<html><head><meta http-equiv="content-type" content="text/html; charset=utf-8"></head><body dir="auto"><div dir="ltr"></div><div dir="ltr">For standard FM, you write the instantaneous frequency as an initial frequency plus a sinusoidal modulation. To get the phase you integrate the instantaneous frequency. This results in w_init t + Integral(Acos w_m t), where the second term is (A/w_m)sin w_m t . The difference between PM and FM is just the factor of 1/w_m . </div><div dir="ltr"><br></div><div dir="ltr">I’m out of the country for a few weeks, but I’ll try to keep up some with this discussion.</div><div dir="ltr"><br></div><div dir="ltr">Ian</div><div dir="ltr"><br><blockquote type="cite">On Dec 2, 2022, at 6:38 AM, Donald Tillman <don@till.com> wrote:<br><br></blockquote></div><blockquote type="cite"><div dir="ltr"><meta http-equiv="Content-Type" content="text/html; charset=us-ascii"><div><blockquote type="cite" class=""><div class="">On Nov 29, 2022, at 5:29 PM, Ian Fritz <<a href="mailto:ijfritz@comcast.net" class="">ijfritz@comcast.net</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><meta charset="UTF-8" class=""><br style="caret-color: rgb(0, 0, 0); font-family: Monaco; font-size: 11px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><span style="caret-color: rgb(0, 0, 0); font-family: Monaco; font-size: 11px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;" class="">Oh, you should look at the Chowning/Bristol book again. They go step-by-step teaching how to understand FM. And as mentioned before they treat the DX7 as an FM synth. Their DX7 exercises and examples would not work for a PM synth.<span class="Apple-converted-space"> </span></span><br style="caret-color: rgb(0, 0, 0); font-family: Monaco; font-size: 11px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""></div></blockquote><div><br class=""></div><div>Okay, let's check it out...</div><div><br class=""></div><div>The book is called "FM Theory & Applications, By Musicians for Musicians" by Dr. John Chowning and David Bristow. A pdf scan is easy to find on the interwebs.</div><div><br class=""></div><div>Oh dear, this is very badly written. No matter...</div><div><br class=""></div><div>So let's try an experiment. I've got a DX7II-FD here. It's been a long time; dusty, presets rotted away, 'forgot how to use the thing...</div><div><br class=""></div><div>Okay, Alg 3.</div><div>Op2, 2x frequency, level 70</div><div>Op1, 1x frequency.</div><div><br class=""></div><div>And this is how you make a DX-7 square wave:</div><div><br class=""></div><div><img apple-inline="yes" id="767BB134-5E82-48EE-A9A0-3368C89AB1D7" alt="IMG_0666.png" src="cid:9484B3D9-6CD4-4319-94C2-4FBE98D572DB"></div><div><br class=""></div><div>One of the cool things you can do with PM is to use an audio signal to modulate a low frequency oscillator. (Huh? That sounds so backwards.) This creates a phase shifty chorus sound, so it's a sweet trick for Hammond patches.</div><div><br class=""></div><div>If the DX-7 used frequency modulation, that would integrate the above square wave into a triangle, while phase modulation would preserve the square wave.</div><div><br class=""></div><div>Move Ops 1,2 up to 2,3 and set Op1 to 1Hz.</div><div><br class=""></div><div>Groovy:</div><div><br class=""></div><div><img apple-inline="yes" id="B9BDA0A4-96CB-4A05-AF32-EDF09B5BD458" alt="IMG_0665.png" src="cid:F1DEFD91-FB7F-4BF4-888D-70D7BC5642C6"></div><div><br class=""></div><div>And this works across the keyboard.</div><div><br class=""></div><div> -- Don<br class="">--<br class="">Donald Tillman, Palo Alto, California<br class=""><a href="https://www.till.com" class="">https://www.till.com</a></div><div><br class=""></div><div><br class=""></div></div></div></blockquote></body></html>