<div dir="ltr">I stand by my statement: "Same thing with the P12th ET."<div><br></div><div><span class="Apple-style-span" style="font-style: italic;">Brekne's</span> way of tuning a P12th temperament may very well be to "actually tune Perfect 12ths", but I would suggest that a real-world approach to P12th tuning would and should allow some modifications to yield the most pleasing results.</div> <div><br></div><div><br></div><div>Kent</div><div><br><br><div class="gmail_quote">On Mon, Oct 13, 2008 at 5:54 PM, Richard Brekne <span dir="ltr"><<a href="mailto:ricb@pianostemmer.no">ricb@pianostemmer.no</a>></span> wrote:<br> <blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">I knew there was something about this sentence that bothered me... and I just hit on it.<div class="Ih2E3d"><br> <br> <br>       When we tune 12 tone to the octave ET we modify the tuning for<br>   aesthetic reasons and to deal with the change in inharmonicity<br>   across the scale and to<br>       tune the treble as sharp as we like to hear.<br> <br>       Same thing with the P12th ET.<br> <br></div> Wrong... its not the same. The whole point of tuning a P-12th tuning is to actually tune Perfect 12ths. Indeed... that orientation IS the stretch priority and our personal preferences for treble stretch are disposed of.  The reason the P 12th works like it does in the piano is that it takes each instruments inharmonicity into consideration on the fly. You tune D3's 3rd partial to 440... so A4 gets its fundamental to 440.  You read the resultant 3rd partial for A4 and you tune E6's fundemental to that. B7's fundemental is then already decided in similar fashion. And of course... what these all turn out to be is different for each piano.  Tuning the treble as sharp as we like to hear simply defeats the purpose and the effects of tuning to a strict perfect 12th priority scheme.<br> <br> Cheers<br> RicB<br> <br> </blockquote></div><br></div></div>