Olivier Messiaen - a closer look at his modes of limited transposition

Olivier who?

Olivier Messiaen was a French composer (December 10, 1908 – April 27, 1992), known for inventing a new musical language. He wrote a book about his ideas on rhythm, melody and harmony and is generally regarded as one of the great innovators in music. He drew inspiration mostly from his Christian beliefs and from bird songs. I personally fell in love with this musical language after hearing his work "Vingt Regards sur l'Enfant-Jésus".


One key element of his compositions is a set of scales that he "invented" (or rather, selected from the vast space of possible scales). They consist of symmetrical note groups. While writing music he would often adhere to using only notes from one or more of his scales, leading to special music (with very rewarding harmonies).

I was curious about these special scales and wondered about the mechanisms that cause the scales to "work so well" with a listener, so
I set up my own private investigation and took a close look at his scales.
I discovered quite a number of interesting things (which may be known already in literature, I don't want to claim I found something new, but they were certainly new to me)

I've written up what I came up with so far and put it online on github. The pdf can be seen here: https://github.com/shimpe/mints/blob/master/out/document.pdf?raw=true . All the code required to reconstruct the article is available here https://github.com/shimpe/mints:

Feel free to contact me with questions or remarks about this document.