[MD] Ham on Esthesia

[Ham Priday]

Case and all other non-esthetes --

[Case said]:
> Harmony is a mathematical idea.
> It was discovered by Pythagoras.

[Ham said]:
> Harmony is primarily an aesthetic experience.
> What do you suppose prompted Pythagoras to explore
> the chordal relationship of musical pitches in the
> first place?  He was pleased by the sound of harmony.

[Case replied]:
> As for Pythagoras you could not be more wrong.

Here's what the Pythagoras website says about this man's alleged
"discovery":

"This harmony indeed existed only in the abstract -- just as numbers and
mathematical formulas are abstractions.  But to Pythagoras -- this was the
realm of the truly Real.  It was not the world of "things" and daily events
that was the truly Real.  It was the mathematical abstractions or harmonies
standing behind such things that was the Real.  And thus it was his
determination--and the goal of his school--to uncover this hidden, even
"secret" or "mystical," abstract realm of numerically perfect "harmonies"
permeating the universe."

"Aha!" I can hear Case saying; "You see, I told you so!  Harmony is a
mathematical abstraction, a numerical formula.  Only objective scientists
like Pythagoras really understand it."

But then, I read a little further ...

"For instance, the story is told that he remarked in passing a blacksmith's
shop that the ringing sound of different hammers on the anvils produced
distinctly steady and consistent tones (like that of today's tuning fork).
He noticed that the tonal difference was related to the relative size and
weight of the hammers. This supposedly gave him the idea that musical tones
could also be expressed in mathematical terms.  He experimented with
stringed instruments and soon realized that an octave's difference in tone
could be produced by the exact doubling (or halving) of the length of the
string of a musical instrument.  In fact the whole musical scale could be
produced precisely by differing the lengths of such string.  In short, even
sound was reduceable to such mathematically perfect 'harmonies'."

It was the aesthetic value of the harmonious sound from the blacksmith's
shop that sparked Pythagoras' interest.  But harmony had been discovered
long before Pythagoras "defined" it.  It was recognized and had been
demonstrated by Greek musicians like Terpander of Lesbos (7th cent. B.C.),
Archilochus, Sappho, and Anacreon, and by the choral music of the following
century.  Sure, we credit Pythagoras for "reducing" musical harmony to its
mathematical correlates.  But, had Pythagoras been deaf, his work in this
connection would likely have been done by someone else.

Of course it was J.S. Bach who tempered the (mathematical) pitches of the
scale so that music could be played in all 24 major and minor keys without
having to retune the instrument, and composed his "Well Tempered Clavier" in
1722 to prove it.

The moral:  Value is what drives mankind.  Let's not let the joy of what we
experience be reduced to intellectual symbols.

[As a post-script, Case adds]:
> Music majors tell me you can not really appreciate the
> underlying beauty of some composer's work without being
> able to read the score.

As a music major myself, I think this is mostly elitist snobbery.  The
beauty of music is in the hearing, and the "underlying" structure is
designed toward that end.  One can be trained to sight-read music with some
proficiency as a keyboard performer or vocalist, and arrangers are
sufficiently adept at reading (i.e., analyzing) orchestral scores to compose
musical bridges or correct wrong notes.  But even if gifted with perfect
pich, given the choice of playing or reading, a musician will invariably opt
for playing.

Beethoven and Smetana were the two most notable composers to suffer deafness
in their later years.  Beethoven's mastery of composition enabled him to
complete (and conduct) his 9th symphony ("The Ode to Joy") while totally
deaf, and he went on to compose some very advanced chamber music.  Smetana
agonizingly finished his final composition, a string quartet ("From My
Life"), in which a high E written for the violin in the last movement echoed
the sound he was hearing as deafness overtook him.

Thanks for relating music to the subject of aesthetic values, Case.  It's
most appropriate.

Essentially,
Ham