[sdiy] saw vs ramp, audible?

[Donald Tillman]

On Dec 19, 2024, at 10:44 PM, Mattias Rickardsson <mr at analogue.org> wrote:
> 
> On Thu, 19 Dec 2024 at 17:18, Donald Tillman <don at till.com <mailto:don at till.com>> wrote:
>> 
>> Mellow waveforms, with 1/n^2 harmonic content, have harmonics that are naturally cosine-alined, while bright waveforms, with 1/n harmonic content, are naturally sine aligned.
> 
> Because the mellow ones are 1-pole filtered versions of the sine-aligned bright ones, and thereby lagging 90 degrees in phase?

Yes.

If you happen to have a bright 1/n waveform with an identifiable shape, it's easy enough to integrate it to create a matching mellow 1/n^2 waveform with a shape that you can also identify.  And if that bright 1/n wave shape is sine-aligned, then the integrated mellow 1/n^2 version will necessarily be cosine-aligned.  Examples include square wave to a triangle wave, square bipolar pulses to a trapezoid wave, and sawtooth wave to a parabolic wave.


> Perhaps the sine alignment is actually typical also in acoustic sound sources... :-) 
> 

Maybe.  Though true 1/n waveforms, with immediate transitions, don't actually exist in nature.

A bowed string has a natural sawtooth-ish movement; the friction of the rosin in the bow pulls the string until it snaps back. 

Non-bowed string instruments (guitar, piano) sustain a set of "standing" sine waves, but the harmonic content is changing phase as the harmonics naturally run a little sharp due to the mechanics of the strings being less flexible at the endpoints.

And reed instruments probably slap between two positions.

But it's a funny area... I mean, it's easy to make a DX-7 style FM synthesis patch that sounds a lot like an acoustic instrument, even though that's nothing like the way acoustic instruments work.

  -- Don
--
Donald Tillman, Palo Alto, California
https://till.com
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