Re: TD 391: Thanks to Paul Erlich for correction -- Lemme Rossi

Hello, there, and thanks to Paul Erlich for another helpful correction
(two in one day may be a lot, but better a correction than an unseen
mistake). In my reply to "the Monz," by the way, I give more on
Guillaume Costeley (c. 1531-1606) and his formulation of 19-tet (1570)
-- as opposed to 31-tet and related systems.

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

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

Thanks for catching this slip, but I'm delighted to have provided the
opportunity for more dialogue on a fascinating theorist.

My source for Lemme Rossi is Henry W. Kaufmann, "More on the Tuning of
the _Archicembalo_," _Journal of the American Musicological Society_
23:84-94 (1970). Clearly I'd like to learn more about Rossi's life and
musical activities, and your post prompts me to look into this, but
Kaufmann does include some very interesting information about Rossi's
treatise regarding the tuning of Vicentino's archicembalo.

This treatise, _Sistema musica overo musica speculativa_ (1666), gives
two tunings compared by Kaufmann. The first is a _sistema participato_
or "tempered system" with 19 notes in 1/4-comma meantone, i.e. Gb-A#,
the notes found on the usual "chromatic harpsichords" popular in
Naples around 1600. For a comparison of Rossi's string lengths for
these 19 notes in this system and in Rossi's interpretation of
Vicentino's tuning, see p. 88, Table I, citing Rossi at pp. 83, 86.

For a table showing Rossi's string lengths for his version of
Vicentino's complete 31-note tuning, see Kaufmann's Table 2, p. 93. As
Kaufmann explains: "Lemme Rossi has given a diagrammatic representa-
tion of this tuning according to string lengths. From these string
lengths, the value of each tone of the cycle in cents can be derived
(Table II). It will be seen that each diesis amounts to from 38.6 to
38.74 cents, and thus, for all intents and purposes, is uniformly
equal." (Ibid. p. 93).

Rossi's mathematics thus indicate that by 1666, at least one theorist
was interpreting Vicentino's "31-division" on the archicembalo as what
we might well call more specifically "31-tet."

Although I happen to like an interpretation in 1/4-comma meantone, in
part because of "historical tuneability" under 16th-century conditions
and in part because of the elegance of having pure 5:4 major thirds,
Rossi's tuning does indeed constitute a germinal document for 31-tet.

By the way, could the other musician connected with 19-tet be the organist
Jean Titelouze (1563-1633), whom Mersenne (1636) says had a special
_Epinette_ that "divides the tone in three equal parts." This is mentioned
in Kenneth J. Levy's article on Guillaume Costeley which I cite in the
reply to Joe Monzo (maybe in this same Digest), at pp. 249-250. While I'm
not sure I mentioned Titelouze previously, he certainly deserves to be
mentioned under the heading of 19-tet, based on Levy's short reference.

Most appreciatively,

Margo Schulter
mschulter@value.net