Re: Intonation for earlier and later Dufay

Hello, there, and I'd like to propose a possible distinction between
the early and the later compositions of Dufay (c. 1397-1474), whose
career indeed seems to mark the transition from 3-limit to 5-limit
harmony in much of Continental Europe.

Equally important, the problem of tuning Dufay (especially the earlier
works) is a good reminder that keyboards are keyboards and voices are
voices -- the latter not being bound to fixed-pitch schemes.

In my view, Dufay's earlier works (say 1420-1440) are still trinic:
that is, the complete stable harmony remains the full trine, with
outer octave, lower fifth, and upper fourth (e.g. D3-A3-D4). As with
the triad in late 19th-century practice, this "full harmony" had by
this point become not so full and rich as in earlier Gothic times; but
the instability of thirds and sixths is still a vital element of the
young Dufay's cadences, however pervasive these intervals may be in
the texture.

(See Paul Erlich's excellent recent post on the tendency of both late
Gothic 3-limit and late Romantic 5-limit music to become harmonically
blurred as unstable sonorities become more pervasive.)

On keyboard, I would favor a "modified Pythagorean" intonation,
preferably with 15 or 16 notes per octave (easy with a synthesizer
supporting "part-tunings" for two conventional 12-note manuals, with
one keyboard for example tuned Eb-G# and the other to the "modern"
early 15th-century arrangement Gb-B).

The idea of this tuning is to use the true Pythagorean sharps (a
16-note tuning could also include D#, although this might not be
needed so often) for cadences where major thirds expand to fifths and
major sixths to octaves, for example:

C#4 D4
G#3 A4
E3 D4

Where noncadential sonorities involving thirds or sixths occur,
especially prolonged ones, substituting the Pythagorean flats for the
regular sharps produces near-pure schisma thirds, e.g.

B3
Ab3
E3

If only 12 notes were available, I would go with the Gb-B tuning,
which has all the sharps tuned as flats. This has the interesting
effect of making thirds and sixths involving sharps (cadential or
otherwise) nearly pure, but other thirds and sixths Pythagorean. The
result, as Mark Lindley describes, is a kind of "modal color"
analogous to the key color of 18th-century well-temperaments.

Please note that I've been speaking here of the _early_ Dufay. Let's stick
with keyboards for the moment. By around 1450, meantone tuning was
evidently starting to influence keyboard composers (e.g. Conrad von
Paumann). Dufay's later works, where thirds and sixths might be said to
shift from "mildly unstable" to "almost stable but inconclusive," might
nicely fit that tuning, as Lindley remarks in his article on "Pythagorean
Intonation" in the _New Grove_.

However, going back first to the early 15th century, the question of
vocal intonation is really an open one. A clue as to "conservative"
practice during Dufay's youth comes from the Italian theorist
Prosdocimus of Beldemandis, who prefers regular Pythagorean thirds and
sixths, especially at cadences where these "perfected" intervals
efficiently resolve to stable ones. A somewhat more modern perspective
is provided by Ugolino of Orvieto, another writer of Dufay's youth,
who share the views of Prosdocimus in favor of the wide cadential
major thirds and sixths, but also notes the popularity of the new
sharps-as-flats tuning.

One possible ideal for singers would be to seek Pythagorean thirds and
sixths at directed cadences (which still often follow typical
14th-century patterns in the early Dufay), but pure or near-pure
thirds and sixths at other significant points. My 15 or 16 note
keyboard tuning, in fact, is designed to approximate such a process.

However, singers are not restricted to 12 or even to 17 notes per
octave, and even if we assume that they were influenced by keyboard
intonations (a hypothesis cautiously proposed by Lindley), would they
necessarily emulate all the fine points of such intonations. For
example, while a keyboard sonority such as C3-G3-E4 would always be
regular Pythagorean (only thirds with sharps sometimes or always are
realized as schisma thirds), might not a singer tune E4 close to a 5:2
in relation to C3?

Descriptions of the "English countenance" in Dufay and Binchois during
the epoch of around 1420-1440 certainly provide a motivation for making
at least some of the prominent thirds and sixths just in vocal
intonation, and keyboard intonations may have both reflected and
reinforced such tendencies. However, we cannot be sure that even in
England _all_ thirds and sixths were necessarily intoned as in
5-limit (e.g. in Dunstable); possibly the regular Pythagorean
intervals were appreciated at cadences.

By around 1450, changes in cadences as well as the more and more
consistently tertian flavor of the texture noted by Lindley do suggest
something like 5-limit for voices; Ramos describes 5:4 and 6:5 thirds
in 1482. Thus I would say that performing the later Dufay in 5-limit
is a very reasonable historical decision.

Incidentally, some recent performances of Ockeghem have used
Pythagorean, maybe as a way of making the melodic lines more
distinct. While conventional wisdom would say that his music invites
5-limit (or meantone on a keyboard), these experiments have received
some positive reception -- and also some not unexpected controversy.

Most appreciatively,

Margo Schulter
mschulter@value.net