Vicentino and Isacoff (was "wolf pack")

Hello, there, everyone, and on the topic of Isacoff (who I haven't yet
read, but would like to, maybe offering the author any helpful
feedback) and Vicentino, I might offer a few comments.

First, I wonder if Isacoff's comment about Vicentino's archicembalo
doing "JI, commas and all" might have been based on the potentially
confusing factor that Vicentino uses the term "comma," among other
things, for the amount by which the fifth is tempered, that is, in a
31-note cycle something at or close to 1/4 syntonic or Didymic comma.

The second tuning of the instrument in "just fifths," with the two
manuals having notes "a comma" apart -- about 1/4-comma, that is --
could lead a reader to take the "comma" in some more conventional
sense.

Barbour also, I would guess, may have been puzzled by some of
Vicentino's language -- what I suspect is that he may have taken the
"perfect fifths" of the second tuning as a feature of the first
tuning, something that leads him to question whether the scheme really
makes sense, although he correctly (in my view, at least) identifies
the first tuning as a 31-note cycle of 1/4-comma meantone or the like,
with each whole-tone divided into five nearly equal parts.

Incidentally, Maniates and Palisca, at least -- and maybe also you,
Graham, if I recall your remarks correctly -- have suggested that the
few "comma keys" in the _first_ tuning could actually represent a
"comma" Vicentino describes as equal to half a minor diesis, or about
20 cents, quite close to the Didymic comma at 81:80 (~21.51 cents).

Also, a reason occurs to me why Vicentino may have expressed his
"proximate minor" or neutral third as close to 5-1/2:4-1/2 rather than
simply 11:9. The first notation might suggest his concept that this
intermediate third tends toward the major third at 5:4, something
which he sees as giving it a relatively concordant quality.

Similarly, while his description of the "proximate major third" as
having a ratio of approximately 4-1/2:3-1/2 could have written this
ratio as 9:7, the fractional form might express his viewpoint that it
tends toward the fourth (4:3), in this case, for him, taking on a
quality tending somewhat toward dissonance. While regarding the fourth
as a perfect concord (as does Zarlino in his treatise of three years
later), he evidently sees it as having some "mixed" qualities, in
contrast to the concord of the major third toward which the
5-1/2:4-1/2 tends.

In fairness to Barbour and Isacoff, I would add that interpreting
Vicentino is indeed a process of _interpretation_: while I like the
idea of the "comma keys" in Vicentino's first tuning providing a few
JI fifths and sonorities of the kind generally available in his second
tuning, that is indeed an educated (I hope) interpretation rather than
_the_ obvious and correct reading.

Most appreciatively,

Margo Schulter
mschulter@value.net