Mazzola

Mazzola

[Peter Freyd]

  He [Guerino Mazzola] completed his PhD in mathematics and gained academic
  recognition in algebraic geometry and representation theory in 1980

  The next step was for Mazzola to apply his abstruse mathematical concepts,
  such as topos theory, to music theory

  [I have appended the Colin McLarty's MathSciNet review of Maxzola's "Topos of
  Music". Mazzola is still active as a reviewer for Math Reviews.]


                     Copyright 2006 The Jakarta Post Source
                             Asia Intelligence Wire
                                The Jakarta Post

                             May 27, 2006 Saturday

ACC-NO: A2006060563-11449-GNW

LENGTH: 916 words

HEADLINE: GUERINO MAZZOLA A WALKING MUSICAL CONTRADICTION

BODY:

from THE JAKARTA POST -- SATURDAY, MAY 27, 2006 -- PAGE 24 Acid rockers the
Grateful Dead have done it at the Great Sphinx of Giza; New Age instrumentalist
Yanni has done at the Acropolis; jazz pianist David Benoit has accomplished it
at India's Taj Mahal and China's Forbidden City

Two years ago, Swiss jazz pianist Guerino Mazzola also did it at the Prambanan
Hindu temple in Kalasan, Yogyakarta, when he made his first shot at performing
under the shadows of world's greatest monument

Next August, Mazzola will finally fulfill his dream of staging a show at one of
the Seven Wonders of the World and will have a chance to outshine the musical
greats

The 59-year-old musician is expected to stage a show under the shadow of
Borobudur temple in Magelang, Central Java, the world's largest Buddhist temple

Performing at one of the world renowned heritage sites would be a glorious feat
for lesser musicians, but Mazzola had the experience before when he staged a gig
at an Aztec ruin in Mexico

The planned Borobudur show -- slated for mid-August and to be the subject of a
documentary film by award-winning Indonesian filmmaker Garin Nugroho -- will,
however, be much more different

"It (the Aztec site show) was nothing, it was a flop as I absorbed no energy
from the historical site

"The planned Borobudur show, however, will be different as we have studied the
temple and the philosophy behind it and I hope I can absorb the energy from
ancient times," Mazzola said recently over a dinner in Kotagede, Yogyakarta

But even without Borobudur as a backdrop, Mazzola will likely deliver an
electrifying show and in turn draw a large crowd, among them knowledgeable jazz
fans

Known as the "Jackson Pollock of jazz", Mazzola has peddled for years the
so-called free jazz, a left-of-the-dial genre that champions musical exploration
to the fullest and sets aside any pretention to producing market-friendly music

A direct descendant of free-thinking jazz musicians like Ornette Coleman and
John Coltrane, Mazzola has adopted a technique that gives primacy to speed,
accuracy and dynamism, without abandoning sensitivity

Together with drummer Heinz Geisser, Mazzola have given a new meaning to jazz
improvisation, with each of their compositions being played in a different style
at each show

The duo has recorded several free-jazz CDs that have become a must- have for
jazz lovers in Europe. Mazzola has recorded music with jazz luminaries such as
Matt Maneri, Scott Fields and Rob Brown

"Unlike classical musicians who follow the direction from a conductor, a jazz
musician is a master of his own time and does not obey anybody," Mazzola said of
his esthetic

Casual fans, however, will be bewildered once they discover that Mazzola is also
a professionally trained mathematician who graduated from the University of
Zurich in mathematics, theoretical physics and crystallography

Someone who worships free musical expression -- unbound by technical constraints
-- he approaches his music with the precision of mathematical and physical
theories

He completed his PhD in mathematics and gained academic recognition in algebraic
geometry and representation theory in 1980

The next step was for Mazzola to apply his abstruse mathematical concepts, such
as topos theory, to music theory

"Music is a language that is very near to mathematics and there is a kind of
convergence between the two," Mazzola said, before launching into a lengthy
lecture about a new discovery in physical science that the elementary particles
that moved in space floated around and vibrated like strings on a violin

In spite of his verbose speech on mathematics that lent weight to his authority
in physical science, Mazzola dressed so casually that he could pass for, well, a
jazz musician

It took him 15 years of training in classical music before he found out about
jazz and became fascinated by it

And jazz proved to be much harder and more painful road to take

"I heard Errol Garner and was completely fascinated. I started listening to jazz
and learned his technique for 10 years. When practicing, my finger bled and the
keys were red everywhere," he said, referring to the American jazz pianist and
composer that played the greatest influence on his playing technique

He later found that the classical approach to piano was completely useless

After growing tired of imitating his idol, Mazzola started to use his sense to
guide him open up new musical terrain. "After spending many years imitating
others, you finally want to know what is inside you," he said

The decision to embrace free jazz could have also sprung from his contempt of
any authoritarian structure

A former communist well-versed in Karl Marx's works, Mazzola abandoned Marxism
and Communism after learning about its authoritarian tendencies

When he was a postgraduate university student in Paris, Mazzola was also drawn
to the Black Panther organization and protested against racism and the Vietnam
war

"Later, I learned about the abuse of authoritarian regimes that claimed to
espouse Marxism, and decided to leave it behind," he said

He also abandoned Christianity from learning that the church also showed a
similar authoritarian tendency, as in the Grand Inquisition

"I don't believe in God in a narrow sense. The only thing that I could agree
about God is that He has constructed the world through music," he said, with a
mixed expression between glee and solemnity

     **********************************************************************
Mazzola, Guerino(CH-ZRCH-MMI)
The topos of music. (English. English summary)

Geometric logic of concepts, theory, and performance. In collaboration with
Stefan Gvller and Stefan M|ller. With 1 CD-ROM (Windows, Macintosh and UNIX).
Birkhduser Verlag, Basel, 2002. xxx+1335 pp. ISBN 3-7643-5731-2 00A69 (18B25)

The author transposes the Pythagorean theory of harmonies into commutative
algebra because, on one hand, linearity is the modern version of additivity and
proportion, and on the other hand there are standard means for programming with
modules as data types. This working Pythagoreanism includes a CD with software
for analyzing scores and preparing them for electronic performance, and
recordings of some examples. Indeed the CD includes a pdf of the entire book,
nicer than the printed copy as it has color graphics plus active links to the
bibliography and to cross-references in the text.

There is an extensive mathematical analysis of musical structures
operationalized as categorical semantics for the programs. And the book gives a
very great deal of more cognitive scientific, semiotic, and literary music
theory. The author is known as a composer and a jazz pianist, and has other
publications in scheme theory, such as .ref[J. Algebra 78 (1982), no. 2,
292--302; MR0680361 (84d:16039)].

A key use of commutative algebra is given as "alterations are tangents". For
example, F-sharp and G-flat name the same tone and the same key on a piano
keyboard. The two names denote two different structural roles in
composition -- it matters that F-sharp is not just a note, but an alteration of
F-natural. The author regards the space of tones as an abelian group  M
so any single note is an element of the group, which the author treats as a
Z-element, a homomorphism  Z --> M  from the group of integers. Then an altered
note can be considered as a pair of notes, a base plus an altered value, and so
as a  Z x Z element of  M. In the traditional alterations, to sharps or flats,
the altered value is near the base note, and the author models these by
infinitesimal deformations, or tangent vectors. That is, he uses the ring of
dual numbers  Z[h], and all of this is applied over other ground rings than
Z, and thus brings us to scheme theory.

Symmetries within scores, and structural relations between scores, drive the
mathematics up to sheaves, and very briefly to toposes and Grothendieck
topologies. The author candidly states he is unsure whether this musicological
perspective can use topos cohomology (p. 436).

The remaining 800 pages of the book are more concrete (until the 100-page
appendix surveying concepts from group theory through schemes to vector fields
and differential equations). They deal with major semioticians, philosophers,
music critics and music theorists, especially computational music theorists.
They apply algebraic and geometric notions of symmetry, along with the
physiology of perception, to analyze harmony, cadence, motifs, tempo and
counterpoint. Examples analyzed at length focus on work of Bach and Beethoven,
but include Mozart and Debussy, Glenn Gould's eccentric performances, and the
author's works on the CD. All is operationalized as computational musicology, in
the software.

  Reviewed by Colin McLarty