<HTML><BODY style="word-wrap: break-word; -khtml-nbsp-mode: space; -khtml-line-break: after-white-space; ">Comments interspersed:<BR><DIV><DIV>On Jun 26, 2007, at 2:14 AM, Bernhard Stopper 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: 16px; 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; ">More important (if not sensational, sorry for the self-praise) is my finding of the beat symmetries (or symmetric interfenrence phenomene) inherent in only this equal temperament four years ago, cancelling out the beats in octave and fifths combinations and thus turning a tempered tuning into pure tuning when playing chords.<BR></SPAN></BLOCKQUOTE>I've been experiencing, and talking about, my perception and use of the cancellation phenomenon, which I have always referred to as a psych-acoustic illusion, for many, many years. I believe my body is profoundly capable of perceiving those fine and custom differences that make up a great, musical tuning. I know many, many other whole-tone, open-string aural tuners who have experienced the same cancellation phenomenon, and have developed a massive skill in using it to maximize tuning beauty. <BR><DIV><BR class="khtml-block-placeholder"></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: 16px; 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; "> And this the proof why this tempermant is superior to any other.</SPAN></BLOCKQUOTE><DIV><BR class="khtml-block-placeholder"></DIV>WHOA! How can you possibly say that? I have heard many great tunings, all over the world, using all kinds of methods to arrive at beauty. I could never let the above statement pass without challenge.</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV>My brother, that's going too far. Your tuning is beautiful, and I respect your passion and desire to aspire to tuning excellence---but to say that your temperament is superior to any other can only diminish and tarnish your perception in our community; there is no "proof" as you speak of it, and your colleagues have and will take offense and umbrage</DIV><DIV>if you keep insisting there is.</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV>Let it rest; create beauty with your tunings, and your tuning software, and let a hundred other flowers bloom.</DIV><DIV>Life is too short for these kinds of trumped-up arguments and sturm und drang. </DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV>With best hope and intention,</DIV><DIV>David Andersen</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV>P.S. This is my last word on this, so please feel free to remove my name from the subject line if the thread continues.<BR><BR></DIV><BR></BODY></HTML>