ring Music TheoryRocrygic
Scale 1879Scale 1879: Mixoryllic, Ian Ring Music TheoryMixoryllic
Scale 1847Scale 1847: Thacryllic, Ian Ring Music TheoryThacryllic
Scale 1975Scale 1975: Ionocrygic, Ian Ring Music TheoryIonocrygic
Scale 2039Scale 2039: Danyllian, Ian Ring Music TheoryDanyllian
Scale 1655Scale 1655: Katygyllic, Ian Ring Music TheoryKatygyllic
Scale 1783Scale 1783: Youlan Scale, Ian Ring Music TheoryYoulan Scale
Scale 1399Scale 1399: Syryllic, Ian Ring Music TheorySyryllic
Scale 887Scale 887: Sathyllic, Ian Ring Music TheorySathyllic
Scale 2935Scale 2935: Modygic, Ian Ring Music TheoryModygic
Scale 3959Scale 3959: Katagyllian, Ian Ring Music TheoryKatagyllian

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.