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Topic: Re: Harmonic series
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Doug Kuhlmann

Posts: 3,630
Registered: 12/6/04
Re: Harmonic series
Posted: Jan 7, 2002 11:30 AM
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Xu,

It does have a relationship to music. If one plucks a string, the
frequencies of the standing waves that it can sustain (I am assuming the
string is fixed at each end much the way strings on a cello are) are
integer multiples of the fundamental frequency. The pitches are
proportional to the reciprocals of these integer multiples.

Now this is a VERY simplified version of what really happens, but that is
essentially how the series came to be called the harmonic series.

I have below a few wep page addresses that will give some (at time
confusing) information. Some draw nice pictures.

Good luck.

Doug

At 9:26 AM 1/7/02, Xu wrote:
>However the recommented book by William Dunham
>is unavailable for me at present. So my problem remains.
>Again, can anyone tell me directly why the series
>1+1/2+1/3+...+1/n+...
>is called a "harmonic series"? Does it have any relation with
>harmony? Thanks a lot.
>
>Xu
>


Doug Kuhlmann
Math Department
Phillips Academy
180 Main Street
Andover, MA 01810
dkuhlmann@andover.edu



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