I'm trying to understand why synch siteswaps might feel like a bad
system. To
me, something like naming a vanilla siteswap and then separately telling
the
correct timing is far inferior. (Different ways of doing this have been
suggested, and I guess it can have it's uses in patterns with more complex
rhythms.) Your example of calling (4x,4x) as 53 with altered rhythm (one
hand
throws everything a beat too early) works but it doesn't illustrate the
pattern
nearly as well. Using (4x,4x) clearly shows it to be a symmetric pattern
at
first glance, it indicates the pattern being synchronous, and the relative
heights of the throws are similar to that of someone juggling an asynch
fountain with four. With the other way, there is room for confusion on
which
hand is throwing too early, which results in more than one way to notate
the
same pattern, like (6x,4)(6,4x) derived from both 7463 and 6455 , and 53
could
also mean (6x,2x) . Of course this can be worked around, but if for
instance
you are making a list of all the patterns, this is a large issue.
I can't help but feel the statement you reference as being very
old-fashioned,
or even close-minded in a way:
This [synchronous notation] no longer really quite fits in with "The
Siteswap Idea" that a throw be labeled by one plus the number of throws
while it's in the air - shouldn't we just be calling those things 1's
and 2's instead of 2's and 4's? Basically, mathematically, the answer is
yes. But this doubling of all the numbers in "synchronous siteswap" is
by now pretty standard, because it gives the proper indication of the
relative heights of the throws. For example, most people asynchronously
fountain 2N balls at the same height as they synchronously fountain 2N,
so it would be a little weird calling the throws 2N's in vanilla siteswap
and N's in synchronous siteswap. Also, the averaging theorem is still
true only if you double the numbers.
Having extra beats in between the synch throws relates nicely to asynch
patterns. If you want to show what happens on those beats, you can use
something like (4x,4x)!(0,0)! or even <2p|2p> and explain that your hands
are
the passing partners. For me synchronous siteswaps are a very natural way
to
extend the siteswap idea into something a little different.
As for the averaging theorem, it would still hold, even if we didn't
double
the numbers. Of course it needs to be explained how to use it in such a
pattern
(or multiplex, or passing etc.) but this applies to any formula in any
system
that you want to expand to include some other system as well! In any case
the
argument for doubled numbers comes down to it being practical, not just
theoretically sound.
Of course this thread started about causal diagrams, easily confused with
ladder diagrams. Not much to say about those right now, but they look good
on
the Juggling Edge!
Just thinking,
-Miika
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btw, tämä on toinen viestini tältä sivustolta
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