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<p class=MsoPlainText>Read it all. I said the 12th root of 2.<span
style='color:red'>0012 </span>was 1.059516053 (or essentially the same as 19<sup>th</sup>
root of 3) not 2.0. I was pointing out the small difference in the 12<sup>th</sup>
root of 2 and the 19<sup>th</sup> root of 3. Differences which are mathematically
significant (if you’re looking at decimals to the 5<sup>th</sup> digit)
but insignificant if you’re tuning real pianos with real inharmonicity with
contemporary tools. The pitch change from start to 4 seconds later is
much wider than that. When in the decay cycle are you measuring this to 5
digit accuracy? <o:p></o:p></p>
<p class=MsoPlainText><o:p> </o:p></p>
<p class=MsoPlainText>I too am a 3:1 tuner and I like the sound I get tuning
that way I just can’t claim that kind of accuracy.<o:p></o:p></p>
<p class=MsoPlainText><o:p> </o:p></p>
<p class=MsoPlainText>dp<o:p></o:p></p>
<p class=MsoPlainText><o:p> </o:p></p>
<p class=MsoPlainText><o:p> </o:p></p>
<p class=MsoPlainText>David M. Porritt, RPT<o:p></o:p></p>
<p class=MsoPlainText>dporritt@smu.edu<o:p></o:p></p>
<p class=MsoPlainText><o:p> </o:p></p>
<p class=MsoPlainText>-----Original Message-----<br>
From: caut-bounces@ptg.org [mailto:caut-bounces@ptg.org] On Behalf Of Richard
Brekne<br>
Sent: Tuesday, October 14, 2008 6:08 PM<br>
To: caut@ptg.org<br>
Subject: [CAUT] P-12ths was: Tuning a Steinway D and aBosendorfer Imperial
together<o:p></o:p></p>
<p class=MsoPlainText><o:p> </o:p></p>
<p class=MsoPlainText>David... Google has it different.<o:p></o:p></p>
<p class=MsoPlainText><o:p> </o:p></p>
<p class=MsoPlainText>The 12th root of 2 is 1.05946309<o:p></o:p></p>
<p class=MsoPlainText>The 19th root of 3 is 1.05952606<o:p></o:p></p>
<p class=MsoPlainText><o:p> </o:p></p>
<p class=MsoPlainText>Which I think you will find are the correct
figures. If you take even a <o:p></o:p></p>
<p class=MsoPlainText>low number like 220hz and multiply that out over an
octave range by <o:p></o:p></p>
<p class=MsoPlainText>each value... you'll end up with a 3rd of a bps
difference at 440. Add <o:p></o:p></p>
<p class=MsoPlainText>in all the intervals we need to take consideration to its
clear that <o:p></o:p></p>
<p class=MsoPlainText>imposing a P 12th system will yield a significantly
different, that is <o:p></o:p></p>
<p class=MsoPlainText>to say discernible to the ear should one take the time to
notice, <o:p></o:p></p>
<p class=MsoPlainText>result. That said... given the famous temperament
tests of a decade or <o:p></o:p></p>
<p class=MsoPlainText>more ago... I'll go along ways down any road with you
that implies it <o:p></o:p></p>
<p class=MsoPlainText>doesnt make all that much difference. At least not
to most people and <o:p></o:p></p>
<p class=MsoPlainText>not all that consciously to most of those who on some
level or another <o:p></o:p></p>
<p class=MsoPlainText>do "notice"<o:p></o:p></p>
<p class=MsoPlainText><o:p> </o:p></p>
<p class=MsoPlainText>Fred... excellent post... I have to read it a couple
times on the morrow <o:p></o:p></p>
<p class=MsoPlainText>and reply. But off hand I'd agree that we are
very much more on the <o:p></o:p></p>
<p class=MsoPlainText>same page then not. Tho to be sure, and as is my wont, I
differ here and <o:p></o:p></p>
<p class=MsoPlainText>there :) Late here... I'm 56 today... and off to
bed<o:p></o:p></p>
<p class=MsoPlainText><o:p> </o:p></p>
<p class=MsoPlainText>Cheers !<o:p></o:p></p>
<p class=MsoPlainText>RicB<o:p></o:p></p>
<p class=MsoPlainText><o:p> </o:p></p>
<p class=MsoPlainText><o:p> </o:p></p>
<p class=MsoPlainText> Fred:<o:p></o:p></p>
<p class=MsoPlainText><o:p> </o:p></p>
<p class=MsoPlainText> The 12th root of 2.0012 is the
equivalent of the 19th root of 3 to 4<o:p></o:p></p>
<p class=MsoPlainText> decimal places (1.059516053 rather
than 1.059526065).<o:p></o:p></p>
<p class=MsoPlainText><o:p> </o:p></p>
<p class=MsoPlainText> dp<o:p></o:p></p>
<p class=MsoPlainText><o:p> </o:p></p>
<p class=MsoPlainText><o:p> </o:p></p>
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