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Modes of limited transposition

Modes of limited transposition are modes for which transpositions possibilities are limited. Unlike major scale that have 12 transpositions available, modes of limited transposition have less than 12 transpositions possibilities.

Modes of limited transposition have been theorized by the french composer Olivier Messiaen (1908 - 1992), and published in his book La technique de mon langage musical ("The Technique of my Musical Language").

The whole tone scale is one of the modes of limited transposition described by Olivier Messiaen but was already used before him.

Abbreviations used in this article:

minor 3rd : minor third
major 3rd : major third
united states of america W = Whole step / H = Half step
united kingdom T = Tone / S = Semitone

Messiaen's first mode (whole-tone scale)



Structure:
united states of america W - W - W - W - W
united kingdom T - T - T - T - T
Number of transpositions: 2

Messiaen's first mode is the whole tone scale, this mode has been use before by W.A. Mozart in Ein musikalischer SpaƟ (A joke musical) K. 522, Divertimento for 2 horns and string quartet:


Messiaen's second mode


Structure:
united states of america H - W - H - W - H - W - H
united kingdom S - T - S - T - S - T - S
Number of transpositions: 3


Messiaen's third mode


Structure:
united states of america W - H - H - W - H - H - W - H
united kingdom T - S - S - T - S - S - T - S
Number of transpositions: 4


Messiaen's fourth mode


Structure:
united states of america H - H - minor 3rd - H - H - H - minor 3rd
united kingdom S - S - 3 - S - S - S - 3
Number of transpositions: 6


Messiaen's fifth mode


Structure:
united states of america H - major 3rd - H - H - major 3rd
united kingdom S - major 3rd - S - S - major 3rd
Number of transpositions: 6


Messiaen's sixth mode


Structure:
united states of america W - W - H - H - W - W - H
united kingdom T - T - S - S - T - T - S
Number of transpositions: 6


Messiaen's seventh mode


Structure:
united states of america H - H - H - W - H - H - H - H - W
united kingdom S - S - S - T - S - S - S - S - T
Number of transpositions: 6


Summary of Messiaen's modes

Modeshalf steps
Semitones
Number of transpositions
first mode2 2 2 2 2 22
second mode1 2 1 2 1 2 1 23
third mode2 1 1 2 1 1 2 1 13
fourth mode1 1 3 1 1 1 3 14
fifth mode1 4 1 1 4 16
sixth mode2 2 1 1 2 2 1 16
seventh mode1 1 1 2 1 1 1 1 2 16

External links to learn more about:

1 - http://jacksonhardaker.github.io/Messiaen/
2 - https://en.wikipedia.org/wiki/Modes_of_limited_transposition



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