Re: Mannerism and 9:7 -- Reply to Daniel Wolf

Hello, there, and in reply to Daniel Wolf, I'd like to agree generally
that the "Manneristic" style in either of its typical senses in music
history (c. 1370-1410, or c. 1540-1640) is not necessarily associated
with a use of the vertical 9:7 for a major third. At the same time,
before getting more into this historical question, I'd like to thank
Daniel for a fascinating discussion of some of the factors that can
make 9:7 seem more "concordant" in a 20th-century setting, such as
pitch range. I'd agree that the typical range of Gothic music, say
G-e'', is likely too low to approach the pitch region of greater
perceived concord.

As Daniel notes, the tuning of the major third expanding conjunctly to
the fifth (e.g. e-g# to d-a) near 9:7 is suggested by Marchettus of
Padua (1318). He belongs to an Italian branch of the _early_ Ars Nova,
as opposed to the _Ars subtilior_ or Manneristic epoch near the _end_
of the Ars Nova, the Ars Nova as a totality being roughly synonymous
with the musical "14th century" (say 1300-1420, or de Vitry to the
earliest Dufay).

It is possible to find one allusion in a short treatise on vocal
intonation in the Berkeley Manuscript or Paris Anonymous, part dated
to 1375, which _might_ imply a cadential M3 close to 9:7. Dividing a
whole-tone into three parts, this author advocates 2/3-tone for the
usual mi-fa semitone, but 1/3-tone for cadential semitones.
Unfortunately, this treatise directly covers only the intonation of a
single vocal line, not vertical intervals. One modern editor, Oliver
Ellsworth, has incidentally read this treatise as a proposal for
19-tet.

However, focusing on the style of both French and Italian music in
this late medieval epoch of "Mannerism" around 1400, I tend to suspect
that the most likely tuning for M3 would be either the standard
Pythagorean 81:64, or possibly at some places the 8192:6561 which may
have already been coming into vogue for sonorities with written sharps
tuned on a keyboard instrument as flats (e.g. e-g# tuned as e-ab).
This is a "schisma third" of about 384.36 cents, only a schisma of
about 1.95 cents from a pure 5:4 at about 386.31 cents.

In fact, if we see the transition as underway by around 1400, as Mark
Lindley suggests, then it falls within the Ars subtilior or
"Manneristic" era. For a composer such as Ciconia or possibly the aged
Landini (1325-1397), a tendency to realize many cadential thirds and
sixths involving sharps as virtually pure might point to a direction
which seems rather than opposite of a tuning closer to 9:7.

Interestingly, the question here is not only whether Landini himself
may have intended such a tuning, as opposed to the more traditional
Pythagorean tuning still championed by Prosdocimus in the early 15th
century, with M3 consistently at 81:64 and m3 at 32:27. Whatever
Landini himself may have had in mind, the new keyboard tunings around
1400 would give late 14th-century pieces an altered harmonic "color"
-- evidently one much liked by the "moderns."

In short, while Marchettus and possibly the later "third-tone"
treatise in the Berkeley Manuscript suggest the use of a cadential
major third not far from 9:7, the general sensibility of the medieval
Manneristic epoch around 1400 suggests the use of more concordant
values: either the traditional 81:64, or the diminished fourth at
8192:6561. By around 1450, as Lindley and others have discussed, the
8192:6561 (~5:4) rendition had apparently become so popular that it
led to meantone tunings seeking to make such thirds available in as
many locations as possible.

Moving now to the "Manneristic" Era in the sense of what is often
known as Late Renaissance and Early Baroque (c. 1540-1640), or from de
Rore through Monteverdi, say, we come to a setting where I would also
agree with Daniel that 9:7 is unlikely as a direct vertical interval,
except possibly as a deliberate "Wolf" (indeed the 32:25 of 1/4-comma
meantone, at about 427 cents, is quite close to 9:7). Note that the
augmented _fifth_, or 25:16, close to 14:9, does sometimes occur as a
"special effect," and here both upper notes are concordant with the
bass:

f#'
bb
d

It is true that the diminished fourth (e.g. f-c#) occurs as a
_melodic_ interval, at any rate, in Wert and Monteverdi, for example
-- something that Artusi criticizes in the latter's madrigals,
although he finds it acceptable for a 12-tet lute. Just how singers
would have tuned this interval is an interesting question.

Vicentino (1555), whom I would call a "Mannerist" in the best sense,
discusses approximations of both the 11:9 ("5 1/2:4 1/2"), or
essentially 9/31 octave (~348 cents); and the 9:7 ("4 1/2: 3 1/2"), or
essentially 11/31 octave (~426 cents). Note that he takes his
archicembalo based on a 1/5-tone tempered tuning -- essentially 31-tet
-- as the standard for the new vocal as well as instrumental music
which he advocates. He himself recognizes that a standard meantone
tuning, or more specifically 1/4-comma with pure 5:4 major thirds, is
virtually a subset of this tuning -- we might say "12 out of 31."

His conclusion is that 9/31 octave, a "proximate minor third," is
rather concordant. He describes it as a minor third tending toward a
major third, the latter being a prime concord; therefore it not
surprisingly tends toward a concordant effect.

With 11/31 octave, a "proximate major third," he finds the effect not
so good: this is a major third tending toward a fourth, the latter
interval in a Renaissance context having an equivocal status,
sometimes being treated in theory and practice either a discord
(especially in relation to the lowest voice) or a concord. Thus the
proximate major third, being somewhat "fourthlike," may take on the
equivocal character of this interval.

In principle, Vicentino holds that _any_ interval or combination may
be useful to express an appropriate text -- a position similar to that
of the Monteverdi brothers half a century later (1607). Thus it is
possible to imagine using the 9:7 or 32:25 or 11/31 octave in some
expressive setting, and winning Vicentino's appropriation; but I don't
recall him doing this himself.

Now for Daniel's very important point, if I read it correctly, that
although the vertical 9:7 doesn't seem to be associated with
historical "Manneristic styles" (late 14th century or 16th-17th
century), there's no reason it _couldn't_ be featured in some new
Mannerism.

As it happens, the harmonic trends around 1400 or 1550 weren't
especially favorable to the emergence of 9:7 as a favored vertical
interval; the _melodic_ diminished fourth (close to 9:7 in 1/4-comma
meantone or 31-tet), however, does take a prominent role in late
16th-century music.

In a late 20th-century or early 21st-century setting, I see no reason
why 9:7 might not be used in a "Manneristic" fashion.

Most appreciatively,

Margo Schulter
mschulter@value.net