Philip Sheppard <[log in to unmask]> wrote:

>Thanh-Tam Le wrote:
>
>>Socially speaking, [...] I could say that both worlds are quite ignorant
>>of each other.
>
>I couldn't disagree more...  musicians and mathematicians have enjoyed
>and appreciated both the abstract and the literal parallels between their
>subjects for centuries - and I cannot think of a composer who has been
>'quite ignorant' of the numbers, patterns, and structures which often form
>the skeleton of their work. ...

Since some readers had perfectly understood my post and agreed with it, I
was surprised not to meet some sharp disagreement.  Thank you for this!

Well, I think that we could disagree more, actually.  I never suggested
that there were no mathematics in music!  There are more than many of us
think, precisely.  Your references are excellent, of course, although I
doubt that *every* musician in Europe has read them or would even care
about them (that they should is something on which I'd certainly agree with
you).  What I meant was that the reasons why a mathematician and a musician
devote their days and nights to their respective fields were much less
similar than many people thought they were, and that -- for instance --
it was by no means easy for any of them to imagine what essentially and
formally is the stuff the other's life was made of.

Composers definitely are more interested in theoretical aspects than most
instrumentalists (if this, again, sounds utterly wrong to you, then French
musicians and quite a few British musicians I know must not be living on
the same planet as most British musicians!).  However, Bartok's use of the
golden section is one of the reasons why his obsession for symmetry and
proportions are famous among 20th-century composers.  Mozart's numerology
in the Zauberflote certainly is mathematically more elaborate than many
operas of the same period.  Their interest in numbers is not exceptional
but, let me say, of a singular extent.  That a composer of any century
should use at least some mathematical tools is normal and a good thing.
Now, when some composers of our time use theoretical notions whose names
refer to actual mathematics unknown to most musicians, they can appear
as mathematicians among musicians, but as far as I know almost all of
them would find it difficult to compete with actual top mathematical
researchers.  Indeed, this is nothing to be ashamed of, since they are
composers.  Only, saying that they could have become brilliant scientists,
but did not because they *also* had a creative gift, strangely resembles
pretense in most cases.  Nonetheless, many composers have at least a
minimal knowledge in arithmetics, which is an important part of
mathematics, if only one among many.  I would not be sure that all
instrumentalists have such a knowledge, beyond standard rhythms and
fingerings.  But certainly some do have it, no doubt about that.  (Oh, of
course, many scientists can play the notes of some Liszt pieces decently,
and thus think that they could have been Horowitz if they had not had more
serious tasks to do...)

Somehow I seem to have offended you, which obviously was not my aim.
I would certainly not doubt your mathematical abilities, which happen to
be clearly higher than many of my fellow musicians could possibly boast.
I simply believe that identifying music and mathematics misses the point,
and please believe that many people do identify them to a large extent.
As fields of human thought and culture, they share a number of common tools.
This does not make individuals working in these fields identical in their
essential impulse and in their everyday life.  Conversely, some persons can
have both music and mathematics in their minds (I am an instance of this,
and this alone does not always elicit kind comments, especially in the
musical milieu -- how do I know? I lived there and talked with musicians!).
But if they actually meet in one body and partly coincide, this common part
*generally* is not the very potent motive which gave us the strength to
devote ourselves to either or both of these demanding fields.  This seems
to be a reasonable statement and comes, at least but not exclusively, from
my own experience.

Please note that I always said "most" and "at least in France".
Fortunately, there are quite a few exceptions to various degrees, but this,
I hope, does not make my point false in the whole.  Believe me, I wish it
did and both worlds were (socially) more open to each other, less defiant.

Best wishes,

Thanh-Tam Le