[sdiy] Fundamental tone generation questions

[Peter Blackett]

Hi,
I just saw this email on the Harpsichord list and thought I might get 
some better ideas here than any I've been able to provide.
please reply also to ahclark at AOL.COM [ Al Clark ]
as they are the original poster. [ and yes I did ask their permission 
before it posting here. ]

regards Peter



original email by Al Clark >>>>>>>>>>>>>>>>>>>>>>

Most of us are familiar with the heterodyning effect which allows one to 
hear the fundamental of the lowest bass notes in the harpsichord. The 
effect is described in the Benade and the (2) Kottick books. Since the 
instrument has such low radiating power in the fundamental, our ear/brain 
system mixes the signals from the higher harmonics and thus supplies the 
fundamental.

I've volunteered at the local science center to try to develop a 
demonstration module of this effect. Since I only have a book knowledge of 
the effect, I would be grateful for any advice on how to proceed. Perhaps 
there is a paper in some science education journal, where someone has 
already done it.

Here's what I'm thinking of doing, but I may be all wet.

I thought I would first breadboard a collection of 6 or 7 audio 
oscillators, tuned to say 50 Hz, 100 Hz, etc. Then I would either feed 
these signals through a summing amplifier or use separate amps going to 
small speakers. If I use speakers rather than earphones I'll probably have 
to build a small enclosure, since a science center on Saturday morning is 
a pretty noisy place. I would have switches for each harmonic so that the 
visitor could see how (hopefully) even just using say the 6th and 7th 
harmonic will still provide the fundamental.

How should I adjust the relative intensities of the harmonics? Intensity 
inversely proportional to frequency?

How critical is harmonic distortion in the electronics? If I use a summing 
amplifier and/or earphones, I'm concerned that some of the mixing might 
occur in the electronics rather than in the ear/brain system. The user of 
course wouldn't know the difference, but it wouldn't be honest. And of 
course I definitely would not want the user to turn on only say the 2nd 
harmonic and hear the fundamental due to distortion!

I suppose I could do the whole thing digitally with digital synthesizers 
and approprate software. I'm concerned, however, that this approach might 
not be as transparent as seeing the oscillators, wires, etc.

BTW, I use the physicist's definition of harmonics (fundamental is the 1st 
harmonic, first overtone is the 2nd harmonic, etc). If someone responds 
and uses a different nomenclature and it's relevant, kindly note it.

All advice gratefully received.

Thanks, Al