Re: Nature, nurture, history, and style (fwd)

Hello, there, everyone, and given the original exchange of views
involving Daniel Wolf and Julia Werntz, and the subsequent discussion
about nature, nurture, style, and history, I'd like just to express a
few points about medieval practice and theory, and a few general
points of philosophy.

First of all, while the possible role of popular music in the origins
of the Western European polyphonic styles first recorded around
850-900 remains an open question, the consonances used in this music
nicely reflect the concept of _symphonia_ or consonance between
simultaneous voices presented by Boethius (c. 480-524), based in good
part on earlier Greek theory.

Boethius says that consonance results from multiplex (n:1) or
superparticular (n+1:n) ratios: 2:1, 3:1, 4:1, 3:2, 4:3. Additionally
he notes that Ptolemy would include 8:3 (the eleventh, or fourth plus
octave), although the Pythagoreans hold that it does not fit the
pattern of a multiplex or superparticular ratio, and therefore should
be excluded from this category.

The _Musica enchiriadis_ and _Scolica enchiriadis_ from around the
late 9th century show how these _symphoniae_ may be used, singly or in
combination, to make _organum_ or harmonious polyphony.

In my view, the practice nicely fits the theory of Boethius -- which
might in turn reflect some kind of undocumented popular style of
polyphony, who knows? The use of fifths and fourths as vertical
intervals in various parts of the world is so widespread that I
wouldn't be surprised if theory reflected practice. Certainly it's
fair to say that the many communities around the world favoring these
forms of polyphony don't need manuals to tell them which intervals to
sing or play.

For example, I've seen an example of Chinese polyphony favoring
fourths which looks very much like the examples in the 9th-century
treatises we're discussing -- cited, not so surprisingly, in Richard
Hoppin's _Medieval Music_.

Of course there's a creative interaction between practice and theory.
While 9th-century examples include passages in oblique or contrary
motion, often involving unstable intervals, it's Guido d'Arezzo
writing around 1030 who describes and approves the deliberate use of
these intervals at cadential points, especially the _tonus_ (9:8
whole-tone) and _ditonus_ (81:64 ditone or major third).

By the 13th-14th centuries, we have what I consider one of the most
sophisticated schemes of concord and discord in the history of
European music, often with four, five, or six gradations from the
purest concord to the most acute discord.

This theory is immensely important to my own music, in concept and
practice, and the approach of multiple categories on a spectrum of
concord/discord has been developed by modern theorists such as
Ludmilla Ulehla in her _Contemporary Harmony_.

Of course, acoustical science has developed a great deal since the
Gothic era, and the practice and theory of temperament has much added
to our creative possibilities.

However, if one aims for an appreciation of medieval or neo-medieval
style, I would say that the treatises of that era are an excellent
guide to many aspects of the music.

Also, I would agree that a 9th-century or 13th-century theorist would
be unlikely to write: "What we're composing and performing is
'3-limit' music." Neither would Rameau or Kirnberger be likely to
write, "What we're composing and performing is 'pre-atonal' music."

Medieval theory is one viewpoint, and Partch's n-limit paradigm is
another. Each outlook has its own language, a language reflecting a
given stylistic practice or agenda. This isn't a matter of "progress"
or the opposite; it's a matter of changing musical fashions, in
practice and theory alike.

Often theory in a given time and locality can reflect practice, and
medieval Europe may be no exception. During the 9th-11th century era,
we can deduce that some areas leaned more toward fifths, others toward
fourths (e.g. Guido).

Given the report by Coussemaker's Anonymous IV (c. 1275?) that people
in the "Westcountry" of England consider thirds "the best consonances,"
we shouldn't be surprised that Theinred of Dover (12th or 13th century)
and Walter Odington (c. 1300) discuss simple ratios for these intervals
at 5:4 and 6:5.

With Marchettus of Padua, in my view, we have an equally interesting
description of what is likely an opposite kind of modification of
Pythagorean tuning, with cadential major thirds expanding to fifths
and major sixths expanding to octaves widened maybe to around 9:7 or
12:7, or maybe closer to 13:10 and 26:15. For a recent paper on this
kind of interpretation, please see

http://value.net/~mschulter/marchetmf.txt (plain ASCII text)
http://value.net/~mschulter/marchetmf.zip (ASCII and PostScript)

If one chooses to follow this kind of reading, the question arises:
was Marchettus championing a radically new practice, or at least in
part reporting a tradition of intonation, maybe with popular elements?

Also, this discussion provides an opportunity to cite another view,
that of our "Monz," Joe Monzo:

http://www.ixpres.com/interval/monzo/marchet/marchet.htm

More generally, I would say that the most important reality concerning
human music is the vast range of intervals, indeed a continuum, from
which beautiful music can be made.

Let's suppose, for example, that certain simple ratios are found to be
widespread in many world musics, rather as certain vowel or consonant
sounds may be more common than others in natural languages.

Should this constrain people speaking languages with less common
consonants -- or composers leaning toward less common consonances --
to conform to the most frequent practice?

Or does this in some ways make the "unusual" all the more precious and
significant, as an exercise in artistic choice and judgment?

Julia Werntz and Daniel Wolf, when I read your dialogue -- one which
graces this forum with the views of two outstanding composers,
theorists, and music educators -- I'm tempted to say that a conclusion
that "simple ratios have a special 'recognizablility' cutting across
cultural lines" would not radically change the artistic issues.

Now, as in the 16th century when Vicentino's use of "unusual"
intervals was debated, we might have at least two viewpoints:

(1) "CLASSICISM": Art should imitate nature, and therefore
either small-integer JI or some tempered approximation
is the artistically most productive approach;

(2) "MANNERISM": Art should not merely imitate nature but
creatively distort it, defining its own reality of
coherence and pattern, and deliberately seeking out
something other than the "obvious" ratios.

By encouraging singers to learn to sing his fifthtones or enharmonic
dieses (around 128:125 or 1/31 octave), Vicentino was aware that he
was advocating a skill both novel and not so easy; he recommended his
_archicembalo_ or "superharpsichord" as a guide, and opponents
regarded such steps as "unnatural" for the human voice and ear.

Is it really that important whether 16th-century Italian singers found
it easier to sing fifths than fifthtones as a result of nature or
stylistic nurture? Vicentino considered the new artistic possibilities
worth the effort, and maybe that's the main question.

With music, as with natural languages, I would consider variability
and choice to be the most important factors, and the differences of
view on concord/discord among members of this List could serve as an
example.

If someone decides, "I want to tune a third to an integer ratio of
n:m, or to a ratio of x cents," there are two possibilities. Either it
is an established interval size in some world music(s), or it is a new
choice. Either way, it is a legitimate part of the continuum.

The question of how an interval _should_ be tuned, a sonority
selected, or a composition organized, is one of style. To affirm the
elements of pluralism and choice is not to exclude any music, but
instead to affirm the continuum which leaves room for all the styles
and cultural traditions celebrated on this List.

Most respectfully,

Margo Schulter
mschulter@value.net

--- In tuning@y..., mschulter <MSCHULTER@V...> wrote:

> Boethius says that consonance results from multiplex (n:1) or
> superparticular (n+1:n) ratios: 2:1, 3:1, 4:1, 3:2, 4:3.

Monz, this seems to contradict what you just said about Boethius. When I say organum
was 3-limit, I mean that the _vertical sonorities_ were ratios using odd numbers no
higher than 3. So it seems Boethius's theory accords well with this view, if something like
organum existed in his day. If not, I would still claim that the extant music was
influencing Boethius's theories, and not the other way around (though I would be happy
to be proved wrong on that). But in either case, it seems clear that Boethius was _not_
proposing anything like a 5-limit standard of consonance -- right?