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.
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 firstname.lastname@example.org