| Original Message (ID '153629') By Claudia: |
| In Response To 'Re: Re: Re: Play[a sum of Harmonics]'
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Hi and thanks.
The complete signal I am working with is actually
Re[Sum[Exp[-.2 k] Exp[I*k*t*2 Pi], {k, 1, 20}]]
Thus the first harmonics (as in most musical instruments) already have a larger amplitude compared with the following ones.
I also tried different coefficients instead of Exp[-.2k], such as Exp[-.pk] varying p, 1/k, (20 - PrimePi[k]). These sounds are, as you expected, better than the ones without the falling coefficients but still they are not really nice to listen to. See (resp. hear) for example
Manipulate[
Play[Re[ Sum[Exp[-p*k] Exp[220 I*k*t*2 Pi], {k, 1, 20}]], {t, 0, .5},
SampleDepth -> 16, SampleRate -> 20000], {p, 0, 2, .1}])
I also tried manipulating the phases of each harmonics, adding a coefficient Exp[I*f(k)], where f(k) is a function, but again: no angel's voices were to hear.
I don't understand why in natural sounds the harmonics do not ruin the sound as much through interference as in these computer sounds. Or rather the other way round: I would like to know how to create nice sounds with harmonics (as in real life) in mathematica.. |
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