Can the level of pleasure derived from music be measured?

As it happens, there is a field of psychology called psychometrics that deals specifically with measuring subjective experience. It turns out that brain waves are rather crude for discerning small changes in one's experience. Better are rating scales targeting specific dimensions of perceptual experience. There are four dimensions: a) Valence (good vs bad), b) Potency (strong vs delicate), c) Arousal (relaxing vs stimulating), and d) Novelty (familiar vs. unfamiliar). All of our perceptions are really just a composite of these four factors much like all perceived colors are just a composite of red, green and blue (with a brightness factor thrown in).

I have used psychometrics professionally to measure all manner of perceptual experience including sound quality. Here it is important to note that there is a difference between the physical qualities of sound and the emotional qualities of sound. I always aim to correlate the two to reveal which physical qualities are most predictive of desired perceptions. Not all physical qualities are equally relevant, perceptually. Knowing the differences is what is important.

When I can close my eyes and the music keeps me enthralled, that’s what it’s all about to me. If something is keeping from that happy place, then the research starts on how to make it better.

By definition, a phenomenon is measured whenever numbers are attached to manifestations of that phenomenon.

Unfortunately, that process is amongst the most intellectually difficult enterprises known to man. The trouble is, everyone thinks he can do it.

Speaking crudely, there are four levels of measurement: nominal (in which different numbers represent different names), ordinal (in which bigger numbers represent relatively bigger effects), interval (in which the ordinal property holds and the difference between 1 and 2 is the same as the difference between 101 and 102), and ratio (in which the interval property holds and zero represents none of the property).

Each level of measurement determines which statistics are appropriate. Again unfortunately, as a former university statistics teacher, I can assure you that this is rarely taught, not even the crude and vastly oversimplified version above. This is a serious problem for society as a whole.

So yes, it can be easily done. Correctly done? Only a few could reasonably attempt it. Hint: if you've never heard of Hoelder's Representation Theorem, please don't bother.

Very difficult, unless you finesse the problem by tying your measurement to a known physical measure such as time.

An anthropologist set up a boom box in a jungle and invited some villagers to come and listen. When he played Mozart, they wept. When he played disposable music, they left.

All he had to do was measure the time it took for individuals to leave, and he would have solved the OP's problem.  

@terry9 cool and encouraging