Re: Chace/caccia, fuga, fugue -- Judith Conrad and Paul Erlich

Hello, there, Judith and Paul and everyone.

Apparently my article on "Chace/caccia, fuga, fugue -- and tuning" has
prompted a bit of discussion, and I'd like to respond to a few points.

First of all, Judith is very right to point out that Willaert's
"chromatic duo" of around 1518 or 1519 _does_ represent a
circumnavigation of the circle of fifths during the meantone era,
although keyboard tunings to accommodate such maneuvers apparently did
not become the norm until around the end of the 17th century. Her
example reminds us that sweeping historical generalities such as mine
are indeed only generalities, and also illustrates how composers are
not necessarily limited in their imagination and realization by the
prevalent tuning paradigms of a given time.

To her account, I might add one story that Willaert may have written
this piece in part as a kind of artistic retaliation against the Papal
choir for having the less than flattering taste to perform a certain
motet of his regularly -- until they learned that it was indeed by
him, not by Josquin as they had assumed.

As Paul points out, a Renaissance meantone tuning would seem most
unlikely for this vocal piece, which some modern commentators have
suggested could be a kind of theoretical as well as practical
demonstration of 12-tone equal temperament (12-tet). To say that
_most_ 16th-century vocal as well as keyboard music comfortably fits
within the range of a 12-note meantone temperament is not to deny this
and other important exceptions.

Curiously, the quasi-Pythagorean temperament of Henricus Grammateus
(1518), where he indulged in an "amusing reckoning" by showing a
geometric method for measuring organ pipes to divided the Pythagorean
9:8 whole-tone into two equal semitones (~101.95 cents each), might
have permitted a marginally tolerable rendition of Willaert's
chromatic duo (possibly lending itself to a quartet realization also)
on a 12-note keyboard. In this tuning the diatonic notes are is in a
pure Pythagorean tuning, with 9:8 whole-tones and 256:243 semitones
(e.g. e-f, b-c'); accidentals split tones into equal semitones. This
tuning includes "semi-Wolf" fifths, but avoids outright Wolves; its
Pythagorean thirds and sixths might be less than ideal for Renaissance
music of this era, however.

It may be something of a moot question to what extent lutes were tuned
in 12-tet by the epoch around 1520, although by 1550 or so this tuning
was well-documented as the norm. Certainly Willaert's duo could be
played on such an instrument. Although the exigencies of playing
polyphonic music on a lute, where unequal semitones on different frets
could much complicate the performer's task, seem to have been a major
motive for tuning with equal semitones, as early as 1567 a collection
of pieces by Giacomo Gorzanis using all 12 notes of the chromatic
scale as finals signals that composers were well aware of the
enharmonic equivalences of this tuning and ready to exploit
them. However, I'm not aware if any piece in this collection
"circumnavigates" the circle of fifths, although one might say that
the collection as a whole represents a kindred kind of exploration.

In 1555, Nicola Vicentino published his description of the
_archicembalo_, based essentially on 31-tet (which Vicentino
apparently recognized was virtually identical to 1/4-comma meantone,
although he does not attempt to demonstrate this equivalence
mathematically). While he certainly explored the diatonic, chromatic,
and enharmonic styles of music made possible by this instrument
(urging singers to emulate it in order to learn the novel intervals
involved), I'm not aware of his circumnavigating this system in a
piece.

Around 1570, as Paul mentions, Guillaume Costeley proposed 19-tet, and
his chromatic spiritual chanson _Seigneur Dieu ta pitie/_ is open to
more than one interpretation for some of the accidentals. For
alternative transcriptions of this piece, and also the text and
translation from a preface by Costeley very clearly describing a
19-note keyboard dividing each whole-tone into three parts, see
Kenneth J. Levy, "Costeley's Chromatic Chanson," _Annales
Musicologues: Moyen-Age et Renaissance_, Tome III (1955),
pp. 213-261. Interestingly enough, Costeley describes the instrument
as having eight white keys, the usual five black keys, and seven extra
black keys per octave -- evidently counting the white keys at both
ends of an octave, to get 20 keys in all rather than 19.

Levy notes that one solution of the accidentals in fact results in a
"drop solution" where "the piece describes a complete circle through
musical space, ending as it began in the Dorian key of g." However, he
argues that a different solution based on absolute piece is preferable
in terms of the musical style and textual expression (ibid. 232-240).

Aside from presenting a fascinating discussion of Costeley's 19-tet in
theory and practice, Levy also discusses some trends in 16th-century
chromaticism, mentioning the Willaert piece as one example.

Incidentally, while advocacy of 12-tet for keyboards as opposed to
fretted instruments was evidently unusual in the 16th century, Zarlino
(1588) does quote a treatise by a certain Abbot Girolamo Roselli who
advocates this tuning as a "spherical music" where composers are free
to transpose the gamut however they desire, and where singers and
performers on assorted instruments can have the pleasure of being
mutually in tune. Thus I would like to credit Roselli as a source for
my "circumnavigation" metaphor.

Most respectfully,

Margo Schulter
mschulter@value.net