On Tue, 29 Sep 2009, Chris McCormick wrote:
Thx hard off! I have found a good way to get appealing melodies is to
have a bit of fractal stuff going on. One way to do this is to have the
same melody at different speeds (double speed, half speed, triple speed,
quadruple speed) laid over the top of eachother, and then switch
randomly between the normal speed melody and the other speeds. It means
you get melodies which are internally self similar and for some reason
the brain likes that (well my brain does anyway).
Hmmm, can this be called self-similar? well, if you do have speeds 0.5,
1.0, 2.0 and 4.0 at once, then doubling the speed of the whole thing will
cause the speeds to increase speeds to 1.0, 2.0, 4.0, 8.0, so with 3 out 4
speeds (or 3 out of 5) the system displays a large amount of approximative
self-similarity, but if you add 3.0, 5.0, etc. then depending on which
ones you actually choose, it may match much less. Usually, it's called
self-similar when the whole thing is equal to a simply transformed (e.g.
uniformly scaled) version of itself, but I'd gladly extend it to
not-exactly-equal things as well... as long as it's more equal than
non-equal...
In general, exact powers are a key concept in getting more
self-similarity... so for example, you could use just a bunch of powers of
two, but if you do use three as a multiplier, use it multiplied by each of
those powers of two, and also use many powers of three multiplied by each
of those powers of three. This would be more self-similar but it doesn't
mean that it'd be any easier to follow. It seems that powers of 2 are a
lot, lot easier to think about than powers of 3, 5, 7, ...
otherwise, there's not just self-similar patterns that stimulate the mind:
also perfect harmonics do (just intonation, etc). so if you use the speeds
0.5, 1.0, 2.0, 3.0, 4.0 at once, it's like using the harmonics 1,2,4,6,8
at once in a timbre, or like making a chord of four consecutive
fundamentals and a fifth. (actually, unrolled, that's degrees I, VIII, XV,
XIX and XXII).
On a related note (pun intended), music history started with a
predominance of just intonations, because that's what struck a c(h)ord in
the mind at first, because it's made of perfect harmonics, but then the
less-harmonically-perfect equal-intonation has largely replaced it,
because equal-intonation is more self-similar than just-intonation is!
Here, self-similarity is important because it allows transpositions of the
same melody to appear more closely related.
Hoping that those ideas will in turn give you some ideas of how you could
tweak your list of speeds, or come up with any other new concepts.
_ _ __ ___ _____ ________ _____________ _____________________ ...
| Mathieu Bouchard, Montréal, Québec. téléphone: +1.514.383.3801
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