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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

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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

Cardinality9 (nonatonic)
Pitch Class Set{0,1,2,4,5,6,8,9,10}
Forte Number9-12
Rotational Symmetry4, 8 semitones
Reflection Axes1, 3, 5
Palindromicno
Chiralityno
Hemitonia6 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections3
Modes2
Prime?yes
Deep Scaleno
Interval Vector666963
Interval Spectrump6m9n6s6d6t3
Distribution Spectra<1> = {1,2}
<2> = {2,3}
<3> = {4}
<4> = {5,6}
<5> = {6,7}
<6> = {8}
<7> = {9,10}
<8> = {10,11}
Spectra Variation0.667
Maximally Evenyes
Maximal Area Setyes
Interior Area2.799
Myhill Propertyno
Balancedyes
Ridge Tones[2,6,10]
ProprietyProper
Heliotonicno

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.