PostgreSQL interval division
As @a_horse_with_no_name mentions in his comment, division can be achieved by conversion to milliseconds.

SELECT 
  (1000*EXTRACT(EPOCH FROM tend - tstart) 
    + EXTRACT(MILLISECOND FROM tend - tstart))
  / (1000*EXTRACT(EPOCH FROM ticklength) 
    + EXTRACT(MILLISECOND FROM ticklength)) AS numticks
FROM recordings;