Re: Correction on Salinas, etc. (Thank you, Joe Monzo!)

Hello, there, and here I'd like to offer a few odd observations in
response to some posts by Joe Monzo and others.

First, I'd much like to thank Joe Monzo for calling to my attention
that Salinas published his 1/3-comma meantone tuning (and also a very
interesting just intonation scheme) in 1577, not 1571 as I surmised in
a response to Bill Alves.

Secondly, as to the role of instrumental music in late medieval and
Renaissance Europe, I would certainly agree that vocal music is both
the prevalent form and the "perfect" ideal of these eras. However,
this does not mean that instrumental music was inconsequential, or
that its influence on vocal intonations was necessarily negligible.

Mark Lindley, for example, argues with due caution that the new
modified Pythagorean tunings of the early 15th century, possibly
sometimes implemented on keyboards with more than 12 notes per octave,
may have influenced the vocal writing of composers such as Dufay,
intriguing them with the sound of nearly pure schisma thirds involving
written sharps.

Lindley also shows how, around 1400-1450, keyboard sources such as the
Italian Faenza Codex and the German Buxheimer Organ Book used
prominent sonorities with schisma thirds as a very popular "special
effect," indeed sometimes a "stock in trade," as he puts it. While the
"explosion" in lute and keyboard tablatures around 1500 was yet to
come, these trends may have played a role in the stylistic change
around 1420-1450 which marked what Tinctoris (1477) regarded as the
beginning of truly "modern" music. In current historical terms, this
is often regarded as the Gothic/Renaissance transition.

While the formal vocal forms of sacred and secular polyphony continued
to hold center stage in the 16th century, instrumental forms played a
very important role also, and madrigals, for example, might be
sometimes be performed by mixed consorts of voices and instruments. In
fact, the complications and conflicts resulting from such mixed
ensembles (e.g. meantone keyboards and 12-tone equal temperament or
12-tet lutes) was one topic of discussion in late 16th-century
treatises.

During the first half of the 16th century, an incredible flowering of
instrumental forms occurred, ranging from dances and improvisatory
lute and keyboard preludes to Willaert's ensemble _ricarcare_. By
1555, Vicentino was prepared to advocate the use of his 31-tet
_archicembalo_ as a standard for intonation by singers.

In discussing either the 3-limit JI of the Gothic era or the 5-limit
JI of the Renaissance, it may be helpful to remember that these are
_ideals_ of intonation, guiding singers of some natural variability in
their intervals. In performances involving mixed voices and
instruments, common for example in the various Florentine
entertainments chronicled by Howard Mayer Brown, instrumental and
vocal intonations would interact, making the former not irrelevant.

As early as 1516, by which year Castiglione's _Courtier_ is said to
have been completed (it was published in 1528), an author argues that
the most pleasing court music is a vocal solo accompanied by the
_viola a mano_ -- that is, actually, a lute or similar plucked
instrument. Various Italian _frottole_ around 1500 may have performed
in this manner, and arrangements of Italian madrigals by Verdelot, for
example, for the lute may have represented a continuation of this
tradition.

This is not at all to minimize the importance of the view taken by
various theorists of the later 16th century that there are three
distinct types of intonation: (1) Just intonation for voices,
specifically 5-limit; (2) Meantone for keyboards; and (3) 12-tet for
lutes. However, in forms where these varieties of instruments (the
voice being considered the most "perfect") interacted, mutual
influence or accommodation might come into play.

The influence of instrumental intonations in practice is suggested by
Vicentino, who describes the conventional practice of his time as
"mixed and tempered music." The "mixed" refers to his view that even
compositions typically classified as "diatonic" in fact use elements
of the chromatic and enharmonic genera; and the "tempered" evidently
refers to the kind of accommodations made in meantone tunings for
keyboard.

Because the topic of the Pythagorean-Aristoxenian-Ptolemaic debate is
often raised here, I would like to conclude with one point about at
least the late medieval theorists of polyphony and Pythagorean
tuning. This really isn't addressed to any one previous article in
particular, but maybe to a general trend of thought.

In medieval versions of the Pythagoras story, this theorist heard an
amazingly harmonious striking of blacksmith's hammers, and the set out
to investigate how this could come about. Such curiosity led to
experimentation, and the discovery of the ratios of the principal
concords. Thus the sense of hearing and the intellect are partners in
the kind of theorizing advocated by Pythagoreans such as Jacobus of
Liege: concord and discord themselves are described in terms of
smoothly blending or roughly "colliding" sounds, as well as in terms
of numerical ratios.

Further, to such medieval theorists, concord/discord classifications
reflect style as well as mathematics. For Jacobus, while _stable_
concords are generally limited to the classic 3-(odd)-limit intervals,
a variety of other intervals are also recognized as "medial" or
"imperfect" concords. These include the major third (81:64), minor
third (32:27), major second (9:8), minor seventh (16:9), and major
sixth (27:16). Not all of these ratios are mathematically so tidy, but
Jacobus hears the intervals as more or less blending, and so describes
them as "concordant" to various degrees.

Possibly the hallmark of "Pythagoreanism" in such a medieval setting
is a desire to explain artistic perceptions in a precisely quantitized
way -- something rather different from considering such perceptions
irrelevant. Thus in the early 15th century, Prosdocimus portrays his
fellow Paduan theorist Marchettus of about a century earlier as a very
bad mathematician, but a good practical musician. In fact, without
necessarily joining with Prosdocimus in his value judgment, one can
say that the mathematics of Marchettus are at best a bit unclear, as
compared with the 17-note Pythagorean scheme of the later theorist.

Further, as Prosdocimus shows, it is quite possible to champion a
Pythagorean approach to intonation while showing an awareness of the
role of perception. Thus, having recognized the distinction between
intervals such as A3-F#4 (major sixth, 27:16) and A3-Gb4 (diminished
seventh, 32768:19683), he wonders aloud whether this distinction might
be "imperceptible" to the ear.

In my view, our answer might depend on how "perceptible" is
interpreted. Certainly it is possible for an attuned listener to
discern this difference of a Pythagorean comma (~23.46 cents), but at
the same time, one might guess that in the early 15th century, as now,
many listeners might find either interval an acceptable representative
of the "major sixth" class. Indeed, keyboard works of the period which
in popular keyboard tunings would use both flavors of sixths lend
support to this view.

Here I wish not at all to minimize the importance of our ongoing
dialogue regarding the traditions of Pythagorus, Ptolemy, and
Aristoxenes, only to caution against any blanket equation of
"Pythagorean" theory during the medieval period with an indifference
to the evidence of the senses or to the vital dynamics of style.

Most respectfully,

Margo Schulter
mschulter@value.net