I'm assuming that "nicest" in this case means "consonant". 7 is OK ish, but not good enough for us apparently.Įdit: The other answers do an excellent job of describing the difference between pythagorean and tempered tuning systems and the related maths, so this answer is to add additional information regarding the other part of the question as well as a followup answer the original poster added. After that the next one that's really good is 31, and like how many keys do you want man. The next one that works well is 19 but it's not really better. Why 12? Because it's the first low number where the numbers work out nice and close to "just" intervals, like 3:2 (1.5) 4:3 (1.333.) 5:4 (1.25) 5:3 (1.666) etc. On modern keyboards we take this difference and spread it out between all 12 notes, so each fifth is made just a tiny bit narrower, but after 12 of them, you end up exactly where you started. On old keyboards you would have 11 perfect fifths, and one fifth called the "wolf fifth" that was out of tune but got you to where you needed to be. This difference is not small, it's about a quarter of a semitone. if you stack 12 tempered fifths on top of each other, you will be at a note 128 times higher than the start, or exactly 7 octaves up. which sounds almost exactly like 1.5 but it's cleverer. The existing answer does a good job of explaining that it's because of equal temperament, but as to why we use equal temperament, an equal temperament fifth is 1.4983.
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