Hit-&false-alarm-rates: cases of undefined denominator I wish to apply SDT for an experiment whereby, while listening to a piece of music, subjects were asked to press a key when detecting a certain cue in the music. Based on the parts of the piece where the cue was actually present, it was simple enough to define each keypress as either a hit (filled dot) or as a false alarm (empty dot):

However, less clear is how to get to the hit- and false-alarm rates (HR, FAR) of each subject, since these imply dividing the total number of hits/false alarms by the total number of "signal present" and "signal absent" trials respectively.
The problem would be easier if the music (or: the time series of the keypresses) were discretised in time, but since it is continuous, my questions are:
1) For the FAR, since the number of "signal absent" trials is difficult to define (it's all the moments where a cue is NOT present in the music!), does it make sense to - as an approximation/compromise - divide instead by the total number of keypresses employed by the subject?
2) For the HR, is it correct to divide by the total number of cues that exist in the piece, since these are indeed all of the "signal present" moments in the timeseries?
3) As an even more non-orthodox SDT adaptation, does it make any sense to define both HR and FAR by diving by the same quantity, namely total number of keypresses?
 A: I am not an expert on SDT, but to me, a more natural solution is to divide the times when the cue is not active into segments with lengths comparable to that of the cues. Then each of those inactive segments can be considered a single "signal absent" trial. Also, each cue would be a single "signal present" trial with any number of keypresses treated as success.
Dividing by the number of total keypresses seems weird. Imagine two subjects A and B, each having pressed the key once when the cue was not present. But A has pressed the key twice for each cue, while B has pressed it only once for each cue. Would you say B has made twice as many mistakes?
More generally, it would make much more sense to think about the signal present/absent instances before collecting data. This could have let you to costumize the experimental setup for your needs. For example, if the cue was a specific chord, it could make sense to define each bar as an instance and always play the chord for a whole bar. 
Defining this part of analysis post-hoc means that your results are less reliable - how can you assure anybody (including yourself) that you didn't define the trial instances to make the data fit your preconcieved narrative?
