Tuning various edos by ear: Difference between revisions

Unsurprisingly, 9 and 19 are the clear winners overall, being buildable from the simplest ratios, and having some of the lowest errors, which I already knew before, but this also revealed a few unexpectedly good alternatives that are improvements if you can distinguish and tune to more complex ratios. Sometimes doubling makes things much more than twice as bad, and sometimes it's actually easier to get an evenly spaced small scale by building one considerably larger and then only using a subset. It is particularly interesting that neither 7 or 12 are good numbers for an equally spaced scale on their own, while 24, 28 and 36 are substantial improvements. There's also definite islands of good and bad numbers, and it would be interesting to see how that extends up into higher EDO's if anyone has the time to crunch the numbers. Hope this has been interesting and helped reveal a bit more about the mathematics that music is built upon.