Temper is actually a little more complex than that. It stems from the oddity that if you set perfect intervals going up the scale, then perfect intervals coming down, you wind up with a slightly different note from where you started. Tempering is an attempt to deal with this remainder. If the error is distributed among all the intervening notes it's equal tempering. However, this seems to just make any key sound bad. The more common strategy is even tempering which distributes the error unevenly, assigning more of the error to keys that are used less frequently. That's why transposing a piece of music to a different key can make it sound different. If all things were equal, transposing a piece would make it just the same except at a higher or lower pitch. Because of the uneven distribution in even tempering the color of a piece can change in a different key. In modern times we've become accustomed enough to even temper that we hardly notice, but in the Baroque era they were much more sensitive and struggled with how to solve the problem. There some instruments made with multiple keys for the "same" note tuned for diffent keys so you could actually play the correct note in that key. Didn't turn out to be a very viable solution.
Originally Posted by topct
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