[sdiy] Screwing with Square Waves

[Mattias Rickardsson]

On 2 November 2013 21:48, Donald Tillman <don at till.com> wrote:
>
>> It appears that an infinite number of sines of completely random phases is the closest you're going to get; no spikes, no discontinuities, but a lot of what looks like high frequency noise.  Or another way to describe it... it looks like any normal oscilloscope waveform of an acoustic source.
>
> Here is an example waveform, with the spectrum of a Square Wave, but with random phases:
>
>     http://www.till.com/random/square-randomed.png

Thanks for a good example and interesting reasoning!

> See?  It looks like sound.  (That's an interesting phrase.)

:-)

The reason for wondering about the existence of continuous, limited
variants of the square & sawtooth spectra is that it would be
interesting to see how they compare to the ordinary waveforms. And it
would be interesting to discuss if they would be more useful than the
ordinary ones in some synth contexts. They may be near impossible to
generate, but they should be easier for an electronic circuit to
reproduce perfectly since the slewrate and amplitude could be chosen
sufficiently good.

But would they sound "better" or "worse" than the originals? There is
a chance that the error introduced in the discontinuity of standard
synth waveforms is what makes some synths sound better than - or at
least different from - others. I'd expect the new complex waveforms to
sound either quite wonderful or pretty useless. :-)

And would they give rise to any other interesting phenomena?
Phasing/flanging has been mentioned before in this thread... detuning
two of them wouldn't give the flanging effect that we're used to,
since the overtones aren't faded in/out in a specific order. I guess
we'd need to hear it to understand it!

Often it feels like we use synth waveforms near the limit where our
hearing starts to sense the separate edges of the waveforms. In bass
frequencies very much so. And I get the feeling that it can give a
kind of listening fatigue, especially when hearing very dry synth
sounds. Maybe the random-phase variants are the solution?

> I believe the overall outcome here is that, while the slopes of Square Waves can get pretty steep when the harmonics are aligned as sines, the Harmonic Series rises in value so, so, slowly that
> the spikiest spikes never really get up very high.
>
> With 1000 harmonics, the peak value of a Hilbert Wave is 4.1.
> With 1,000,000 harmonics, the peak value of a Hilbert Wave is 7.54.
> With 10,000,000 harmonics, 8.6.
> With 100,000,000 harmonics, 9.85.

That's an interesting observation as well. The Hilbert wave might be
easier to electrically reproduce with a minimum error than the square
wave, even if the signal amplitude has to be lower.

Be there or be Hilbert!

/mr