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<DIV><FONT face=Arial size=2>Hello Bob</FONT></DIV>
<DIV><FONT face=Arial size=2>Yes, I agree. There is no likelihood of =
the
<EM>exact</EM> science of sound and its harmonics being produced =
text-book
fashion in the piano. The <EM>principle</EM> applies though - and =
I doubt
it's far removed from the "text book" version. What say =
you?</FONT></DIV>
<DIV><FONT face=Arial size=2>Michael G (UK)</FONT></DIV>
<DIV style="FONT: 10pt arial">----- Original Message -----
<DIV style="BACKGROUND: #e4e4e4; font-color: black"><B>From:</B> <A
title=BobDavis88@aol.com =
href="mailto:BobDavis88@aol.com">BobDavis88@aol.com</A>
</DIV>
<DIV><B>To:</B> <A title=pianotech@ptg.org
href="mailto:pianotech@ptg.org">pianotech@ptg.org</A> </DIV>
<DIV><B>Sent:</B> Monday, October 20, 2003 4:54 PM</DIV>
<DIV><B>Subject:</B> Re: "The Invisible Tool"/beat rates - and where =
they come
from</DIV></DIV>
<DIV><BR></DIV><FONT face=arial,helvetica><FONT lang=0 =
face="Bookman Old Style"
size=3 FAMILY="SERIF">In a message dated 10/20/2003 8:24:56 AM =
Pacific Standard
Time, <A
href="mailto:michael@gambles.fsnet.co.uk">michael@gambles.fsnet.co.uk</=
A>
writes:<BR><BR>
<BLOCKQUOTE
style="PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: #0000ff 2px =
solid; MARGIN-RIGHT: 0px"
TYPE="CITE"></FONT><FONT lang=0 style="BACKGROUND-COLOR: #ffffff" =
face=Arial
color=#000000 size=2 FAMILY="SANSSERIF">Take your M10 based on =
A# (which
computes at 466.16376.....)The 5th. harmonic of that A# = =
2796.9826...... the
M10 is F(which computes at 1396.9129.......) The 2nd. harmonic of
=
that &nb=
sp;
F =2793.8259...... There we have a difference of 3.1567..... Hz =
which is the
beat you hear</BLOCKQUOTE></FONT><FONT lang=0 =
style="BACKGROUND-COLOR: #ffffff"
face=Arial color=#000000 size=3 =
FAMILY="SANSSERIF"><BR></FONT><FONT lang=0
style="BACKGROUND-COLOR: #ffffff" face="Bookman Old Style" =
color=#000000 size=3
FAMILY="SERIF"><BR>Sorry, no. Have you read the recent replies on =
inharmonicity?
You might be correct for organ tuning, but not for piano. On the piano, =
partials
are not exact multiples on ANY note, covered or metal; and not even in =
the
temperament octave are notes PRECISELY related by the 12th root of two. =
It's
just a little wider.<BR><BR>Bob Davis</FONT> </FONT></BODY></HTML>