David Olofson wrote:
actually and mathematically proving this
unfortunately is
beyond me, you have to try it yourself.
Well, why don't we ask someone who actually plays this kind of music
seriously? I can only tell you how *I* count when dealing with
complex rhythms - and I don't do it all that often. (I've done 5 + 4
beats per bar and that sort of stuff, and it's basically the same
thing; you need to "lock" on more relations that 1:1, or there's no
way you can both "drift" and not at the same time.)
Well what a coincidence! :) I just got back from a rehearsal coaching a
60-piece wind ensemble on this sort of thing. Most people these days
really do think of complex meters as non-integral values. (A lot of
musicians would be hard-pressed to explain it that way, though,
because at least in western pedagogy so much rhythmic terminology
is still highly subjective - think about terms like "feel" or
"groove".)
A very comon case might be the following: an initial meter of 4/4,
with a metronome makring of quarter=60. After 3 bars of 4/4, we
come to a 3/8 bar, then resume 4/4. That 3/8 is functionally equivalent
to 1.5, because the quarter note is *still* the counting unit, despite the
temporary change to a meter with an eighth-note denominator.
A more complex case, and one which is popping up with greater frequency
in some kind of music, involves divisions other than 2. For example,
imagine
we had been going along in 4/4, but each beat had been subdivided into
quintuplets.
(5 divisions per quarter). Thus, in 4/4 we have 20 such units. Now
imagine that we
needed to have a bar consisting of 7 of these units. (This is
occasionally notated 7/20).
Then we want to go back to 4/4 after a bar of 7/20. I don't think you
could use integers
for this. (Traditional time signature notation, as you see, represents
this very poorly.)
The only way to accommodate this with a traditional sequencer is to
clumsily insert
a tempo change, which I find very awkward.
-dgm
2) the first time somebody uses 1/3 and 1/4 at the
same time,
accumulating beat algorithms don't give the same result
reliably where they should.
Why not?
//David Olofson - Programmer, Composer, Open Source Advocate
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