[sdiy] Better waveforms of our nature

[David Moylan]

Ah, yeah, got confused about which was at twice the frequency.  I do 
think this method would cover a lot of the same ground as the 
bright/even harmonics block in Don's chart.  And could be fairly simple 
to add a x2 saw to a typical saw vco.

That would still leave the mellow/even and mellow/all.  Mellow/all looks 
a lot like a full wave rectified sine (which would automatically be at 
double frequency of the input sine).  Similar mixing as you described 
with sine would cover most of mellow/even range.  For mellow/all (FWR 
estimate) the oscillator could just be retuned or octave switched if 
available.

Of course, this is all theoretical; haven't tried it.  Looks like 
denominator of rectified sine is (4n^2 - 1).  So not mathematically 
equivalent but ballpark and again, low parts count to provide this wave 
in analog hardware.  Here's a table of harmonic divisors scaled against 
n=1 value to get relative divisors.  So, the rectified sine would be 
mellower then the parabolic wave as the amplitude of the harmonics is 
dropping faster.  More specifically, 80% of amplitude at n=2 and 
approaching 75% of amplitude as n increases.

   n2  | 4n^2 - 1
1 1     1
2 4     5
3 9     11.6
4 16    21
5 25    33
6 36    47
7 49    65
8 64    85

I still think it would be fun to experiment with given its simplicity. 
Come to think of it, since the difference in harmonic amplitudes is only 
in the range of 75-80%, you could just mix a bit more of the FWR wave to 
compensate and have a fairly small error.

Dave

On 10/17/2016 08:25 PM, mskala at ansuz.sooke.bc.ca wrote:
> On Mon, 17 Oct 2016, David Moylan wrote:
>> Not quite.  A sine wave only represents one harmonic/overtone.  So if you add
>> one an octave up you're just adding that single harmonic, no other even
>> harmonics.  You can build it up with multiple sines (if you have extra
>
> I said "adding a sine wave to a traditional oscillator at twice the
> frequency" and meant that the traditional oscillator would be something
> like a sawtooth - so the sine wave provides the fundamental and the
> sawtooth at twice the fundamental frequency provides all even harmonics.
>