<div dir="ltr"><div dir="ltr"><div class="gmail_default" style="font-family:arial,helvetica,sans-serif"><br></div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Fri, Jan 28, 2022 at 8:24 AM Fons Adriaensen <<a href="mailto:fons@linuxaudio.org">fons@linuxaudio.org</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">On Thu, Jan 27, 2022 at 08:20:29PM -0700, Paul Davis wrote:<br>
<br>
> To do a linear speedup, you would gradually reduce the time between notes,<br>
> maybe like this: 0.5, 0.45, 0.40, 0.35, 0.30 and so on<br>
<br>
That would be a linear interpolation of beat _duration_. <br>
<br>
The alternative is linear interpolation of beat _frequency_.<br>
<br>
The result of this will be very close to exponential, for<br>
a reasonable relative tempo change (in the range 1/2 to 2/1).<br>
Outside that range, and if the ramp takes more than a few<br>
seconds I wonder if humans will do exponential accurately<br>
enough for the difference to matter at all.<br></blockquote><div><br></div><div><div style="font-family:arial,helvetica,sans-serif" class="gmail_default">For Ardour, we have generally used this as a reference paper:</div><div style="font-family:arial,helvetica,sans-serif" class="gmail_default"><br></div><div style="font-family:arial,helvetica,sans-serif" class="gmail_default"><a href="https://quod.lib.umich.edu/i/icmc/bbp2372.2007.004/1">https://quod.lib.umich.edu/i/icmc/bbp2372.2007.004/1</a></div><div style="font-family:arial,helvetica,sans-serif" class="gmail_default"><br></div><div style="font-family:arial,helvetica,sans-serif" class="gmail_default">with a modified version of the equations (basically switching between duration and frequency)</div><div style="font-family:arial,helvetica,sans-serif" class="gmail_default"><br></div><div style="font-family:arial,helvetica,sans-serif" class="gmail_default"><a href="https://github.com/Ardour/ardour/blob/master/doc/tempo.pdf">https://github.com/Ardour/ardour/blob/master/doc/tempo.pdf</a></div><br></div><div> </div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
<br>
-- <br>
FA<br>
<br>
_______________________________________________<br>
Linux-audio-user mailing list<br>
<a href="mailto:Linux-audio-user@lists.linuxaudio.org" target="_blank">Linux-audio-user@lists.linuxaudio.org</a><br>
<a href="https://lists.linuxaudio.org/listinfo/linux-audio-user" rel="noreferrer" target="_blank">https://lists.linuxaudio.org/listinfo/linux-audio-user</a><br>
</blockquote></div></div>