Combinatorics And Music What's the likelihood that we'll run out of different songs to be able to make?
I know this seems like a difficult question to answer, possibly. But I was just wondering, and I thought of a scale of notes, and then the combinations of those notes. And I was wondering if there's enough  or will be enough music, to account for all of these combinations.
Since most songs sound a like now anyways.
Any ideas?
 A: Numbers like the "number of possible songs" are way, way larger that then number of people in the world times the number of seconds since the big bang, so, no, we will not run out of songs.
Suppose there are only 10 different notes, and songs can only be 100 notes long. Then there are $10^{100}$ possible "songs".  The universe is ~13 billion years old, so there are $13*10^9*86400*365 \approx 10^{17}$ seconds since the big bang. Multiplying by the population of the world, about 7 billion, brings us to $10^{27}$: if all the people in the world were alive since the big bang, and they all wrote one song every second since then, then they wouldn't even come close to the number of possible songs, even if we limited ourselves to the grossly oversimplified example of 100 note long songs, with only ten possible notes.
Come to think of it, there are only ~$10^{80}$ particles in the universe, so there's many billion songs for every particle.
A: You could try to be more precise and consider also the note durations. Its commom to consider the beats per minute(its like the heartbeat of music) and each note has its own duration, which gives you a fraction of one beat. The more commom durations are $\frac{1}{8},\frac{1}{6}, \frac{1}{4},\frac{1}{3}, \frac{1}{2}, 1, 2, 3, 4$ beats. Here you have 9 choices.
If you take this in account and use only one complete octave(12 notes), just for the first note you will have $9\cdot 12=108$ possibilities. If you want to compose a little melody, lets say, with 10 notes, then you have $108^{10}>100^{10}=10^{20}$ possibilities.
You could also consider the instruments, dynamics, special sound effects and more. 
It will take a long time until we run out of songs, that's my conclusion! 
