Download Musical Apartheid - James Noyes

Humanities, Math, and Science:
Music’s Unseen Scaffolding:
James R. Noyes
© 2009
“[I] have learned more about counterpoint from
[novelist] Jean Paul than from my music teacher.”
- - Robert Schumanni
As you may have noticed, in recent months a temporary framework has been assembled at
the site of historic Riverside Church. Presently utilized for the purpose of repairs, it reveals that
which was the most fundamental element in erecting this church: its scaffold. This carefully devised
system is used to support workers and materials during construction, but once a structure is able to
support itself and function on its own, the scaffold is dismantled – not so much as “removed,” as
merely “hidden from view.” And, while most people clearly understand the indispensable
relationship between scaffolds and buildings, it may come as a great surprise that musical
compositions (apart from traditional “visible” formulas such as sonata or theme and variations) are
often built in much the same way, not with the aid of poles and planks, but with that of humanities,
math, and science.
There are those who have long thought musical composition to be the product of divine
inspiration and nothing more. Here, one must be reminded (on this two-hundredth birthday of
Darwin), that creationism, be it applied to the origin of species or the origin of a work of art, has no
empirical basis. And, while Bach often quoted Gerhardt Niedt, who stated, “The sole purpose of
harmony is the Glory of God,” the composer is said to have insisted himself, “I had to work hard;
those who work as hard as I did will achieve the same.”
And what of this hard work? Consider his Cantata 106: are most aware that its structural
design follows exactly the formal elements of the six-part Aristotelian oratory? Or, that Baroque
music is based in the ancient rules of rhetorical speech as well as in the philosophies of Descartes?ii
Consider also the Fugue in C minor, from the Well-Tempered Clavier, Book 1: are most aware that
Bach went through four successive stages (from simple to complex) in composing this single work?
Or, that his typical plan for fugues was one of equal balance between thematic and non-thematic
sections?iii Consider also his “Canon per Tonos” from the Musical Offering, with its potentially
infinite modulations: are most aware that this style of composing shares technical elements found in
the work of graphic artist M. C. Escher and mathematician Kurt Gödel?iv
One better understands the reverence with which Schumann held writer Jean Paul upon
hearing the intricate musical plotlines as they unfold, indeed take unexpected twists and turns, in the
composer’s piano cycles. And, it was in the twentieth century that the compositional techniques of
Luciano Berio followed closely those of author James Joyce and the idea of “Work in Progress.”v
Claude Debussy revealed his literary obsession by confiding to a friend, “E. A. Poe…exerts over me
an almost distressing tyranny.” Looking at his career from beginning to end, Debussy was always
involved in projects heavily influenced by or entirely based on Poe, and in particular it was “The Fall
of the House of Usher” that cast the greatest shadow. Poe’s “The Philosophy of Composition” was
considered to be a “virtual catechism” by Debussy as well as the entire symbolist movement in art of
late 19th-century France.vi
Debussy was also a counter of measures (as was Bach and many others), and used
mathematical formulas based in the Fibonacci summation series (0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55,
etc.) to create naturally proportioned musical scores (including spiral shapes) based on the “Golden
Section,” which expressed as a number equals 0.6180…, or as an equation equals a/b = b/a + b.vii
Use of such proportions by Renaissance architects, as well as painters such as da Vinci or Hokusai is
widely known, and as applied in music, can be traced as far back as Monteverdi and the late 16th
century. The ancient Greeks named this number Phi, and discovery of certain geometrical concepts
(including that of the 5-pointed star) based on Phi is attributed to Pythagoras (whose tuning system
based entirely on 3:2 is still in use by modern string orchestras). Looking even further into the past,
we see this proportion in snail shells, pinecones, sunflowers, and throughout the natural world. As a
phrase, Phi is expressed as: “The smaller is to the larger, as the larger is to the whole,” which is an
exact description of fractal geometry. Translated into the language of music, it means that by
looking at the first few measures of any Beethoven score, one will find everything needed to
construct the entire work!
And what of the science of music? According to David Finckel, ‘cellist for the Emerson
String Quartet, “When I listen to this music [Bach] I feel my brain cells being re-aligned.”viii In fact,
many scientific studies have now linked musical training to enhanced spatial reasoning, as well as
higher scores on math, verbal and other aptitude tests. One astonishing fact is that nearly 100% of
past winners in the prestigious Siemens Westinghouse Competition in Math, Science and
Technology (for high school students) play one or more musical instruments.ix And, it has recently
been shown that dopamine neurotransmitters in the brain, which are activated during sexual activity
or eating chocolate (among many other pleasurable experiences), are the same neurotransmitters
activated while listening to one’s favorite music.x So, that’s the reason for those tingly feelings!
To be sure, the scaffolding of humanities, math, and science provides substance and
structure to the music we hold dear, and in a much greater sense, music is the scaffold of our lives.
It supports us in times of crisis and offers greater heights in our celebrations. It reinforces our
togetherness as brothers and sisters of a common humanity, and it does so by providing meaningful
nourishment for the body, soul, and spirit. Indeed, our relationship to music is utterly
indispensable, which begs the question: if this musical framework were taken down, would our
reasons for living still exist? Reminded of Darwin once more, and the tremendous success of our
species, it appears self-evident that music is and has always been our greatest survival skill.
i
Erika Reiman, Schumann’s Piano Cycles and the Novels of Jean Paul, (Rochester: University of Rochester Press, 2004).
Delano K. Kahlstorf, “The Two-Part Inventions of J. S. Bach: A Performing Edition Based Upon the Keyboard
Technique and Performance Practice of Bach and His Circle,” (DMA diss., Texas Tech University, 2002), 11 – 22.
iii
Ulrich Siegele, “The four conceptual stages of the Fugue in C Minor, WTC I,” from Bach Studies, Don O. Franklin, ed.,
(Cambridge: Cambridge University Press, 1989), 197-224.
iv
Douglas R. Hofstadter, Gödel, Escher, Bach: an Eternal Golden Braid, (New York: Basic Books, Inc., 1979), 10-21.
v
Scott W. Klein, “James Joyce and Avant-Garde Music,” a paper originally given at the Contemporary Music Centre's
ReJoyce in Music Seminar, June 2004. On the web at http://www.cmc.ie/articles/article850.html.
vi
James Noyes, “Poe & Debussy, and their Rapsodie,” booklet presented in conjunction with a lecture at the North
American Saxophone Alliance Biennial Convention, February 2006.
vii
Roy Howat, Debussy in Proportion, (Cambridge: Cambridge University Press, 1983).
viii
Emerson String Quartet, liner notes from Bach: The Art of Fugue, Deutsche Grammophon, 2003.
ix
MENC: The National Association for Music Education website, http://www.menc.org/resources/view/why-musiceducation-2007. On a personal note, my father, Russell Noyes, Jr., was a winner of the Westinghouse Competition in
1952 and plays tenor banjo, mandolin, dulcimer, and sings. He is also a distinguished painter.
x
Daniel J. Levetin, This is Your Brain on Music: the Science of a Human Obsession, (New York: Dutton, 2006).
ii