Re: [microsound] math anxiety

[Michal Seta <mis@xxxxxxxxxxxx>]

On Mon, 22 Jul 2002 04:21:37 -0700 (PDT)
paul webb <paulwebb@xxxxxxxxxxxxxx> wrote:

> 
> These examples of relationships between mathematics
> and music are showing how certain musical cultures
> have been determined my mathematical thought and how
> this has coerced composition and instrumental
> development. 
> 
> Pythagorean tunning system was arbitarily based on
> integer relationships and created a scales based on
> integers where other musical cultures has scales which
> are fractional.

Pythagorean system was not arbitrarily based on ratios.  It was intentional and was derived from a very close study of properties of various sound objects (string, bell, hammer etc).

> The mathmatics applied to music are
> cultural artifacts has has effected what we consider
> to be musical.

it's quite the opposite.  It is the sound and music that comes first, which can in turn be explained and represented mathematically.  And, we cannot, yet, determine, through mathematics or other sciences what is 'musical'.  But experience and:

> Our perceptions of consonance and
> dissonance are not stable; until the 14th or 15th
> century, the third was considered extremely dissonant
> and is not in accord with Pythagorean idea of what is
> consonant.

It is mostly a matter of ever evolving taste.  14th-15th century has seen some pretty advanced species counterpoint and the third was rather considered as 'weak' consonance.  You're talking about circa 6th-11th century.  but then again, things moved very slowly then and there was a lot of overlap between different 'new' developments.

> Mathematics
> has been used to explain musical form and syntax - for
> example arriving back in the home key of a sonata.

I think that math was used mostly to help understand certain aspects of music.  And, sorry, I don't recall anyone trying to teach me sonata form in mathematical terms.  Could you point me to some resources?  I'd be interested to know more...

> But
> in fact, psychological experiments show that
> listeners, even very experienced listeners, generally
> cannot tell if a piece ends in the "wrong" key. As
> long as the key is prepared as if it were the home
> key.

I'm not sure about 'very experienced' listeners.  You mean music students, composers and such?  A very experienced listener will simply follow the harmonic progression and will 'know' that it does not finish on the 'right' key even if it 'feels' otherwise.

BTW, i don't think that music is a result of some applied mathematics.  But many things can be explained using simple arithmetics.

cheers

-- 
../MiS

Michal Seta		http://creazone.eworldmusic.com/doc/mis
CreaZone		http://www.creazone.com
No One Receiving	http://creazone.eworldmusic.com/doc/nor

upcoming release:
NOR - "The Release of the Wandering-Eyed Girl"
	http://www.grainofsound.com