<html><head><meta http-equiv="content-type" content="text/html; charset=utf-8"></head><body style="overflow-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;"><div dir="auto" style="overflow-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;"><div><div>On Dec 19, 2024, at 10:44 PM, Mattias Rickardsson <mr@analogue.org> wrote:</div><blockquote type="cite"><br class="Apple-interchange-newline"><div><div dir="ltr"><div dir="ltr">On Thu, 19 Dec 2024 at 17:18, Donald Tillman <<a href="mailto:don@till.com">don@till.com</a>> wrote:</div><div class="gmail_quote gmail_quote_container"><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div><div><div><br></div></div><div>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.</div></div></blockquote><div><br></div><div>Because the mellow ones are 1-pole filtered versions of the sine-aligned bright ones, and thereby lagging 90 degrees in phase?</div></div></div></div></blockquote><div><br></div><div>Yes.</div><div><br></div><div>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.</div><div><br></div><div><br></div><blockquote type="cite"><div><div dir="ltr"><div class="gmail_quote gmail_quote_container"><div>Perhaps the sine alignment is actually typical also in acoustic sound sources... :-) </div><div><br></div></div></div>
</div></blockquote><br></div><div>Maybe. Though true 1/n waveforms, with immediate transitions, don't actually exist in nature.</div><div><br></div><div>A bowed string has a natural sawtooth-ish movement; the friction of the rosin in the bow pulls the string until it snaps back. </div><div><br></div><div>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.</div><div><br></div><div>And reed instruments probably slap between two positions.</div><div><br></div><div>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.</div><div><br></div><div> -- Don</div><div>--<br>Donald Tillman, Palo Alto, California<br>https://till.com</div></div></body></html>