Re: For John deLaubenfels -- clarification on "smoothness"

Hello, there, and I'd like to clarify what may have been an
unfortunately not so transparent attempt at humor in comparing my
classic 16th-century keyboard scheme of 15 notes per octave for
5-limit just intonation (JI) with your elegant variable-note scheme.

Here the humor was that my "classic" 15-note fixed-pitch scheme a la
Zarlino (1558) obviously involves unconcealed comma shifts of a full
syntonic comma or 81:80 (~21.51 cents) -- in contrast to the much
smaller shifts involved in your implementation.

Reflecting on the very serious compliment that someone offered in
commenting that your rendition sounded as if it had been made on a
"fixed pitch instrument," I meant simply to quip, "and in fact with
much smaller and smoother shifts than on some 16th-century JI
keyboards!"

More seriously, and as a timely reassurance in a forum where questions
of "historical authenticity" can generate some appreciable
controversy, I would hasten to add that I did _not_ mean to imply that
your scheme, or more generally any algorithm leading to shifts of less
than a syntonic comma, is "too smooth" for the music <grin>.

Of course, Vicentino's adaptive JI scheme of 1555 with shifts of only
around 1/4 syntonic comma (~5.38 cents), also presented here by Paul
Erlich, would likewise be "inauthentic" by such a test.

As for the possibly synonymous nature of COFT and unequal
well-temperaments of late 17th to mid-19th centuries, I need to look
more carefully at articles about COFT -- but I wouldn't be surprised
if they turn out to be similar concepts.

Again, my congratulations, with regrets for any confusion caused by my
attempt at humor.

Most appreciatively,

Margo Schulter
mschulter@value.net