<HTML><BODY style="word-wrap: break-word; -khtml-nbsp-mode: space; -khtml-line-break: after-white-space; ">Numbers, numbers, numbers. Yes, they can be helpful, but do they adequately represent a piano tuning. Look at it this way. (If you don't want to wade through the first part, jump to "Conclusion" below)<DIV><BR class="khtml-block-placeholder"></DIV><DIV>F#4 aural tests = 2 beats to C#4, nearly pure to B3, 1 beat faster than D3F#3, this makes a stretched octave. If you had to do the equivalent test by the numbers it would take several measurements, and the resulting numbers would probably not end up exactly the same figure.</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV>Now look at B4. Since F#4 was stretched a little bit, F#4/B4 can be 2 beats and the E4/B4 could be nearly pure. The octave could have 1 beat without doing any harm and the 10th (G3/B4) could be one beat faster than the third (G3/B3). If you tried to figure all that out by the numbers, I think you'd get different figures, and those numbers would vary from piano to piano. But aurally, those checks lock in a note. Go too far with any interval and it will show up in the others.</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV>Now look at the B5. Since the B4 was stretched, it would seem that the B5 will also be able to be pushed high. But wait. What about the double octave. Since the B3 is below A4, the B3 is actually stretched a little low. Therefore if you push the B5 too high, it won't fit with the B3. But the 10th/17th can be a little wide, with the 17th a beat faster than the tenth, which is already a beat faster than the G3/B3 third.</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV>Now look at the B6. It can be stretched higher than the other octaves because the double octave B4/B6 uses the B4 which was an upwardly stretched note. The triple octave can be nearly pure because the B3 is stretched slightly low. The only octave to really suffer is the single octave B5/B6. But that octave is also a limiter because no matter how you might want to stretch, there is a limit to stretching that single octave and there's a limit to how fast the 17th (G4/B6) can really be.</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV>Conclusion:</DIV><DIV>All of these aural tests would be possible to calculate, but difficult and time consuming to do, especially for every note of the piano. Numbers and measuring don't, IMHO, capture the essence of tuning. ETD's can crunch some numbers, average them out, and give an excellent calculated result, but whether or not those calculations actually fit the piano depends on what you hear.</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV> Years ago I chose to stick with the aural methods because there was more satisfaction in it. The pattern I described above is what I strive for because it seems to be what the piano "wants" and I think it's safe to say that I'm not the only technician to aim for the same pattern. In fact that's the core of my contention that there really is only one way to tune a concert grand. </DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV>If you can agree that most technicians tune the middle 75 to 80 notes the same, then why haven't we described that pattern? To me, that's the standard that any technician should know about and strive for. Going by the numbers can lead to confusion, because the numbers can create a construct that doesn't really fit a piano.</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV>Also, see comment in text below</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV>Richard West </DIV><DIV> <BR><DIV><DIV>On Feb 4, 2007, at 12:38 PM, Jon Page 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; "><DIV>><FONT face="Arial" color="#000000"><SPAN class="Apple-style-span" style="font-family: Arial; ">For example in tuning a Steinway "D" my C8 ends up at 43.92 cents</SPAN></FONT></DIV><DIV><FONT face="Arial" color="#000000"><SPAN class="Apple-style-span" style="font-family: Arial; ">>and on a "B" 34.76 cents. That means something to me. <BR></SPAN></FONT></DIV></SPAN></BLOCKQUOTE><DIV><BR class="khtml-block-placeholder"></DIV>It doesn't mean much to me without knowing the context of that number, and for me context is everything in piano tuning. 75 cents might be what C8 would have to be if it were pure with C5. The number could be 45 cents if C8 were pure with C6. The number could be lower yet if the single octave C7/C8 were pure.</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV>The numbers in ETD's can be isolated and misleading in the total context of the whole piano.</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV><BR><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; "><DIV><FONT face="Arial" color="#000000"><SPAN class="Apple-style-span" style="font-family: Arial; ">I've heard</SPAN></FONT></DIV><DIV><FONT face="Arial" color="#000000"><SPAN class="Apple-style-span" style="font-family: Arial; ">>of people using a stretch that gets to 75 cents on C8 and that seems pretty s-t-r-e-t-c-h-e-d to me.</SPAN></FONT></DIV><DIV><FONT face="Arial" color="#000000"><BR style="font-family: Arial; "></FONT></DIV><DIV><FONT face="Arial" color="#000000"><SPAN class="Apple-style-span" style="font-family: Arial; ">Me too. Tuned a rental D where C8 was +60c,As I recall I tuned it with +43c.</SPAN></FONT></DIV><DIV><FONT face="Arial" color="#000000"><BR style="font-family: Arial; "></FONT></DIV><DIV><FONT face="Arial" color="#000000"><SPAN class="Apple-style-span" style="font-family: Arial; ">recently</SPAN></FONT></DIV><DIV><FONT face="Arial" color="#000000"><SPAN class="Apple-style-span" style="font-family: Arial; ">Baldwin SD, +43.12</SPAN></FONT></DIV><DIV><FONT face="Arial" color="#000000"><SPAN class="Apple-style-span" style="font-family: Arial; ">S&S D, +33.22</SPAN></FONT></DIV><DIV><FONT face="Arial" color="#000000"><SPAN class="Apple-style-span" style="font-family: Arial; "> B, +29.76</SPAN></FONT></DIV><DIV><FONT face="Arial" color="#000000"><SPAN class="Apple-style-span" style="font-family: Arial; ">Yamaha C7,+32.21</SPAN></FONT></DIV><DIV><FONT face="Arial" color="#000000"><SPAN class="Apple-style-span" style="font-family: Arial; "> </SPAN><SPAN style="font-family: Arial; "></SPAN><SPAN class="Apple-style-span" style="font-family: Arial; "> C2 +32.6</SPAN></FONT></DIV><DIV><BR></DIV><X-SIGSEP><PRE style="white-space: pre; ">-- </PRE></X-SIGSEP><DIV><BR>Regards,<BR><BR>Jon Page</DIV><BR class="Apple-interchange-newline"></SPAN></BLOCKQUOTE></DIV><BR></DIV></BODY></HTML>