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

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Claudia
11/28/12 11:06am

I am using the Play tool of Mathematica in order to hear signals of the form
Re[Sum[Exp[880 I*k*t], {k, 1, 20}]]
In this case this would give
Sum[Cos[880 k*t], {k, 1, 20}]

As long as I only play a cosine wave
f.ex. Play[Cos[880*t] , {t, 0, 1}]
I get a nice sound.

When I add more cosines terms whose phases are not a multiple of each other
f.ex. Play[Cos[880*t]+Cos[900*t] , {t, 0, 1}]
I also get a nice sound.

Nevertheless, as soon as I play a sum of cosines (or sines) with phases that are multiple of each other
f.ex Play[Cos[880*t]+Cos[880*2t] , {t, 0, 1}]
the sound clearly deteriorates.

Notes as we know them are composed of sums of tones with frequencies that are multiples of each other (harmonics), i.e. they are of the form I am using in the last example. Why does this kind of function sound bad with the Play tool? What can I do to get a better sound?

I would be happy for any help!
Thanks,
C.

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Subject (listing for 'Play[a sum of Harmonics]')
Author Date Posted
Play[a sum of Harmonics] Claudia 11/28/12 11:06am
Re: Play[a sum of Harmonics] yehuda 11/29/12 09:10am
Re: Re: Play[a sum of Harmonics] Claudia 11/30/12 03:29am
Re: Re: Re: Play[a sum of Harmonics] WILLIAM STEW... 12/01/12 10:09am
Re: Re: Re: Re: Play[a sum of Harmonics] Claudia 12/02/12 10:38am
Re: Re: Re: Re: Re: Play[a sum of Harmonics] William Stew... 12/04/12 10:50am
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