Why 78rpm, 45rpm, and 33.3rpm?

Does anyone know why these particular speeds were chosen for phono records? Early on there were 80rpm (one-sided) records, and 16 rpm was used for radio broadcast transcription and speech. I think that the CD sample rate 44.1 KHz has something to do with compatibility with movie frame rate. (The CD rpm varies as the disc plays so as to maintain a constant data rate).