<HTML><BODY style="word-wrap: break-word; -khtml-nbsp-mode: space; -khtml-line-break: after-white-space; "><DIV><DIV>On Mar 20, 2006, at 1:37 PM, Ric Brekne wrote:</DIV><BR class="Apple-interchange-newline"><BLOCKQUOTE type="cite"><P style="margin: 0.0px 0.0px 0.0px 0.0px"><FONT face="Helvetica" size="3" style="font: 12.0px Helvetica">I seem to remember reading somewhere that it was around 30 hz.<SPAN class="Apple-converted-space"> </SPAN>Very iffy.</FONT></P> <P style="margin: 0.0px 0.0px 0.0px 0.0px"><BLOCKQUOTE type="cite"><FONT face="Helvetica" size="3" style="font: 12.0px Helvetica"></FONT></BLOCKQUOTE></P></BLOCKQUOTE><DIV><BR class="khtml-block-placeholder"></DIV><DIV>Iffy, in that it depends on the musical training of the listener? Or is it a matter of the mechanics of the inner ear? Do we need an audiologist?</DIV><BR><P style="margin: 0.0px 0.0px 0.0px 0.0px"></P><BLOCKQUOTE type="cite"><P style="margin: 0.0px 0.0px 0.0px 0.0px"><BLOCKQUOTE type="cite"><FONT face="Helvetica" size="3" style="font: 12.0px Helvetica">Is the point which beat rate is too fast to <SPAN class="Apple-converted-space"> </SPAN>be unusable for us aural tuners any higher than 12 bps? Maybe that's <SPAN class="Apple-converted-space"> </SPAN>another measurement for an ETD.</FONT></BLOCKQUOTE></P> <P style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica; min-height: 14.0px"><BR></P> <P style="margin: 0.0px 0.0px 0.0px 0.0px"><FONT face="Helvetica" size="3" style="font: 12.0px Helvetica">Definatly not.<SPAN class="Apple-converted-space"> </SPAN>You can use 15 - 20 bps no problem.<SPAN class="Apple-converted-space"> </SPAN></FONT></P> </BLOCKQUOTE><BR></DIV><DIV>I may having been thinking of the visual, when apparent motion between two alternating blinkers becomes a blur. As for the aural, it's definitely above twenty, but I can't tell how much higher be cause of the equipment I'm using. (I made a percussion chart for clave in Finale, subdividing various note values into 4,5,6 and then on. I noticed that varying the metronome during playback in varying, there was a point at which the speed of clave clicks didn't seem to pick up speed and that seemed to be somewhere around 20 bps. Probably due to the low-speed midi software internal to Finale. A drum machine would do a better job.</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV><BLOCKQUOTE type="cite">That is to say if you are comparing two intervals in which the reference note yeilds roughly 20 bps for both intervals... an aural comparison is easy enough to accomplish.</BLOCKQUOTE><BR></DIV><DIV>Are you describing the situation for a 10th and a 17th where the 2:1 beat rate between the two upper notes is 1bps, and all three notes are high enough in pitch that the 10th might beat @ 19 bps and the 17th 20bps? And the tempo difference between the two rates would be noticeable?</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV>Anther way to run that experiment would be to use a contiguous mi3d/M3d as in the 6:4 5th test, in the middle of the piano so the partial tones would be louder. Say, mute out 2 of 3 strings on F3 (that's amur'can, y'all) and C4. Tune that 6:4 fifth ą at 1bps. Now mute out the LH string on G#3, and temporarily muting out the middle string also, tune the RH string of G#3 pure to C4. The mi3d between this string on G#3 and the F3 will now beat at one bps.</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV>Now increasingly flatten the center string of G#3, and the beat rates of the mi3d and M3d will increase, but the difference in their beat rates will remain at 1bps. On up to 19 and 20 bps respectively......and maybe beyond.</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV>A drum machine could certainly do this better.</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV>What I'm getting at is this. If at A440 (A4), 1 bps is 4˘ and if we take 20 bps as the maximum practically usable beat speed, then a beat rate range of 20 bps would cover 76.95˘ towards A#4. If we're now using that same 20bps range up at the top of the 7th octave, to tell us how close to a pure 2:1 octave we have between A6 and A7, that 20 bps now translates to a ą9.81˘ window within which to set octave widths aurally. Because of quick decays, 20bps might even be reduced by half.</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV>Lots to ponder, I hope this threads continues on in an illuminating direction.</DIV><BR><DIV> <SPAN class="Apple-style-span" style="border-collapse: separate; border-spacing: 0px 0px; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: auto; -khtml-text-decorations-in-effect: none; text-indent: 0px; -apple-text-size-adjust: auto; text-transform: none; orphans: 2; white-space: normal; widows: 2; word-spacing: 0px; "><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Bill Ballard RPT</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">NH Chapter, P.T.G.</DIV><DIV><A href="mailto:wbps@vermontel.net">wbps@vermontel.net</A></DIV></SPAN> </DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 12px/normal Helvetica; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">"Trust me, you've got all the equipment, You just need to read the manual"</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "> ...........Reese Witherspoon in "Legally Blonde"</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">+++++++++++++++++++++</DIV><BR></BODY></HTML>