Re: Counterpoint

Hello, there, everyone, and thanks to a number of people for a really
engaging dialogue on counterpoint and related subjects.

Here's I'll try to address a few important points, some of which have
led me to ideas about how Gothic and Renaissance styles may indeed
differ in the degree of "fusion" between parts, although both are
based on a harmonious cooperation between vertical and melodic
dimensions. My warmest thanks to Robert Valentine, Joseph Pehrson,
Kraig Grady, and others for their perspectives and insights, although
any flaws in the "intonational fusion/differentiation" hypothesis I
present are, of course, my own responsibility.

Also, Graham Breed, your remarks raise for me a very interesting
question: does counterpoint have a tendency to favor tunings with
certain characteristics, and if so, is circularity or the more general
quality of regularity a factor here? Since this type of question may
have lots of intricate and often controversial aspects, I'll save it
for a separate post, responding also to Joseph Pehrson's remarks on
this kind of question.

Thanks also to Alison Monteith for recommending what sounds like a
fascinating text on medieval organum and discant, a text I might have
heard about but haven't yet seen.

Alison, I want very warmly to agree with your remarks that experience
with medieval materials could be helpful for dealing with various
kinds of tuning systems where transpositions may not be the most
important factor. For example, lots of 12th-13th century pieces have
an immense variety to offer with 7 or 8 notes used per octave
(diatonic notes plus Bb), although other accidentals in the range of
Eb-C# do get used also now and then.

---------------------------------------------------------------
1. Established styles and the personal touch (Robert Valentine)
---------------------------------------------------------------

Robert Valentine, thank you for raising some very important questions
about motivation and method in learning a given style of Western
European counterpoint -- or any established musical style of any era
in any world culture.

First of all, I would say that the decision to compose or improvise in
_any_ established style has its own advantages and disadvantages,
whether the style is that of a 13th-century cantilena, a 16th-century
madrigal, a 12-bar Blues or a rock song in a conventional 20th-century
manner, or an opus in extended just intonation after the manner of
LaMonte Young.

How old or new the style happens to be may not be that important to
the basic point that if one seeks to follow an established style, some
"artificial" conventions or patterns are involved, however natural
they may seem to the composer or performer.

Of course, one might add: if one has really made a style one's own,
then there likely will be not only obvious similarities to colleagues
and well-known works, but also some distinctive traits and quirks.

For example, in a more or less "Vicentino-like" style, I find the
minimal third of 1/4-comma meantone (the augmented second, close to
7:6) rather concordant, and like fifthtone progressions featuring this
interval; Vicentino himself describes it in his treatise of 1555 as
leaning toward dissonance. Here I feel free to be true to my own
taste, which might also reflect my penchant for the narrow minor
thirds of various neo-Gothic tunings.

This raises a more general point: as someone for whom medieval,
Renaissance/Manneristic, and derivative styles are a routine musical
mode of expression, my "Top 40" so to speak, I nevertheless may have a
different musical and intonational viewpoint simply because I am
immersed in _both_ Gothic and Renaissance practices, and the hybrid
outlook naturally generated from this mixture.

Personally, I find that a kind of balance may be involved: playing now
a "classic" Gothic or Renaissance style, now in an often classic style
but with some new intervals here and there, and now in something like
20-tone equal temperament (20-tET) where the _neo_-Gothic angle
definitely comes to the fore. Maybe this is a bit like the situation
of a performer with roots in traditional Blues, but lots of rock or
other influences also.

From this viewpoint, learning counterpoint in a given historical
European style is one example of learning a new style -- whether as a
first musical language, or maybe after an immense amount of experience
with other styles of music, European or otherwise. The motives and
applications can be as varied as the learners.

-----------------------------------------------------------
2. For Joe Monzo: on 14th-century polyrhythms and mannerism
-----------------------------------------------------------

In discussing the 14th century, Monz, you've called to my attention a
point not always appreciated.

While the term "Manneristic" as applied to the late Gothic typically
refers to the last two or three decades of the 14th century and the
first decade or so of the 15th century (say 1370-1410), the elements
of polyrhythm and syncopation reaching a height in this epoch have
indeed been developing throughout the century.

(For unsuspecting readers, I should explain that while the term
"Manneristic" is often applied to the era of around 1540-1640, Willi
Apel and others have applied it also to the era around 1370-1410,
which is seen to have certain analogous artistic qualities of
complexity and calculated distortion of a "classic" model.)

As an advocate of the _Ars Nova_ or "New Art" of the early 14th
century, the composer and theorist Philippe de Vitry used the device
of "coloration" -- notes in red rather than the usual black -- to show
a change in meter in a given part. The result is a texture where one
part may be in meter corresponding to the modern 6/8, for example, and
another in 2/4.

This kind of polymeter reaches its culmination in the "Manneristic"
epoch or _Ars subtilior_ ("more subtle art") near the end of the
century, when one voice in 9/8 may be set against another in 2/4, for
example, or a 9/8 measure (in terms of modern time signatures) may be
split into two equal parts of 9/16, or a melodic line may take on a
rhythmic pattern such as "3 + 2 + 3" or the like.

Sometimes I attempt to capture a small part of this in my keyboard
improvisations, with a usual Pythagorean tuning having a beautiful
effect and related neo-Gothic schemes offering some shadings and
variations.

Anyway, Monz, we both seem to be captivated by this music, and I'd
much agree that in terms of the rhythmic independence of the parts, it
may be the high point at least until the 20th century. There are lots
of recordings by medieval ensembles, including more recent ones on CD,
and one source on these is Todd McComb's fine Early Music FAQ site:

http://www.medieval.org/emfaq/

Incidentally, Joe Pehrson, this reminds me of our discussions about
musicology, and your remarks about how it's curious that _more_ is
known now about medieval or Renaissance music now than in 1700, say.
Maybe both the quest of the 20th century to rediscover as it were the
art of counterpoint apart from 18th-19th century tonality, and the
interest of such styles as serialism in the kind of mathematical
construction practiced by 14th-century composers (e.g. isorhythm),
helped to encourage interest the _Ars subtilior_. Stravinsky, for
example, wrote an introduction to Willi Apel's collection of 1950,
_French Secular Music of the Late Fourteenth Century_.

--------------------------------------------
3. Discant, counterpoint, and florid writing
--------------------------------------------

In response to a query from Joe Monzo, I would explain that discant
(_discantus_, literally "singing apart") is the older term, dating
back to around the 12th century, and counterpoint (_contrapunctus_)
the newer one, dating to around the opening of the 14th century.
However, both terms continued to be used in the 14th-16th century
era.

Styles other than note-against-note -- "counterpoint" in the strict
14th-century sense -- are sometimes referred to as _cantus fractabile_
or the like if I remember correctly: literally "breakable song," where
the notes are ornamented or "broken" into smaller values.

However, medieval discant and late medieval and Renaissance forms of
counterpoint could also generically refer to "part-music" or
"polyphony," not necessarily note-against-note.

---------------------------------------------------------------
4. Texture, fusion, and differentiation: Gothic and Renaissance
---------------------------------------------------------------

Thank you, Robert Valentine and Joseph Pehrson, for some remarks about
"simultaneity" and "texture" which have helped lead me to a distinctly
intonational view of the way in which 16th-century counterpart may
differ from that of earlier 13th-14th century Gothic styles, with the
15th century serving as a kind of transition.

While people sometimes refer to Renaissance style as more "vertical"
than Gothic style, I tend to respond that both melodic and vertical
dimensions interact in either style, and that it's quite possible to
find 13th-14th century pieces where we have something like a leading
upper melody supported by accompanying lower parts, as well as
16th-century pieces with all kind of complex interweaving of melodic
strands.

However, while _simultaneities_ are vital to both styles, I realize
that indeed in one way 16th-century style is more "harmonic" in a
certain acoustical interpretation of that word: sonorities with
closely fused or potentially fused partials pervade the texture, with
other kinds of sonorities subject to rather cautious restraints.

In other words, apart from suspension dissonances and the like, the
prominent sonorities making up the texture are based on simple ratios
of 2, 3, and 5 (e.g. 4:5:6 or 10:12:15), inviting a pervasive "fusion"
of partials.

While the stable 2:3:4 trines of Gothic music similarly achieve this
fusion, other sonorities serve from this acoustical perspective to
differentiate the voices and melodic lines even while uniting them in
meaningful and often compellingly directed vertical progressions. We
have a harmonious concourse of stable and unstable ratios, but
something quite different from the seamless or almost seamless fusion
of the 16th century.

In a _relatively_ concordant Gothic sonority like 64:81:96, or for
that matter a neo-Gothic sonority like 28:33:42 or 14:17:21, the
voices concord to a degree, and yet "are heard to differ greatly," to
quote a 13th-century description of major and minor thirds as
"imperfect concords." Sonorities with simpler ratios such as 6:8:9 or
4:6:9 may have a similar effect, because they have "trine-like"
qualities but also major seconds or ninths adding an element of
excitement and tension -- and differentiation.

When people draw a distinction between Pythagorean and "Just" tunings,
rather than considering the former as one example of the latter, this
may reflect an ideal of "just intonation" as involving a _pervasive_
fusion of the converging melodic lines. This is the distinction made
by scholars such as Carl Dahlhaus and Mark Lindley: thirds and sixths
represent a moment of differentiation in Gothic music based on
Pythagorean intonation (or neo-Gothic music based on typical
temperaments), but a moment of fusion in 16th-century music.

Both intonational and more general categorical considerations may
contribute to this contrast: in Gothic music, as in much 20th-century
music, just about any category of diatonic interval may be used quite
boldly, with seconds and sevenths often playing a prominent role. In
16th-century music, categories other than thirds and sixths are
subject to a range of restraints (the rules on fifths by parallel or
similar motion, the treatment of seconds and sevenths as incidental
tones or suspensions).

The intonational factors seem often to mesh with these categorical
ones: Pythagorean or neo-Gothic schemes offer a mix of simple and
complex ratios in prominent places, while Renaissance meantones and
just intonation systems favor simple ratios of 2, 3, and 5.

In short, "harmony" as a vertical dimension of beautiful ratios,
sonorities, and progressions is common to both eras of discant and
counterpoint. It is "harmony" in the narrow sense of "pervasively
merging partials" which may distinguish the vertical fusion of the
Renaissance from the bold Gothic contrast between fusion and
differentiation as approaches for unifying the parts in an
artistically satisfying whole.

Most respectfully,

Margo Schulter
mschulter@value.net

--- In tuning@y..., "M. Schulter" <MSCHULTER@V...> wrote:

/tuning/topicId_20658.html#20658

> This kind of polymeter reaches its culmination in the "Manneristic"
> epoch or _Ars subtilior_ ("more subtle art") near the end of the
> century, when one voice in 9/8 may be set against another in 2/4,
for example, or a 9/8 measure (in terms of modern time signatures)
may be split into two equal parts of 9/16, or a melodic line may take
on a rhythmic pattern such as "3 + 2 + 3" or the like.
>
> Sometimes I attempt to capture a small part of this in my keyboard
> improvisations, with a usual Pythagorean tuning having a beautiful
> effect and related neo-Gothic schemes offering some shadings and
> variations.
>
> Anyway, Monz, we both seem to be captivated by this music, and I'd
> much agree that in terms of the rhythmic independence of the parts,
it may be the high point at least until the 20th century. There are
lots of recordings by medieval ensembles, including more recent ones
on CD, and one source on these is Todd McComb's fine Early Music FAQ
site:
>
> http://www.medieval.org/emfaq/
>
> Incidentally, Joe Pehrson, this reminds me of our discussions about
> musicology, and your remarks about how it's curious that _more_ is
> known now about medieval or Renaissance music now than in 1700, say.
> Maybe both the quest of the 20th century to rediscover as it were
the art of counterpoint apart from 18th-19th century tonality, and the
> interest of such styles as serialism in the kind of mathematical
> construction practiced by 14th-century composers (e.g. isorhythm),
> helped to encourage interest the _Ars subtilior_. Stravinsky, for
> example, wrote an introduction to Willi Apel's collection of 1950,
> _French Secular Music of the Late Fourteenth Century_.
>

Hello Margo!

Thank you so very much for your interesting commentary and also for
the clarification of the "Euler's constant" method of deriving your
scalar material which is now perfectly clear...

There is probably more to say in the discussion of counterpoint
and tuning which took place with Graham Breed. Graham seems to feel
that counterpoint (sorry if I'm speaking for you here Graham!)
flourishes in a CLOSED system... and I could certainly see how he
could come to these conclusions. HOWEVER, in another of his posts he
seems to feel that, in a contradiction, counterpoint might actually
EXPAND an OPEN system.... Frankly, I might tend toward THIS view,
since it seems if there were possibly MORE notes to use in a system
that hadn't been used, counterpoint might DISCOVER them! Anyway,
perhaps it's something worth more discussion and investigation...

Since I'm in the mood for something subtle, perhaps I will go for
something even "Subtilior" and investigate some of the interesting
CDs mentioned in Todd McComb's incredibly comprehensive Medieval and
Renaissance site... Maybe a recording of some of the works of the
Chantilly Codex would be "illuminating." (Presuming it's an
"illuminated" manuscript!)

Thank you for information on Stravinsky. Curiously I hadn't heard of
his introduction to the Apel book... I'll have to find that. More
familiar, of course, is his work reorchestrating Gesualdo madrigals
for instruments in his monumental MONUMENTUM PRO GESUALDO DI VENOSA.
I have never listened to these orchestrations "side by side" with the
originals... that might be an interesting project for a recording...

Thanks again for the listening tips, and I think, like Joe Monzo, I
will also be fascinated with the _Ars subtilior_ period...

________ _____ _____ ___
Joseph Pehrson