On 2 Dec 2014 at 9:11, James Propp wrote:
That is some great popular mathematical writing, in my opinion!
And another aspect is that you *can* "perfectly" tune, but only in a limited domain of notes (for example, f# and gflat are different, and so you can't have both0. When we had a harpsichord, there were many medieval works that sounded quite different when we used "simple" tuning [I think it was called "just" tuning or something like that] versus "well tempered" [which is standard tuning]. I remember learing that to properly tune the harpsichord, when you tuned "G" against "C", you first got the perfect fifth, and then you flattened it a bit [I think you listened for something like five beats per second or the like] and did the same as you worked your way up. /bernie\ -- Bernie Cosell Fantasy Farm Fibers mailto:bernie@fantasyfarm.com Pearisburg, VA --> Too many people, too few sheep <--