<html><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; ">Hi Kent,<div><span class="Apple-tab-span" style="white-space:pre"> </span>So you believe that Stopper's tuning is substantially different from the 3:1 tuning achieved on Tune Lab that David Porritt describes?</div><div><span class="Apple-tab-span" style="white-space:pre"> </span>What I described wasn't a lot of calculations, it was simply a means to create a tuning "on the fly." It actually involved very little calculation - mostly raw measurement and simple addition and subtraction. I frankly don't think dividing a 12th evenly into 19 is significantly different from dividing an octave evenly into 12. Not different at all if the octaves are equal.  I suppose you will say the proof is in the pudding. And, though your files sounded fine to my ear, they certainly didn't blow me away. The match between the two pianos was quite good, certainly. Why? Well, I think that any tuning system based on the 3rd partial will markedly reduce the differences, for the simple reason that you are "staying within close range." 3rd partials vary much less than higher partials. Inharmonicity is  logarithmic in nature. You could get a better match with a tuning based on 2nd partials, and the very best based on 1st partials.</div><div><span class="Apple-tab-span" style="white-space:pre"> </span>So, fine, the VTD is good at creating acceptable tunings that will make pianos of varying inharmonicity match. That's all to the good, if that is a problem you face. You face it with your Bosey. I have two Ds on my stage, so it is very rarely an issue for me. I am more interested in a tuning that, to my ear, sets off the individual pianos to their best effect. And I think that a tuning based on higher partial matches (whether done electronically/mathematically or aurally) does that better. </div><div><span class="Apple-tab-span" style="white-space:pre"> </span>Of course, all this is very subtle compared to the primacy of unisons and stability. Which is where the art and craft of tuning really lies. The rest is really quite variable, both stretch and temperament, though we spend so much time and energy arguing about stretch and temperament and trying to develop our own skills in those areas. Ironic, no?<br><div apple-content-edited="true"> <span class="Apple-style-span" style="border-collapse: separate; 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; orphans: 2; text-align: auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0; "><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><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="webkit-block-placeholder"></div></div></span><br class="Apple-interchange-newline"> </div><br><div><div>On Oct 1, 2008, at 5:52 PM, Kent Swafford wrote:</div><br class="Apple-interchange-newline"><blockquote type="cite"><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><br><div><div>On Oct 1, 2008, at 3:59 PM, Fred Sturm wrote:</div><br class="Apple-interchange-newline"><blockquote type="cite"><span class="Apple-style-span" style="border-collapse: separate; 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; orphans: 2; text-align: auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0; ">I'm afraid statements ... make me very, very skeptical and wary.</span></blockquote><div><br></div><div>Of course. Likewise, I am sure.</div><div><br></div><br><blockquote type="cite"><span class="Apple-style-span" style="border-collapse: separate; 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; orphans: 2; text-align: auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0; ">Personally, I don't believe in magic.<span class="Apple-converted-space"> </span></span></blockquote></div><br><div>New technology is indistinguishable from magic, and I do believe that new technology comes along from time to time.</div><div><br></div><div><br></div><div>Your spreadsheet construction is very interesting, but it would not, after all of those calculations, match two pianos that differ wildly in inharmonicity. Or, if you say it would, I await the audio files.   8^)</div><div><br></div><div>No one said that 19 tone to the perfect twelfth equal temperament is new. (Although Stopper does claim to have been among the first to publish it many years ago.) Stopper's approach to realizing the tuning across a whole piano scale and indeed across a wide variety of <i>differing</i> piano scales in such a way as to produce a characteristic and pleasing synchronous effect, however, <i>does </i>appear to be new.</div><div><br></div><div><br></div><div><br></div><div>Kent</div><div><br></div></div></blockquote></div><br></div></body></html>