<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>On Dec 9, 2024, at 4:03 AM, Mattias Rickardsson <mr@analogue.org> wrote:</div><div><blockquote type="cite"><br class="Apple-interchange-newline"><div><div dir="auto"><div><div class="gmail_quote"><div dir="ltr" class="gmail_attr">Donald Tillman <<a href="mailto:don@till.com">don@till.com</a>> skrev:<br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div style="line-break:after-white-space"><div>Note that a sawtooth ramping down has all the harmonics in phase with the fundamental.</div></div></blockquote></div></div><div dir="auto"><br></div><div dir="auto">Yes.</div><div dir="auto"><br></div><div dir="auto"><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div style="line-break:after-white-space"><div>And a sawtooth ramping up has its harmonics alternating in phase (+1, -1/2, +1/3, -1/4,...) from the fundamental.</div></div></blockquote></div></div><div dir="auto"><br></div><div dir="auto">But are you counting from the midpoint now? Surely they must still be in phase if you just flip the sawtooth backwards around its discontinuity?</div></div></div></blockquote><div><br></div>(I had to think about this...)</div><div><br></div><div>Good point! When you play it backwards the even harmonics reverse polarity but the odd harmonics don't. So yeah, it's consistent that way.</div><div><br></div><div> -- Don</div><div>--<br>Donald Tillman, Palo Alto, California<br>https://till.com</div><div><br></div><div><br></div></body></html>