[sdiy] Better waveforms of our nature

[Matthias Puech]

Hello,
Thank you Donald for the interesting read!
I've been wondering: is there a known relationship between an arbitrary
waveform's spectrum and its integral/derivative's? Are all integral
waveforms "mellow" versions of their derivatives?

I've asked recently on another DSP mailing list but did not get any answer.
It might be very simple maths...
    -m

On Mon, Oct 17, 2016 at 10:45 PM, David G Dixon <dixon at mail.ubc.ca> wrote:

> 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.
> > >
> >
> > _______________________________________________
> > Synth-diy mailing list
> > Synth-diy at dropmix.xs4all.nl
> > http://dropmix.xs4all.nl/mailman/listinfo/synth-diy
>
> _______________________________________________
> Synth-diy mailing list
> Synth-diy at dropmix.xs4all.nl
> http://dropmix.xs4all.nl/mailman/listinfo/synth-diy
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://synth-diy.org/pipermail/synth-diy/attachments/20161018/96615ef3/attachment.htm>