<HTML><BODY style="word-wrap: break-word; -khtml-nbsp-mode: space; -khtml-line-break: after-white-space; "><DIV><DIV>On Feb 3, 2007, at 11:14 AM, David Porritt wrote:</DIV><BR class="Apple-interchange-newline"><BLOCKQUOTE type="cite"><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; "><P class="MsoNormal"><FONT size="3" color="blue" face="Times New Roman"><SPAN style="font-size:12.0pt;color:blue; color: rgb(0, 0, 255); font-family: Times New Roman; font-size: 16px; "><SPAN class="Apple-style-span" style="color: rgb(0, 0, 255); font-family: Times New Roman; font-size: 16px; ">This discussion of wide and narrow stretch is difficult using plain English. Frankly RCT stretch numbers are to me just as obscure. We can discuss particulars in terms of partial ratios (4:2, 8:4 etc.) and that is a little more revealing. Or if one at least has an ETD of some kind we can talk of the stretch of C8 in numbers. For example in tuning a Steinway “D” my C8 ends up at 43.92 cents and on a “B” 34.76 cents. That means something to me. I’ve heard of people using a stretch that gets to 75 cents at C8 and that seems pretty s-t-r-e-t-c-h-e-d to me. </SPAN></SPAN></FONT></P><P class="MsoNormal"><FONT size="3" color="blue" face="Times New Roman"><SPAN style="font-size:12.0pt;color:blue; color: rgb(0, 0, 255); font-family: Times New Roman; font-size: 16px; "><SPAN class="Apple-style-span" style="color: rgb(0, 0, 255); font-family: Times New Roman; font-size: 16px; ">Revealing where C8 ends up might make this a little clearer.</SPAN></SPAN></FONT></P><P class="MsoNormal"><FONT size="3" color="blue" face="Times New Roman"><SPAN style="font-size:12.0pt;color:blue; color: rgb(0, 0, 255); font-family: Times New Roman; font-size: 16px; "><SPAN class="Apple-style-span" style="color: rgb(0, 0, 255); font-family: Times New Roman; font-size: 16px; ">dave<SPAN style=""><SPAN style=""><FONT class="Apple-style-span" face="Arial" size="4"><SPAN class="Apple-style-span" style="font-size: 13.3333px;">____________________</SPAN></FONT></SPAN></SPAN></SPAN></SPAN></FONT></P><P class="MsoNormal"><FONT size="3" color="blue" face="Times New Roman"><SPAN style="font-size:12.0pt;color:blue; color: rgb(0, 0, 255); font-family: Times New Roman; font-size: 16px; "><SPAN class="Apple-style-span" style="color: rgb(0, 0, 255); font-family: Times New Roman; font-size: 16px; ">David M. Porritt, RPT</SPAN></SPAN></FONT></P><P class="MsoNormal"><FONT size="3" color="blue" face="Times New Roman"><SPAN style="font-size:12.0pt;color:blue; color: rgb(0, 0, 255); font-family: Times New Roman; font-size: 16px; "><A href="mailto:dporritt@smu.edu" title="blocked::mailto:dporritt@smu.edu"><SPAN class="Apple-style-span" style="color: rgb(0, 0, 255); font-family: Times New Roman; font-size: 16px; -khtml-text-decorations-in-effect: underline; ">dporritt@smu.edu</SPAN></A></SPAN></FONT></P></SPAN></BLOCKQUOTE></DIV>Hi Dave,<BR><DIV><SPAN class="Apple-tab-span" style="white-space:pre"> </SPAN>For my part, I end up with C8 at +65¢. This may be misleading, however, as C6 is about 5, C7 about 18, far more "conservative" figures. Partials I use to arrive at this for the concert grand are 12:1. (I would look at 16:1 as well, but the 16th partial is pretty weak. 16:1 closely follows 12:1 almost all the way). This means beatless 26ths (triple octave +5th), throughout the piano. I found that that was pretty much what I had already, tuning aurally in a relatively conservative fashion, A0 to C6. I matched that using ETD when I started using one 12 years ago. A few years ago I decided to see experiment with extending that partial match to C7, then, later, all the way to C8. I liked the results. 12:1 mirrors 8:1 and 6:1 fairly consistently and only begins to diverge widely around G6. So I have a fairly steep curve, if you will, upward from G6 to C8.</DIV><DIV><SPAN class="Apple-tab-span" style="white-space:pre"> </SPAN>Note I have mentioned nothing of 2:1, 4:2, 6:3, 8:4 octave sizes. They are not what I, personally, focus on. I let them fall where they may at this point. Granted, in getting to this point, I paid plenty of attention to them, fussing and fretting, and tearing hair out when facing various models of piano where things I thought I had figured out simply wouldn't work. But essentially I would say that all my single octaves from A0 to at least C6 "sound relatively beatless" and are wide of 4:2. The top octaves definitely beat, but it isn't very noticeable to most ears. And it _is_ noticeable (to my ear) that the triple octaves and quads and 19ths and 26ths don't beat. To my ear, that is more important than the individual octaves, for reasons I have stated in earlier posts. It is also very nice to have those highest notes sounding "musically" closer to where the human ear wants to hear them.</DIV><DIV><SPAN class="Apple-tab-span" style="white-space:pre"> </SPAN>On smaller pianos, I follow 6:1 and 8:1, abandoning them where there are big inharmonicity breaks and picking them up later in the scale. Typical C8s range usually from 35 to 55 in my tunings (occasionally as low as 20-25 on bizarre pianos). For a Steinway B, typical is 50-55. I have two, in our piano prof's studio, that hits 65, per his request for more stretch (I had it at 55 when he asked for more). I don't mind the sound of his pianos. </DIV><DIV><SPAN class="Apple-tab-span" style="white-space:pre"> </SPAN>For mid-range, typically my octaves are wide 4:2, bass wide 6:3 (where mid-range changes to bass varies somewhat in smaller pianos). In the bass I am, again, more concerned with 6:1 and 8:1 than with octave size per se, though the octave size tends to end up pretty consistent.<BR><DIV><DIV>Regards,</DIV><DIV>Fred Sturm</DIV><DIV>University of New Mexico</DIV><DIV><A href="mailto:fssturm@unm.edu">fssturm@unm.edu</A></DIV><DIV><BR class="khtml-block-placeholder"></DIV></DIV><BR></DIV><DIV><BR class="khtml-block-placeholder"></DIV></BODY></HTML>