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Student Support Forum > General > > "Play[a sum of Harmonics]"

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Original Message (ID '153629') By Claudia:
In Response To 'Re: Re: Re: Play[a sum of Harmonics]' --------- 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..