Yahoo Tuning Groups Ultimate Backup tuning Open Letter to Page Wizard

Hello, there, Gene, Paul, and others, and please let me reply to your
recent post which I saw at Yahoo after posting what I wrote yesterday on
the question of Dufay.

First, as the person who wrote the Pythagorean Tuning FAQ at

http://www.medieval.org/emfaq/harmony/pyth.html

I'd like to thank you for quoting the discussion on Dunstable and
Dufay fairly and accurately, and very wisely observing that questions
of intonation for this epoch in the early 15th century _are_
left ambiguous in the FAQ, and especially this portion of it.

Your post makes explicit something that maybe I was drifting around
when I wrote that passage in 1998: the FAQ doesn't address all the
possible nuances of vocal intonation in this epoch, and just maybe
that was the wisest policy, especially for a document focusing mainly
on the 13th-14th centuries. The complication with the early 15th
century is that it's a transitional epoch -- making it intriguing, and
also maybe a bit elusive, especially for flexible pitch intonation.

As the passage you quoted makes clear, we're quite in accord on the
nature of Renaissance music: meantone or some kind of 5-limit system
rather than Pythagorean tuning is what fits.

Here the problem comes in deciding how we approach the transition
between the medieval and Renaissance eras, a kind of transition
bridged by Dunstable and Dufay. Are they medieval or Renaissance from
an intonational viewpoint -- or maybe represent a distinct
"transitional" viewpoint mixing elements of both the earlier and later
eras?

Certainly we agree, as the FAQ text you quoted also suggests, that
Dunstable and Dufay are stylistically distinct from Perotin-Machaut.
At the same time, I might ask: are Dunstable and Dufay also distinct
from Josquin and Isaac around 1500, say, let alone Jannequin or
Verdelot, say, in the epoch around 1530 of the chanson and emerging
16th-century madrigal?

Also, while we learn as early as Martin Le Franc (1442) that Dufay and
Binchois followed the "English countenance" of Dunstable to obtain
"sprightly concords," might there by some distinction between
Dunstable and Dufay, who especially in his earlier years was also
influenced by French and Italian traditions?

Here I'd like to suggest that while "smoothed" or "5-limit-like"
thirds seem to play a vital role in the music of Dunstable and of the
early Dufay (say 1420-1440) alike, there may be some possible
distinctions, and some mixtures of Pythagorean and "5-limit-like"
elements.

We have some direct and indirect evidence, in fact, that intonational
tastes may have varied in the early 15th century, with a 14th-century
style Pythagorean tuning at one end of the spectrum, and something
like pervasive 5-limit JI (or its adaptive approximation) for flexible
pitch performances at the other.

Along with Mark Lindley, I would suggest that keyboard tunings of the
era may give _some_ clue to how vocalists or players of flexible pitch
instruments _may_ have approached these choices, and how composers
_may_ have conceived the kind of tuning likely for their pieces.

For more on this, see Section 4.5 of the FAQ, some of which I'll try
to sum up below -- but only as one possible approach, taking keyboard
intonation as a possible guide, something not always so definitive
when it comes to flexible pitch ensembles.

In my earlier response, you may note, I focused on Dufay rather than
Dunstable, and that reflects my possible perception that as closely
related as these composers are, they may represent somewhat different
stylistic traditions.

Let's first consider some elements of the English tradition which
might make a pervasive 5-limit interpretation for some of Dunstable's
music quite attractive, although some kind of Pythagorean tuning seems
the main documented kind of approach for keyboards.

As early as the 13th century, we find English pieces with thirds in
closing sonorities, and Coussemaker's Anonymous IV comments on this
practice in the "Westcountry" of England of treating thirds as "the
best concords." Writing around 1300, Walter Odington notes the
proximity of the Pythagorean ratios to 5:4 and 6:5, and suggests that
singers make some kind of adjustment (in pitch or in timbre?) to make
these intervals fully concordant in practice.

While English music of the 13th-14th centuries follows a spectrum of
styles ranging from Continental-like to pervasively tertian or
"5-limit-like," the music of John Dunstable (c. 1370-1453) often leans
toward the latter style, although thirds to my best (and not so
comprehensive) knowledge always remain inconclusive -- that is, do not
occur in closing sonorities. Please anyone feel free to correct this
statement if there are counterexamples.

What I recall hearing in some of Dunstable's motet textures, for
example, is a treatment of thirds which I might term "static" although
not quite stable: they just seem to "hang around," with the melodic
lines flowing around them or from one such "static" tertian sonority
to another. There are also some Continental pieces around 1400 with
this kind of effect on me, specifically one by Jean Vaillant -- in
contrast to other of his pieces with a typical 14th-century feeling of
directed motion.

Here a 5-limit-like style seems a very attractive interpretation, with
possible Pythagorean touches at certain directed cadences. The English
precedents, and the nature of the music, make this at least one likely
historical interpretation, maybe more so if fixed pitch keyboards are
not involved.

With much of Dufay's early music, I would say that the "coloristic"
role of thirds might still have some ties to the Ars Nova tradition in
France and Italy where they serve as points of motion, relatively
concordant (as they are regarded in much 13th-14th century theory) but
unstable and somewhat tense also.

It's easy to say this for the "14th-century-like" portions of the
Missa Sine Nomine from the 1420's -- evidently based on the chanson
_Resvellies vous_ written for a marriage taking place in 1423. I would
say that many of Dufay's chansons, also, carry for me expectations
of 14th-century "directionality" and cadentiality, whether fulfilled
or sometimes diverted.

Lindley has observed, more specifically, that the treatment of
intermediate cadences and phrasing may suggest that Dufay often
composed with expectations based on some kind of keyboard instrument
(an organ or clavichord) for 12 notes tuned in the Pythagorean Gb-B
arrangement. He notes that sonorities such as A3-C#4-E4 often have
what he calls a "stable" and I might call a "prolonged noncadential"
role, the sonorities where schisma thirds (e.g. A3-Db4-E4 as realized
on a Gb-B keyboard) would have a smooth, quasi-5-limit, effect.

In contrast, he finds that sonorities such as G3-B3-D4, with regular
Pythagorean thirds on such a keyboard, are not used in this fashion by
the early Dufay. He thus suggests that Dufay's vocal music of the
early period could have been based on such a keyboard.

Here I would like to suggest that the new element is not the use of
thirds, sometimes prolonged, at points of inconclusive phrase or
sectional endings -- this can be found in the French music of the 13th
and 14th centuries also. In the Perotin-Machaut era, such thirds are
evidently regarded as _partial_ concords, with some emphasis on
"partial," and I find pausing on a usual Pythagorean sonority such as
G3-B3-D3, or A3-C#4-E4 in the Eb-G# tuning likely popular in the 14th
century, quite pleasing and stylistically fitting.

Sometime around 1400, however, there was evidently a perception,
discussed by Lindley, that using schisma thirds for these points of
pauses had a different and pleasing effect -- and Dufay around
1420-1440 seems to make the most of it.

In this interpretation, the contrast between usual Pythagorean and
schisma thirds is part of the attractiveness of the music, an element
not present in either a traditional 14th-century interpretation with
its more consistently regular Pythagorean thirds, or a later 15th-16th
century interpretation with its pervasive 5-limit sonorities.

Like Lindley, I have found that the kind of moving fauxbourdon or
related textures often favored by the young Dufay can be served very
nicely by Pythagorean intonation -- something I might not have guessed
before trying it on a keyboard. Here we have thirds in motion, and
Lindley and I both like the dynamic quality of the more complex
Pythagorean texture.

At the same time, schisma thirds on prolonged noncadential sonorities
can have a very striking and luminous effect, like rays of sunlight,
like the announcement of the fresh breeze of a new era.

What I find credible, although this is a matter of guessing and of
personal taste alike, is that the taste for those schisma thirds could
have been combined with a taste for Pythagorean thirds in directed
cadences, the latter advocated by Prosdocimus in 1413 and Ugolino of
Orvieto around 1430-1440 or so, when they propose a 17-note
Pythagorean system.

On a 12-note Gb-B keyboard, the constraints of fixed intonation
dictate that thirds will be either usual Pythagorean or "smoothed"
schisma versions depending on their position, and regardless of the
musical context. Thus A3-C#4-E4 or A3-C#4-F#4 will have schisma thirds
and sixths whether occurring in a cadential context or some other; and
G3-B3-D4 will always be a usual Pythagorean sonority, the _quinta
fissa_ or "split fifth" described by Jacobus of Liege around 1325.

Lindley compares this "modal color" to the key color of an
18th-century well-temperament, and interestingly suggests that the
prominent schisma thirds available in a mode such as D Dorian where
cadential accidentals are applied could have influenced Renaissance
modal patterns, which in turn helped shape the tonal patterns emerging
by the later 17th century.

Vocalists or players of flexible pitch instruments, however, would not
be so constrained -- they might produce either traditional or
"schismalike" thirds at various locations, singing for example
A3-C#4-F#4 before G3-D4-G4 at a directed cadence, and getting the
regular Pythagorean thirds and sixths with their dynamic qualities;
but A3-Db4-E4 for a prolonged noncadential sonority. A 17-note
Pythagorean keyboard affords these choices for sonorities involving
written sharps, for example.

How would early 15th-century singers use this freedom? Would they tend
toward the kind of contrast between regular Pythagorean and schisma
thirds found on keyboards in a Gb-B arrangement, but possibly based on
musical context rather than strict position of sonorities? Or might
they tend toward the approach: "If we can sing these smooth thirds
anywhere we want, why not sing them just about _everywhere_?"

The latter approach, 5-limit JI or its adaptive approximation, may
have attractions for the early music of Dufay, as well as for
Dunstable and some of the English carol repertory; I would consider it
as _one_ "historically likely" reading. We might say that it
emphasizes the "Renaissance-like" aspects of the music.

A more "modified Pythagorean" approach for the early Dufay may give
greater weight to the "Ars-Nova-like" elements, as well as to the
keyboard tunings of the era and the cadential ethos of writers such as
Ugolino, who expresses a preference for regular Pythagorean thirds and
sixths at cadences but also recognizes the prevalence of the Gb-B
tuning scheme.

One could actually argue that the second interpretation gives
near-pure schisma thirds a special import, since they stand out
against a context of more active regular Pythagorean thirds.

More generally, I would say that transitional epochs often present
dilemmas of this kind: which elements are treated as more prominent,
or more pervasive, or more likely in situations where performers have
discretion of a kind not always addressed in theory, or covered by
fixed-pitch tunings?

For example, I find it rather easy to say that a minor sixth before an
octave constitutes a standard progression in Perotin around 1200, but
typically would be inflected to major (by flatting or sharping) in the
era of Machaut or Landini, at least in a prominent cadential setting.

However, what about the epoch of 1270-1300 say, the period of Adam de
la Halle and Petrus de Cruce?

There are enough manuscript accidentals in this epoch to suggest that
unwritten inflections might sometimes have been made, but I tend to
regard this as "optional" and not necessarily prevalent. By the Ars
Nova of Philippe de Vitry or Marchettus of Padua, we tend to regard it
as "standard" practice.

Also, if a cadential sixth is indicated in a late 13th-century piece
as inflected to major, should a cadential third in the same sonority
also be inflected to major, as in this type of example from Adam de la
Halle ((c. 1237-1287 or 1288):

C#4 D4
G[#?]3 A3
E3 D3

For the major third before the fifth, one might quote Jacobus of Liege
(an early 14th-century advocate of the 13th-century style of his youth
against the "moderns" of the Ars Nova), as well as a treatise around
1300 suggesting that inflections are used to get pure fifths or
fourths which would otherwise be tritonic (here between the upper
voices).

An interesting implication of this specific example is that one is
introducing an accidental, G#, not to my best knowledge found in
13th-century manuscripts, although it becomes routine in the early
14th century (e.g. Marchettus).

To sum up, I would like very warmly to thank you not only for raising
the Dunstable and Dufay questions, and quoting the FAQ in a way which
maybe shows me how I may have diplomatically skirted around a delicate
question, but also inviting a consideration of the more general issue
of transitional styles, intonational or otherwise.

Most appreciatively,

Margo Schulter
mschulter@value.net

Open Letter to Page Wizard

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