Music Timing System

I’m attempting to create a metronome system so that I can trigger musical events at specific (and accurate) musical timings. With a view to creating a generative music generator.
Because we are extremely sensitive to timings within music this needs to be fairly accurate, but more importantly it needs to be consistent and that is the main problem I’m having at the moment…
So, lets say we are using a musical tempo of 120bpm, then every beat (pulse) would occur at 500ms intervals, and then common sub-divisions would be at 250ms and 125ms.
If the tick events were consistent then half a frame’s worth of ‘error’ in the timings may not be that noticeable at the larger interval times, but could become problematic as the intervals get smaller.
In a ideal world I would be able to fire off an event at a specific time interval, but using frame-based systems for timings means that you can’t do this as the ‘ideal’ time point may well fall between frames.

Does that make sense?