simple way to add harmonics to a fundamental signal

[Sean Costello]

Martin Czech wrote:

> 
> 2x, 4x frequency may be obtained by full wave rectifying (proper dc offset
> after each stage).  Input a tri wave, or sine. The result will still
> have some fundamental left, but in a mix with the fundamental, this is ok.
> 
> 3x is harder to obtain. You could try to feed a sine into a Tchebycheff
> polynome function.  3x would require a 3rd-order polynome.

How about doing something like the Serge Wave Multiplier, where the
waveform "folds over" at the top and bottom? With this, you can get
frequency tripling, 5X the frequency, 7X the frequency, and so on. With
a sine wave, you would get some distortion, but hey, that's the way it
goes. 

Perhaps you could have a circuit with several cascaded rectifiers, with
the output tapped after each stage. There could also be a "fold-over"
section, with the output tapped after each stage. Mix the outputs
together in the required ratio, and voila! You have a static waveform,
with the harmonics you wanted! Of course, this is where you realize that
the Helmholz model of sound is seriously lacking...

Sean Costello

P.S. The "mirror" function in Csound implements this sort of "foldover"
distortion. With a sine wave of variable amplitude feeding the function,
the result is a very nice increase in harmonic energy. Probably very
similar to the Serge Wave Multiplier, although the Serge wouldn't have
the aliasing problems that Csound will have.