[sdiy] Better waveforms of our nature

[Ove Ridé]

Interesting, but I sat down to analyze what I saw, to tri to
understand it plain and square. (Ok, enough with the puns.)

I wondered why the even harmonic waves looked so "weird". Naively, the
even waveform should be 2f+4f+6f+8f+10f... Ie, just the same sawtooth
shifted one octave up. Then I realized you had included the
fundamental as well, which is technically not an even harmonic. The
waveform may be useful in its own right, but in practice it's nothing
but a sawtooth wave with a sine suboscillator. Till, how did you
implement the even harmonic waves in the oscillators that you built?

I was also wondering about the seemingly arbitrary choice of using
cosine instead sine for all the mellow waveforms. That made sense in
the end when describing the derivative/integral relationship to the
bright waveforms. But when looking at these thing systematically it's
useful to remember that for every harmonic distribution you can choose
to use sine or cosine for its partials. (Or in general, any given
phase shift for any of the harmonics.) The result will sound the same
to our human ears, but the waveform will look different. Ultimately
what each partial does is to stimulate a certain area of cochlea,
regardless of its phase relation to other partials. If you want to
feed it through distortion or other non-linear signal processing
elements, the waveform certainly matters in a radical way, but not for
plain listening.

In general, if you use cosine, the resulting waveform will be
"pointy", and if you use sine, it will be "smooth". This is because
the cosine's peaks at 0, and for odd harmonics, 180 degrees will
coincide for all partials and add up. For example, a cosine saw will
look very much like the parabolic (mellow saw) but sharper. The cosine
square will look like a shaped triangle that is much more pointy in
the top. If you build any of the mellow waveforms from sines, they
will instead each just look like a slightly distorted sine.

Nevertheless an interesting exploration of oscillatory phenomena.


On 16 October 2016 at 23:26, Donald Tillman <don at till.com> wrote:
> Hey folks,
>
> For those who follow my articles, here's a new one you might enjoy:
>
>     A Palette of Static Audio Waveforms
>     http://till.com/articles/wavepalette/
>
> It includes a demo.
>
> I got bored with the traditional set of audio VCO waveforms.  And instead of just throwing more waveforms at the situation, I looked into the larger issue of what we want from a waveform and the ways use them.  And things got interesting.
>
> I've built a few VCOs with this waveform set over the last couple years, and I've been doing demos at local synth meetups.
>
> In practice, working with a set of timbres like this is a refreshing change from the usual cliche sounds.
>
>   -- Don
>
> --
> Don Tillman
> Palo Alto, California
> don at till.com
> http://www.till.com
>
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-- 
/Ove

Blog: <http://blog.gg8.se/>

"Here is Evergreen City. Evergreen is the color of green forever."