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I talk about this in my maths teaching blog: see the "How Many Tunes" post at

I used a very restricted musical space - just 2 bars, 12 notes (white notes from A below middle C to E an octave above), some constraints for musicality and restrictions on rhythm, and wrote a web app to explore (and listen to) the possibilities. It is at my website "The Mathenæum" at and is called "Computer Composer". The blog post links to it as well.

It's a lot of fun, and quite incredible how many tunes are possible. Here's the conclusion from the blog:

Adding these together, we have a total of 22 059 rhythms (from 3 notes to 16 notes), leading to more than 50 000 000 000 000 000 tunes (that’s 16 zeroes — 50 quadrillion!). Including harmonies, we end up with a final number of 2 300 000 000 000 000 000 songs (2.3 quintillion). And remember, these are not just random arrangements, but we have used rules to greatly increase the chance of a resulting tune sounding musical (matching harmony, starting on C etc).

That’s a lot of tunes! A very lot. So many that it’s actually quite difficult to imagine, but this might help.

- If we were to only keep one in every million songs (assuming the others are too similar or not musically interesting) we would still have more than 2 trillion songs in total.
- If we started composing in this way the very instant the universe began, writing one song every second right up until now, we would still be less than 20% through all the possibilities!
- If we printed out all the songs in a line, each song taking up 15cm, the length of paper would go from Earth to Proxima Centauri (the nearest star after the Sun — about 4.23 light years away) and back more than 4 times. That’s about 36 light years.


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