Can the level of pleasure derived from music be measured?

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.  

Thanks @macg19 . Glad it was useful to someone.

@simonmoon Sorry, it was told to me by an anthropologist when I was a grad student, IIRC. So no reference.

If you trust my memory!!