Music theory games > Lessons > Pitch of sounds > Modes > Modes of limited transposition

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 3^rd : minor third
major 3^rd : major third
W = Whole step / H = Half step
T = Tone / S = Semitone

Messiaen's first mode (whole-tone scale)

Structure:
W - W - W - W - W
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 Spaß (A joke musical) K. 522, Divertimento for 2 horns and string quartet:

Messiaen's second mode

Structure:
H - W - H - W - H - W - H
S - T - S - T - S - T - S
Number of transpositions: 3

Messiaen's third mode

Structure:
W - H - H - W - H - H - W - H
T - S - S - T - S - S - T - S
Number of transpositions: 4

Messiaen's fourth mode

Structure:
H - H - minor 3^rd - H - H - H - minor 3^rd
S - S - 3 - S - S - S - 3
Number of transpositions: 6

Messiaen's fifth mode

Structure:
H - major 3^rd - H - H - major 3^rd
S - major 3^rd - S - S - major 3^rd
Number of transpositions: 6

Messiaen's sixth mode

Structure:
W - W - H - H - W - W - H
T - T - S - S - T - T - S
Number of transpositions: 6

Messiaen's seventh mode

Structure:
H - H - H - W - H - H - H - H - W
S - S - S - T - S - S - S - S - T
Number of transpositions: 6

Summary of Messiaen's modes

Modes	half steps Semitones	Number of transpositions
first mode	2 2 2 2 2 2	2
second mode	1 2 1 2 1 2 1 2	3
third mode	2 1 1 2 1 1 2 1 1	3
fourth mode	1 1 3 1 1 1 3 1	4
fifth mode	1 4 1 1 4 1	6
sixth mode	2 2 1 1 2 2 1 1	6
seventh mode	1 1 1 2 1 1 1 1 2 1	6

---

External links :

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

---