I’m a bit skeptical to this day that a Fourier series can accurately reproduce a musical instrument beyond simple ones. A clean Trumpet, a couple types of bowed strings, a flute, bells.
But anything more complicated like a piano? I have yet to hear any additive or subtractive synthesis that can come close. I think that’s why it was abandoned by the late 1980s.
I think there are 2nd and 3rd order sounds that are emergent that a Fourier series simply can’t capture.
For that reason, and others, I don’t think that the Universe is strictly harmonic in a Fourier series way.
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Even adding partials, inharmonicity, and overtone to fundamentals and harmonics isn’t enough to reproduce.
But there are other ways than Fourier. I think what we learn about Fourier and instruments is a convenient myth, a simplification for learning purposes, but put into practice, doesn’t match up.
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It’s good thinking this stuff through out loud. I find seeing my own thoughts in writing helps.
It helps even more when I do it in an “accountable space” like online among people.
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Turbulence is still an extraordinarily difficult problem to understand. That’s why studying fluids is useful in modeling complex movements There are many kinds of fluid to model and draw from for inspiration and it is sufficiently complex that fluid may be robust enough.
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Good metaphors (or analogs) are hard to find. 🙂
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I haven’t seen any research on the possibility of 2nd / 3rd order arising from instruments but I’m sure I can’t be the first to think of this.
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Oh I think information can have permutations. The question is one of granularity, I suspect. Limitations of our information retrieval plays into issues as well.
But as long as the rules of grammar are followed, you can permutate information, That grammar might be the grammar of math or the grammar of language – whatever rules bind and seperate, provide sense imparting and such.
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Discrete permutations, yes. But this is my bias: I consider continuous as an artifact of greek geometric ideals.
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“I guess, without sacrificing the nonlinear properties, a complete closure may not be possible. The nonlinear system is certainly deterministic but also unpredictab
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What helps me, but I am also not doing any of the math, as I’m basically a curious generalist, is this:
Anytime I have an original idea, look EVERYWHERE for the very same idea already out there.
Saves a lot of time and gives me reading to do.
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