Thu, Apr 01, 2021 at 05:03:58PM +0200, David Kastrup wrote: > Kevin Barry <barr...@gmail.com> writes: > > > That's why, as soon as the mathematics (root extractions) required for > > tempered tuning were discovered, it rapidly became the standard. > > I think your history of mathematics is a bit off. Seriously. And I > have no idea how you think mean-tone tunings work. I was referring to the family of concentric tunings that include equal temperament and other "well" temperaments. Without the 17th century discovery of logarithms and the wide availability of log tables they would not have been possible - there was no method before then to calculate the nth root of a number. In order to divide a comma equally among a number of fifths you need to be able to do that. (Equal temperament is just a special case where you divide the comma over a full circle of twelve fifths.)
Kevin
