Reply to Johnny Reinhard (was: Re : F in G7 as 21/16 rather than 4/3...)

Johnny Reinhard wrote,

>Paul, I might agree that meantone is a better place to start for Bach than
>12TET, but don't you mean 1/6th comma meantone? Bach is reputed to have
>insisted that all major thirds be tuned sharp.

Good question! What we really need to know is: did Bach insist that all
major thirds be tuned sharp so that a circulating well-temperament that
sounded nice in all 12 keys would result; or did he really prefer the sound
of sharp major thirds to pure ones. Since (as far as I know) this statement
on Bach's part was restricted to a discussion of keyboard tuning, I suspect
the former, though we may never know for sure. But in the context of this
thread, namely adaptive JI, where all the major thirds are going to be tuned
pure anyway, you'd end up with smaller melodic shifts if you start in
1/4-comma meantone than 1/6-comma meantone.