On Sun, 01 Oct 2000 00:36:37 GMT, sqv at xs4all.nl.getridofthisone
(Samuel Vriezen) wrote:
>I mean, of course you need a certain amount of mathematical
>intelligence to do the theory of tuning right. But what about
>understanding phrasing? I think it would be more interesting to ponder
>the possible relationships between understanding phrasing, form,
>rubato, etc and mathematical thought. I think it is in that area that
>the possibility to understand patterning comes in.
Interesting thought. I had an observation that has some bearing to
this aspect during my training as a pilot: there is something called
"staying ahead of the airplane" - in other words, knowing what is
going to be needed at various stages of the future flight path well
enough to make actions in the present that will insure certain
outcomes, such as choosing rates of descent that will guarantee
certain airspeeds, taking into consideration things like passenger
comfort, minimum altitudes over certain points, ground speed, time
and fuel consumption, etc. Many factors, but the point is everything
you do now has an effect on events in the future. This is phrasing,
and this is composing form. During training the connection to
musical phrasing and formal understanding was crystal clear. There
were even many characteristic tones that the aircraft would produce
that I used to gauge events. Some of it was "seat of the pants" and
some of it was "mathematical." The same is true, at least for me, in
music. There are many mathematical, or at least arithmetical,
expressions which describe or control rates of change, proportion,
realtive speed, etc. and they can or could be used to describe musical
thought. The intuitive approach that most good musicians use is no
less "mathematical" for being unconcious, many of these questions tap
areas of common "truth" if you will, remembering that mathematics is
the study of the language of nature, and a search for beauty just as
much as music is.
Ken Durling