[sdiy] harmonic generator

[Magnus Danielson]

From: media.nai at rcn.com
Subject: Re: [sdiy] harmonic generator
Date: Thu, 21 Feb 2002 13:26:48 -0500

> >Can anyone recommend a harmonic generator circuit - I need about the
> >first 10 harmonics of a given fundamental.
> 
> I've been trying to do this for awhile.  If anyone has schematics for the
> Buchla 185/285 -- you let me know!!  Serge had one in their catalog, but I
> do not know if they ever made one.

I'd love to have that schematic...

> >1. Phase Lock Loops
> 
> I tried that.  You need to run the input through comparator, then through a
> pulse divider into the PLL, then put another divider in the feedback loop
> of the PLL, then shape it into sine.  You need one of these circuits for
> each harmonic, although you can use logic to change the divider values.
> Besides shaping the sine, the trouble is the lag of the PLL, which is quite
> audible.

You could make a good tracking PLL if you want to, but one has to use
higher degree PLLs to get a good result, which usually is out of scope
for most people.

> >2. Walsh function to sine
> 
> What's a Walsh function??

You sum up weigthed squarewaves of different frequencies (and possibly
phase).

Walsh functions and the related Walsh transform is equivalent to
Fourier functions and Fourier transform with the exception that it
builds on a model of squarewaves rather than sines. It is a completely
linear transform model and have the benefit of not requireing any
multiplications, just alternating signs.

So, with a Walsh generator you could generate any waveform if you know
the weigths of the waveform you are after. You could then build a
waveform generator from a frequency division chain and then have
summing resistors.

I think one of the nutheads on the British Islands did his exam report
on the use of Walsh genertors and music.

> >3. Divider chains
> >4. Look up tables
> >5. Rate multipliers
> 
> How does a rate multiplier work??

There are many means of operation, but if you have a sawtooth, you
simly quantize the level and for each quantizing step you get a new
step out. Look at Jürgen's design for instance.

> >you could try using Jürgen Haible's wave multiplier for the x3,x5 and x7
> >ones or the timbre section in the Buchla 208. the Buchla distorts the
> >input at a variety of levels and then combines it back together to get a
> >multiplied frequency. In the actual Buchla 208 it comes back a kind of
> >odd shape, but it was using a sine as the input wave. With a triangle,
> >you may be able to tweak it into submission;) You wouldn't need all the
> >stages for all the multipliers either. Maybe you could try tweaking the
> >break points. This could get ugly.
> 
> I guess I should look up JH's circuit.  I'm not familiar with the Buchla
> 208.  Is there a schematic on the web??

Yeap!

I have them over at

http://home.swipnet.se/cfmd/synths/companies/buchla/

Feel free to contribute!

> >the even numbers are a simple matter of full wave rectification. Then
> >you need 10 tri to sine converters.
> 
> Wouldn't full wave rectification simply result in octaves??

Yes, but you fail to get other overtones than 2, 4, 8 and 16

> >What you'd need is the electronic analog of a big
> >gearbox that has output shafts at 1, 2, 3, 4, etc
> >times the input RPMs...
> 
> LOL!!  Is there a transmission-diy list?? :)

Where it! ;O)

Gear up ;O)

Actually, there are many tricks around to cook up waveforms. You can
do alot by 4-quadrant multipliers and summers given the sine and
cosine.

Cheers,
Magnus