Re: [microsound] math anxiety

[Michal Seta <mis@xxxxxxxxxxxx>]

On Mon, 22 Jul 2002 02:07:24 +0000
"ian stewart" <artsonics@xxxxxxxxxxx> wrote:

> 
> audisensa:
> >and oh yeah, there is not a shred of doubt in my mind about math and music
> being family... <
> 
> more than a shred of doubt in my mind (although it depends how you mean 
> this).

Since the beginning of the sixth century music was considered, at least by Boethius, as part of what later became the four Platonic scientific disciplines: arithmetic, music, geometry and astronomy.  Boethius wrote a treatise 'De Institutione Musica' which was intended to be read along with his 'De Institutione Arithmetica'.  So the idea of music being part of mathematical (arithemtic, really) education is not new.  In fact, the books Boethius wrote were not his orignal work.  They were records of what he studied in Greece so it goes further than that, at least back to Pythagoras.  And for Pythagoras music is related to numbers very clearly.  Not only music but sound.  And thanks to the quantitative nature of sound one can make music which is related to the sound of instruments through the same numbers.  Think of Pythagorean tunning system, which was based on the numerical ratios of harmonics of a vibrating string.  This relationship has been further explored by physists and mathemati
cians ever since.  One of the most interesting reads and perhaps most influential is 'On the Sensations of Tone' by Helmholtz.  So there is a very obvious relationship.

> although math can be used to model certain musical parameters, it 
> has, in my opinion, essentially nothing to do with what we find rewarding in 
> music.

true.  These days, when we hear 'music' and 'math' in the same sentence we tend to think:'algorithmic composition', which in turn isn't always rewarding (musically, at least.  Perhaps it is much more rewarding on the intellectual/conceptual level).  However, depending of what we think is rewarding, which is dictated by many different factors, our appreciation of music could be related to certain use of mathematics in music.  The tunning systems which were in use in the early (not only occidental) music are a proof of a search for a reward, which was the consonance.

> the math-music connection i think stems from a language confusion. we 
> use words like "logic" in both fields, but mathematical logic and musical 
> logic are fundamentally different things.

Not only logic but their goals are different.  However, it is very clear that (at least until the advent of equal temperament) the numerical relationships inherent to sound (audible or not, may I add - "Music of the Spheres" by Kepler is an example of applied mathematics and astronomy to sound and music) were found to be rewarding in music.  This is reflected in use of musical scales that contained 'perfect' consonances as well as in musical form which often was based on numerical ratios.

Now, I did not intend to imply that Mr audiosensa means exactly this...  Just my own ramblings on the subject.

BTW, are you the same Ian Stewart that used to hang out around the GEMS?

-- 
../MiS

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