This one's challenging. I hear a first section in straight 4/4, then a long midsection in 15/16 and then a last section combining one bar in 13/16 and one in 7/8.
A music teacher of mine introduced a concept to me called "retroactive listening", which is the idea of perceiving something in a different way after hearing what comes after it. Often he referred to it in the context of harmonic progressions, but I think this is highly applicable here to your rhythmic material in the first part, where I first perceived it like 4/4 but when the melody got out of phase I was getting more and more doubtful of my preconceptions of your initial time signature. ;)