[sdiy] Better waveforms of our nature

[David G Dixon]

The Rubicon (Intellijel eurorack) has double-frequency saws as a standard
output.  It also has a "sigmoid" wave (a saw put through a sine-shaper
instead of a triangle), and a double-frequency sigmoid.  I don't know of any
other "commercial" VCOs with these waveforms.  Another nice one is the
"zigzag" wave, which is really just the sum of triangle and square.  This
waveform is the control signal for the core comparator in my VCO designs,
and I just brought it out through a buffer to an output jack.

One thing I'm wondering about lately is the Minimoog "sawtooth" which looks
more like a shark-fin.  What does the spectrum look like for that waveform? 

> -----Original Message-----
> From: Synth-diy [mailto:synth-diy-bounces at dropmix.xs4all.nl] 
> On Behalf Of David Moylan
> Sent: Monday, October 17, 2016 11:33 AM
> To: mskala at ansuz.sooke.bc.ca
> Cc: synth-diy at dropmix.xs4all.nl
> Subject: Re: [sdiy] Better waveforms of our nature
> 
> 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.
> >
> 
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