[Dixielandjazz] Music and Mathematics

[Stephen Barbone]

THIS IS NOT OKOM. IT IS NOT FOR EVERYBODY ON THE LIST, BUT THERE ARE
THOSE LIKE CHARLIE HOOKS WHO I THINK WILL ENJOY THE BELOW OBIT &
DISCUSSION ABOUT COMPOSITIONAL THEORY IN MUSIC.

HIS MUSICAL THEORIES DO APPLY TO THINGS LIKE JAZZ IMPROVISATION, AND
JAZZ COMPOSITION AND WHY MUSICIANS ARE PROFICIENT IN MATHEMATICS,
HOWEVER ON A LEVEL THAT MANY OF US MAY FIND TEDIOUS.

READ OR DELETE AS YOU WISH.

Cheers,
Steve Barbone




June 28, 2003 - New York Times - David Lewin's Obit

A Seeker of Music's Poetry in the Mathematical Realm

By EDWARD ROTHSTEIN

      I am sorry now that I did not write an opera with her every year,"
Virgil Thomson once wrote about Gertrude Stein. "It had not occurred to
me that
both of us would not always be living."

More and more, I am reminded of that sentiment, most recently last
month, when I heard about David Lewin's death at age 69.

His name does not spur widespread recognition. Obituary notices after he
died of heart disease on May 5, tended to be of the paid variety. And
the area
in which he displayed incomparable mastery is the most esoteric branch
of a rarefied subset of a specialized discipline.

David Lewin was a musical analyst — a specialist in the theory of how
musical compositions are constructed. The compositions to which he
devoted
attention tended to be 20th-century works with an already limited
following; he wrote essays on such exotica as Dallapiccola's "Simbolo"
and
Stockhausen's Klavierstück III. And his own work was an attempt to
construct a mathematical theory of musical composition, drawing on
fields in
higher mathematics, including group theory, algebraic topology and
projective geometry.

This meant that few people would read his work and fewer still would
fully understand it. I accomplished some of the former and less of the
latter.
Indeed, his two books are out of print and many of his papers
unavailable. But his influence has been extraordinary.

I first came to know David at the suggestion of the composer Milton
Babbitt, with whom I was discussing a book I was writing on music and
mathematics (later published as "Emblems of Mind"). Mr. Babbitt had been
trained in both areas, and so, too, had David, who studied piano with
Edward Steuermann, received a B.A. in mathematics from Harvard
University in 1954 and, after winning a prestigious fellowship to pursue
graduate
study in mathematics at Princeton University, switched his allegiance to
the music department, where he studied with Roger Sessions and Mr.
Babbitt.

So before contacting David, I spent some time working through his 1987
book with the imposing title, "Generalized Musical Intervals and
Transformations" (Yale). Its style and approach were eerily familiar
from my own studies of mathematics, but here the objects of mathematical
scrutiny
were pitches, timbres, rhythms, phrases. The effect was dizzying.

When we started to talk, I found that there was yet another reason for
David's reputation. He was not just an analyst; he was a consummate
teacher.
Since 1985, he had been the Walter W. Naumburg Professor of Music at
Harvard University; he had also taught at Yale University, the
University of
California at Berkeley and State University of New York at Stony Brook.
And in conversation, the theoretical severity turned welcoming, the taut

arguments solicitous, the pleasures of interaction paramount. When I
showed David my work, he went on to mark up my text, raise questions and
then
advocate it. I looked forward to our intermittent conversations and to
our infrequent meetings at conferences.

Last week I also learned that I was not alone in this sense of his
humane intellect. For four days, some four dozen scholars at the Mannes
Institute for
Advanced Studies in Music Theory, directed by Wayne Alpern, discussed
David's theories. David was originally scheduled to speak; instead, a
session
was devoted to his memory. Scholars from Finland, Germany, the
Netherlands, France and England joined American colleagues and David's
wife, June, and son, Alexander, in praise and tribute.

Mr. Babbitt spoke of his allusive brilliance, of the influence of his
Quaker elementary education, and even of his Viennese teacher, whose
face bore a
scar from defending Gustav Mahler against a heckler. Others, in
sometimes teary tribute, spoke of his influence on the profession, his
generosity, his
attentiveness to young scholars. He wrote fugues using phone numbers to
construct musical themes, dryly punned in multiple languages, championed

his students and often learned from them. "I think he created the
intellectual world I live in," one analyst said.

The personal feeling was remarkable, particularly because his ideas went
against the grain of much musical thinking in the last few decades.
While
colleagues were examining ways in which compositions reflect political
ideologies, or applying literary theory to music, he championed an
abstract
idealism that had its origins earlier in the century, in the works of
such theorists as Heinrich Schenker.

One of his arguments, in fact, was that music could be more profoundly
understood not by seeing it more concretely — not by finding the ways in

which it refers to objects and ideas in the world — but by seeing it
more abstractly, finding the ways in which it creates internal order and
coherence.

He suggested, for example, that we think about how a composition creates
varieties of musical "space." Any space, he noted, is mapped out using
notions of distance and direction, but the nature of that space can be
defined in different ways. Two notes, for example, may be a certain
"distance" apart;
they may interact in certain ways that give them direction; there is a
"space" of pitches within which melody works its wiles. Two moments in
time can
also be used to define notions of distance and direction, creating a
different kind of "space," unfolding in time. So can different timbres
or rhythms or
harmonies. Every composition is a network of these interlinked abstract
spaces.

There is an aesthetic behind this analysis, one that is most clearly
connected with some modernist compositions — severe and tautly
constructed works
that, in recent years, have too often been dismissed as arid or
academic.

But the level of abstraction is so great that Lewin's work, while
inspired by modernism, actually breaks down boundaries between styles
and genres.
Define the space differently and instead of talking about a Babbitt
String Quartet, you could be discussing a Chopin Nocturne or a raga or a
rock
improvisation. If music coheres, if it "hangs together," it is because
similar patterns are being established in different spaces. The way
melody works
may resonate with the ways in which rhythms are ordered or the ways in
which harmonies interact.

I don't think David ever considered his theoretical work complete, but
its possibilities now define a field called "transformational analysis."
There are
many things I wish I had asked him, but it had not occurred to me that
both of us would not always be living.