Re: Fogliano, Vicentino, and JI or Meantone?

Hello, there, and briefly I'd like to comment on the issue of 5-limit just
intonation (JI) and meantone temperament in the writings of Nicola
Vicentino (1511-1576), as raised by others such as Johnny Reinhard and
Paul Erlich.

Briefly, while Fogliano (1529) had advocated Ptolemy's syntonic
diatonic as a system of 5-limit just intonation, Vicentino in practice
champions meantone (with "blunted fifths") as characteristic of
16th-century common practice. His term for this practice is "mixed and
tempered music" -- music which uses a mixture of three Greek genera
(diatonic, chromatic, enharmonic), and which tempers fifths and
fourths in order to obtain fully concordant thirds and sixths.

While taking meantone as the norm, and indeed recommending his
archicembalo (likely tuned in a 31-note version of 1/4-comma meantone
to produce a circulating and very slightly unequal division of the
octave) as a standard for vocalists in finding unusual intervals,
Vicentino at the same time expresses an interest in what would now be
called "adaptive JI," where all vertical concords (5-odd-limit
intervals) are pure. This involves, as has often been discussed here,
an instrument combining two meantone systems spaced 1/4-comma apart,
providing pure fifths and minor thirds as well as major thirds.

In his advertisement for the arciorgano (1561), Vicentino writes about
the special delights of a music where the fifth, major third, and
minor third are all pure -- in other words, adaptive JI.

Incidentally, Vicentino's Italian description for the common practice
is something like _musica participata e mista_ -- the adjective
_participata_ referring to the tempering or narrowing of fifths on a
keyboard instrument, and going back as I recall to an identical Latin
term in Gaffurius (1496).

Thus while Fogliano and Vicentino agree that medieval Pythagorean
tuning cannot provide the fully concordant thirds and sixths required
for 16th-century practice, Fogliano turns to classic 5-limit JI (based
on Ptolemy) as a solution, while Vicentino takes the usual solution of
meantone temperament on keyboards as a new standard.

Interestingly, both Vicentino (1555) and Fabio Colonna (1618) delve into JI
ratios in their treatises before describing their actual circulating tuning
systems, both likely based on 1/4-comma meantone carried to 31 notes.

Incidentally, one controversial assertion of Vicentino is that _any_
use of the melodic minor third or major third involves the
introduction of the chromatic or enharmonic genus, so that the most
routine 16th-century composition typically features all three genera,
and thus is "mixed." This is the assertion which Lusitano in 1551 (in
his famous debate with Vicentino) and Zarlino in 1558 (rebutting the
"chromaticists") vigorously contested.

Most respectfully,

Margo Schulter
mschulter@value.net