After starting a discussion on cadences in modal music on VirtualArtists.com, the subject at some point turned into a discussion of elements of the musical language of Olivier Messiaen (notably his "modes of limited transposition").
After listening to and reading a bit about Messiaen's musical language I was intrigued enough to try and find out why and how his modes work so well with us, the listeners. I wanted to see if there are some things about his modes that are not present in other scales or modes used for musical composition.
I believe I came up with some fascinating insights (if not necessarily new ones? I haven't checked).I've written up my insights so far and if the subject interests you, perhaps you might want to take a peek at the document. It uses some basic mathematics, but everything you need to know to follow the document is explained in a hopefully understandable language.
Comments and especially criticisms are welcome! Also don't be frightened by the length of the document (27 pages so far). The length is caused mostly by the many appendices :)
The current version of the document is attached here in .pdf form. The document itself contains instructions for where to get the latest version of the document, since this represents a work in progress, and also for people who want to reproduce all the results contained therein (this may be a bit difficult if you haven't got any experience with software development).
The latest version of the document should always be available from this link: Link to latest version of .pdf document.