To get the usual BPM range for music of between 40 and 240 BPM, that corresponds to periods of 1500 ms and 200 ms respectively. A BPM of 120 is exactly 500 ms. As it is, the circuit would require an R4 of 14. 5 Mohm to yield a period of 500 ms (120 BPM). I need the value to be exactly 5K (10K pot in the center position). Here`s another version.
That string of parallel transistors provides a 4:1 ratio step-down current mirror so that resistors can be smaller. It also makes the control current relative to ground which is nice depending on how you power your op amp.