Messiaens contribution to the development of music was similar to other 20th century composers insofar as he wanted to get away from functional harmony.

In this sense, he was trying to distance himself from the conventions of Bach, Rameau etc and create an alternative to the baroque concept of tonality.

It was this attempt to create alternative ways of organizing notes and harmony that led him to develop the modes of limited transposition.

If he had a problem with Jazz it was probably because most jazz uses functional harmony and ideas of tonality and key center are central to much jazz analysis and improvisation.

If this was his approach though, then he was being a bit unfair as there are definite overlaps between his work and some jazz theory, notably in the use of the whole tone scale and the diminished (octatonic - wholetone/semitone) scale, both of which are modes of limited transposition.

Messiaen would have made a great jazz musician as he had an amazing set of ears, with which he was able to hear up to 12 partials (harmonics - overtones) on any given note struck on a piano.

It was from these partials that he was able to construct the "chord of resonance", which is an 8 note chord built on the first 8 partials all condensed into a two octave range.

The chord is constructed using the following intervals

Major 3rd
minor 3rd
minor 3rd
Major 3rd
Major 3rd
Major 2nd
Major 2nd

So if C were in the bass, it would be spelt:

C, E, G, B flat, D, F#, G#, B natural.

Play it on the Piano - it sounds beautiful.