Re: Medieval polyphony, humanism, and maximal consonance

Hello, there, and here are my immediate comments on the nature of
medieval music and the presence or absence of "humanism" in this era.

First of all, please let me emphasize that no one need apologize for
anything that has been said so far. The fact that I may take a
different viewpoint on some issues only indicates that there is may be
room for more than one opinion; indeed, the Tuning List might be
considerably less interesting were this otherwise <grin>.

Anyway, to begin with, I would say that although "humanism" is often
associated with the movements around the 15th and 16th centuries often
styled the Renaissance, in fact medieval humanism was a vital force in
its own right. We could discuss the "Carolingean Renaissance" of
around 800, interestingly coming not long before the first treatises
on polyphony dated to around the middle to late 9th century, and the
better known "12th-century Renaissance" accompanying the flowering of
polyphonic composition at Notre Dame and elsewhere.

Were medieval composers interested in saturating the senses with
beautiful harmonies? I would say "Yes, and they admirably succeeded."
Were they interested in "maximizing consonance"? I would say,
"Probably no more and no less than in any other era of Western
European composition -- with one possible and interesting exception
arguable."

Of course, the "maximization of consonance" concept has often been
applied not so much to musical styles of composition as tunings, but
in both cases the issues may be more complex than some recent
discussions might suggest.

From a certain viewpoint, the 16th century might be seen as uniquely
an era of "maximization of consonance" as defined at the time in a
tertian (5-limit) manner. In theory and practice, composers cultivate
smooth motions between saturation tertian sonorities, while applying
rather restrictive treatments to more complex intervals (e.g. seconds
and sevenths).

This "homogeneity" of texture -- suspensions in a sense being the
partial exception that proves the rule -- does give this music a very
special flavor of "maximal consonance" that can make either
13th-century or 18th-century polyphony seem "crude" or "needlessly
offensive to the senses" in comparison.

To complement this smooth tertian flavor, a 5-limit tuning (or
meantone for keyboards, which maximizes the prime concords for the
most part) brings out the sense of balance and delicate shading. One
might be tempted to compare this balance to the visual technique of a
Titian or Botticelli, and of course both arts are part of a scene
influenced by the cultural humanism of the time.

However, would we not be mistaken to assume that earlier and later
styles of composition favoring less homogenously concordant textures
are somehow indifferent to pleasing the ear or uninfluenced by
humanistic movements?

Thus around the end of the 12th century, the advent of regular
compositions for three or more voices by Perotin and his colleagues is
accompanied by a fascination with Classical rhetoric (e.g. John of
Salisbury), as well as an infusion of culture from Islamic
civilizations (reintroducing Greek sources such as Aristotle).

Thus John of Salisbury describes the sheer sensuous intoxication of
hearing part-music of this era, with its amazing mixture of high, low,
and middle voices. He says that too much is not a good thing, but that
in moderation this music can inspire spiritual refreshment and
tranquillity.

To me, the music of Perotin is awesome and exquisite, like a
stained-glass window with its brightly contrasting colors. This is a
very different art than that of a Titian, but is it less satisfying to
the senses in its own way?

In two ways, "maximization of consonance" is just as important in
Perotin as in Palestrina or Bach. First, Perotin in his works for
three and four voices fills the texture with complete trines
(i.e. full 3-limit sonorities with octave, lower fifth, and upper
fourth, e.g. D3-A3-D4). Secondly, the ideal Pythagorean or 3-limit
tuning indeed maximizes these stable concords, as any JI system seeks
to do.

However, while the 16th-century approach of smooth and homogenous
concord is certainly one way of gratifying the senses, bold and
studied contrasts between stable and unstable sonorities is another. A
demand that _all_ intervals have "maximal consonance" -- not just
stable concords -- may conflict with this kind of pleasing contrast,
as well as other stylistic imperatives of intonation.

An unqualified theory of "maximal consonance," for example, would
require that minor sevenths in Monteverdi's bold new dissonant
sonorities around 1600 always or as often as possible be sung at
around 7:4. However, this is likely to present problems for the
intonation system as a whole, and also to conflict with the likely
expectation that minor sevenths be treated as points of tension, not
of ideal euphony.

Note that such considerations do not exclude the possibility that
performers around 1600 (or around 1200) may have sung some minor
sevenths around 7:4. Nor do they exclude the possibility that some
major thirds around 1200 (melodic or vertical) may have been tuned
around 5:4 -- or 9:7, for that matter.

In any case, I might conclude that the idea of saturating a texture
with the most complex stable sonorities possible, and maximizing the
concord of these sonorities by tuning them in pure integer ratios
(e.g. 3-limit, 5-limit, or 19-limit just intonation), may be common to
most eras. The homogeneity of texture achieved in the Renaissance may
make that "early 5-limit" era in some ways unique.

However, each style is its own sensuous universe. A pure 3:2 fifth or
complete trine can seem just as rich and satisfying in a 13th-century
piece as a pure 5:4 major third or complete triad in a 16th-century
piece -- or a complete added-sixth chord or 11th chord in 20th-century
pop music.

Most respectfully,

Margo Schulter
mschulter@value.net

Margo Schulter wrote:

> to begin with, I would say that although "humanism" is often
> associated with the movements around the 15th and 16th centuries often
> styled the Renaissance, in fact medieval humanism was a vital force in
> its own right.

Quite so, and I oversimplified because it seemed to suit my
point. The last thing we need, IMO, is to get sidetracked
onto a topic as flammable as philosophy. But just so you
know whence I come, I follow Francis Schaeffer's view that
humanism, gradually expressing itself in ever greater
degrees of relativism, began to cause the decline of Western
thought and culture at about the transition between the
Middle Ages and the "Enlightenment." (See his book "How
Should We Then Live") If anyone wishes to discuss this
(admittedly unorthodox) idea with me, please do so off-list!
:-) There is, of course, a correlation between philosophy
and musical composition but I don't know whether its
implications for tuning are great enough to warrant
exploration in this forum.

> Of course, the "maximization of consonance" concept has often been
> applied not so much to musical styles of composition as tunings, but
> in both cases the issues may be more complex than some recent
> discussions might suggest.

That suggestion arose at least in part from my misuse of a
term. I confused consonance, which, as you eloquently
demonstrated, is relative to context, with beatlessness,
which as I understand it is a fairly objective ideal. In
doing so I also overlooked the obvious point that
non-beatless, even dissonant, textures can be as sensuous as
near-beatless JI, maybe even more so. Then I overlooked my
own point that medieval singers might not have been as
concerned with beatless sonorities as with other ideals
anyway! Do you still think I don't have anything to
apologize for? ;-) I'll never post anything on 3 hours of
sleep again!

David

David Finnamore wrote,

>I confused consonance, which, as you eloquently
>demonstrated, is relative to context, with beatlessness,
>which as I understand it is a fairly objective ideal. In
>doing so I also overlooked the obvious point that
>non-beatless, even dissonant, textures can be as sensuous as
>near-beatless JI, maybe even more so. Then I overlooked my
>own point that medieval singers might not have been as
>concerned with beatless sonorities as with other ideals
>anyway!

David, it sounds like you're still confused. The consonant sonority that
characterizes most Medieval music is not the Pythagorean 1-3-5 triad, which
was but one of many unstable sonorities, but the 3-limit diad, or what Margo
Schulter calls the "trine" where one note is doubled at the octave. The
3-limit diad is in fact more beatless (less beatful?) that the 5-limit
triad. So I would say that Gothic singers did equate beatlessness with
consonance as much as, say, late Baroque singers. It's just that the musical
language was different -- I don't think you'll find any 3-limit diads/trines
on strong beats in late Baroque music!

Paul H. Erlich wrote:

> David Finnamore wrote,
>
> >I confused consonance, which, as you eloquently
> >demonstrated, is relative to context, with beatlessness,
> >which as I understand it is a fairly objective ideal. In
> >doing so I also overlooked the obvious point that
> >non-beatless, even dissonant, textures can be as sensuous as
> >near-beatless JI, maybe even more so. Then I overlooked my
> >own point that medieval singers might not have been as
> >concerned with beatless sonorities as with other ideals
> >anyway!
>
> David, it sounds like you're still confused.

I didn't mean that I still think I was right, only that I
sort of contradicted myself.

> The consonant sonority that
> characterizes most Medieval music is not the Pythagorean 1-3-5 triad, which
> was but one of many unstable sonorities, but the 3-limit diad, or what Margo
> Schulter calls the "trine" where one note is doubled at the octave. The
> 3-limit diad is in fact more beatless (less beatful?) that the 5-limit
> triad. So I would say that Gothic singers did equate beatlessness with
> consonance as much as, say, late Baroque singers. It's just that the musical
> language was different -- I don't think you'll find any 3-limit diads/trines
> on strong beats in late Baroque music!

A good point. But I was still thinking within the context
of the thread about the possible limit-raising effects of
long reverberant environments on tuning. To be more
specific, while a medieval composition might not use triads
in stable positions "on paper," it would be nearly
unavoidable that even more complex virtual chords would
occur in a performance in such an environment. In fact, the
whole diatonic scale plus ficta would sometimes have to be
heard ringing together.

That said, I hesitate to speculate any longer on what effect
that might have had on intonation in practice. At first I
thought it would inevitably guide Pythagorean singers toward
5-limit JI. As Margo pointed out, to assert that assumption
would be a form of intonational fascism (she chose the less
inflammatory term "politics").

David