>i'd be happy to hear a good example proving this wrong. but
>take note that i don't accept 1/2, 1/3 and relatives as
>qualifying because they can better be (and usually are)
>expressed using integer numbers.
i've been down this road before, either here or on ardour-dev :)
you need to accept them as different. many indian rythmic cycles have
non-integral numbers of beats per cycle, and it doesn't work to simply
multiply them to get an integer. this shifts the entire rythmic
emphasis of the piece, produces a beat-per-measure value that is too
long to count, etc. consider, for example, a tala with 9-1/2 beats per
measure being played against a melodic line with 12 beats per
measure. the entire purpose of the piece is the slow shifting of the
melodic's line structure against the rythmic one. if you convert this
to 19 beats per measure in the tala, and make the melodic players
count 24 measure, they won't know what you are talking about - the
melodic structure (and the tala) are built out of 12 and 9-1/2 counts,
not 19 and 24. in fact, they probably won't want to have anything to
do with you. you're denying the structure of their musical tradition
because you want a simpler software structure. its even worse if you
have a polyrythmic piece with different non-integral beats per bar,
because you now need to find the least common denominator, and the
resulting beats per measure count can get ridiculously large.
western music's emphasis on integral beats per bar has led to a
slipping away of a great deal of the fun and beauty to be found in
other musical traditions. i've recommended it before, and i'll do it
again now:
"Music of the Whole Earth" by David Reck (Da Capo Press)
its a wonderful, humbling guide to the subtleties, variations and
unities to be found in the human-made music of our planet.
a friend of mine who grew up in india once commented to me on the way
that western classical and popular music has emphasized harmony over
melody and rythmnic structure; in contrast, indian classical music has
emphasized melody and rythmnic structure with an almost complete
absence of harmony; far-eastern classical music (bali, java, thailand)
has emphasized rythmnic structure and timbre with very little
development of harmony or melody.
i can't end that quote without his final observation: "and then i
found jazz" :))
>about arithmetic: float operations, as you know, introduce
>round-off error. integers can be used in accumulators with
>much less inconvenience.
sorry, its just wrong.
--p
