Re: TD 388: Reply to Paul Erlich on 19-tet

Hello, there, and in Tuing Digest 388, Paul Erlich wrote:

> you should certainly include the two Renaissance composers known to
> have used 19-tET. One of them is Costeley. Margo, who is the other?

Honestly, I know only of Costeley -- and of the possible implications
of the 1/3-comma meantone of Salinas (1577), almost identical to
19-tet (either tempering the fifth about as much as 22-tet, but in the
opposite direction) <grin>.

If there is another advocate of 19-tet in the 16th century, maybe
among the French circles in which Costeley moved, I'd be very
interested; certainly there were other French musicians experimenting
with chromaticism of a kind which might lead to experimentation with
such a tuning.

Vicentino, of course, favors a division of the octave into fifthtones
of _about_ 1/31 octave, and 1/4-comma meantone carried to 31 notes
nicely approximates this model.

Parenthetically, I might comment that the focus on _precisely_ equal
divisions of the octave might be curious tendency of some modern
theorists and historians. To me, the idea of dividing the octave into
31 _approximately_ equal parts indeed goes back to Vicentino, and that
to place his proposal in a totally separate compartment from the later
history of 31-tet might be a bit artificial.

Certainly I want to recognize the distinction between 1/4-comma
meantone and precise 31-tet, but I'd like to recognize the
similarities also.

Thus if I were doing a table, I might head it "equal or near-equal
divisions of the octave," and list Vicentino (and Colonna in 1618)
under "31-division" with an asterisk (*) leading to a note

* Realized by extended meantone, likely ~1/4-comma

This approach notes the kinship of the older pragmatic 31-division
derived from 16th-century common-practice meantone, and mathematically
precise 19-tet as defined by Lemme Rossi (1666) using string lengths
to within about .1 cent, and by Christopher Huyghens in a more
rigorous mathematical fashion.

Most respectfully,

Margo Schulter
mschulter@value.net

I wrote,

>> you should certainly include the two Renaissance composers known to
>> have used 19-tET. One of them is Costeley. Margo, who is the other?

Margo wrote,

>Honestly, I know only of Costeley

Sorry, I thought I had heard of the other one through you. Can you provide
Joe with a relevant date to attach to Costeley?

>and mathematically
>precise 19-tet as defined by Lemme Rossi (1666)

Did you mean 31-tET? Who's Rossi -- tell us more!