"The only way the answer of this question can be anything other than "no, it's infinite" is to set parameters on everything, and rule that interpretive differences do not make different songs, even if different notes are played (say there is a bend in a guitar solo, we have to say that a bend is a bend is a bend, as opposed to counting every possible frequency the string could bent to. We have to set a time limit, perhaps designate a set of scales, a minimum note duration, a maximum number of notes to be played at a time, limit dynamic markings, and so on. Very complicated.
However, there are limited note combinations that sound musical in a given culture (or even a musical genre... e.g. the common use of the "devil's interval" in metal music), so if you look at songwriting in a formulaic fashion, then yes, there are a finite set of MUSICAL note combinations. (Song formulas even provide convenient length parameters... 3-4 minutes for a pop song, etc.)
Regardless, there are many ways to look at this question."
This guy was really reaching... LOL!:
"-As this question depends on how long the song is I have written a rule at the bottom in which given the number of seconds measuring the duration of the song it is possible to calculate how many songs are possible in that period of time.
(The following numbers I work with are also theoretical but will give you a reasonable answer based on the human processing capabilities).
The human hearing range is 20Hz to 20000Hz.
Therefore range is 19980 (humans can't detect 10ths of hertz)
Humans can hear from 0.00 to 250.00(any greater and you're deaf) decibels
So that's 25,000 (for the loudness distinguishing)
25000 * 19980 = 499500000
Planck's time (smallest unit of time) is about 3.3 x 10-44 sec
so that would be about (1.64835 * 10^53)*seconds of duration = number of possible songs.
For 2 seconds there are a possible:
329,670,000,000,000,000,000,00 0,000,000,000,000,000,000,000, 000,000,000 songs possible, theoretically of course... "