: Will there come a day when there is no more available music to write? For music, there is 12 notes, so I suppose one day every combination of notes will be used, and so there will be one day with no more music to create,

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People will always invent new means of expression in music. For example, when there is nothing more to write in C Major, then people will move on to another scale. When the timbres of our current instruments no longer satisfy, people will invent new instruments. Consider that the music of today has at least these dimensions:

Pitch. Notes are usually selected in different ways from one or more scales, of which there are hundreds of unique ones in 12 tone systems anyway.
Rhythm. Aside from all the possible subdivisions of 2,4,8,16,32 etc, you can subdivide by 3,5,7,9,11 and so on... You can also play any two (or more) rhythms simultaneously, or implying multiple simultaneous rhythms: so-called polyrhythms.
Timbre. Any note played on an acoustic instrument will have its own timbre, its character (essentially the structure of overtones) Consider a violin. Now compare it to a flute. Despite playing the same notes and rhythms, they can never sound the same. This is timbre.
Dynamics. This is, in its simplest definition, the difference in volume between notes. A simple concept, but effective when used well.

Now explore the space(=variety) possible with these dimensions (and more), and you will find it huge.
More appropriate would be to ask: "Will the universe last long enough for all possible music to be written?" If you ask me, i doubt it. If i remember correctly, Vsauce did a video on this, and the number of possible three minute songs turned out to have millions of digits.

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I like Richard's answer, and I think it can be stronger:

Definitely Not

There are not only 12 notes. In fact the four major components of music: pitch, timbre, loudness, and duration, are all continua, which means there are infinite possibilities for each component.

One piece that demonstrates the continuous nature of all of those components is Threnody For The Victims Of Hiroshima by Krzysztof Penderecki. Penderecki basically had to extend the existing notation system and invent new symbols in order to write down many of his pieces.

A person reading this answer might want to argue that organized sound like Penderecki's works aren't really "music", but if it's organized sound used to communicate an emotion that is performed and recorded by major symphony orchestras and discussed in university music theory and appreciation classes, how could it not be music?

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Technically, yes. If we assume a piece of music to have a finite length, then there is only a finite number of combinations of notesinstrumentspitchesrhythmstempietc. However, this yields a very large number of combinations.

Without getting too mathematical, here's an example. Imagine, for a particular piece of music of your choice, you can play each others' parts on different instruments, transpose the piece to another key, repeat certain bars, change the tempo, or any combination of anything!

Here's a good video on it.

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For music, there is 12 notes

Nicola Vincentino would beg to differ; he wrote music with 31 tones in an octave...in 1555! Plenty of composers since have used further divisions of the octave.

But let's do a little experiment with the combinatorics. There's a famous case that, in a 52-card deck, there are more possible shuffle orderings than there are atoms on the Earth. The likelihood that your shuffle has ever been done before is infinitesimally small (see a similar Math.SE question here). Put another way: statistically speaking, your individual shuffling is almost certainly the first time that ordering has ever occurred on Earth.

So that was just with 52 cards; now imagine the combinatorics of rhythm, meter, pitch, harmony, instrumentation, duration, articulation, timbre, dynamics, range, etc., etc. And when you go beyond 12 notes in an octave, it becomes even more extreme! Now imagine computer-generated music, in which it's possible to creates sounds impossible to create by humans...

I can't prove it mathematically---maybe try this on Math.SE?---but I bet you could prove that the combinations exceed the time remaining before the inevitable heat death of the universe. (...maybe this answer just got way too real for this site.)

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Well, you'd be right if there was an unlimited number of days and no combination of notes (not just pitches but also lengths, and arbitrary overlaps/chords) with probability zero. It turns out that the remaining number of days before the sun goes out is pitifully small compared to the combinatorics posed by compositions of reasonable length, and it is quite less than clear that a significant number of them will actually see humans occupied with composing music.

And of course you still have the classification problem: generating loads of "music" is a mathematical feat but figuring out the ones noteworthy of listening to is the actual work.