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<DIV>
<DIV>In a message dated 3/13/2005 11:35:58 P.M. Central Standard Time,
pianotuna@yahoo.com writes:</DIV>
<BLOCKQUOTE
style="PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: blue 2px solid"><=
FONT
style="BACKGROUND-COLOR: transparent" face=Arial color=#000000 size=
=2>Hi
Wim,<BR><BR>You are hearing a 12:1 (a4 at a4); and possibly a 24:2 (a4 at =
a5);
a 36:3<BR>(a4 at e6). Try ghosting to see if any of those match your 6 bea=
ts
(you<BR>would need a 2nd piano to "ghost" the 12:1.<BR><BR>If the piano wi=
ll
only accept a 6:3 octave from d1 to d2 then d1 to a4<BR>would cause a beat=
at
the 12:1 level, because d1 is too sharp. If the piano<BR>will accept a 14:=
7
octave from d1 to d2 then d1 again will beat against a4,<BR>because d2 is =
too
flat. The only time there would be zero beats is if d1 to<BR>d2 is a perfe=
ct
12:6 octave--and all the octaves above it work as perfect<BR>whole multipl=
es
(and the only partial that would be beat free would be 12.<BR>24:2 would s=
till
beat)<BR><BR>i.e.<BR><BR>If <BR><BR>d1 to d2 = 12:6<BR>d2 to d3 = =
;
6:3<BR>d3 to d4 = 4:2<BR><BR>Then<BR><BR>d1 to a4 = zero beating=
at the
12:1<BR><BR>This is unlikely to happen in any real life piano, so almost
always there<BR>will be a beat between d1 and a4.<BR></FONT></BLOCKQUOTE><=
/DIV>
<DIV></DIV>
<DIV>Don</DIV>
<DIV> </DIV>
<DIV>Thank you for this explanation. </DIV>
<DIV> </DIV>
<DIV>When I first into this business, back in the 70's, I got to know a=
very respectable piano technician from Denver, John Block. He was an old cus=
s,
ex-marine. He gave some very interesting classes on repairs, regulating, etc=
.
But when it came to tuning, and especially the theory of tuning, he just thr=
ew
up his hands and said, I don't understand all this ratio stuff. I'm just a g=
ood
old wah wah tuner. </DIV>
<DIV> </DIV>
<DIV>Well, that's me. I appreciate all the research, Don, but to be hon=
est
with you, it might as well have been written in Greek. To me, it looks =
like
a chemical equation, and I flunked chemistry in high school. I am sure =
what
you wrote is correct, but I just don't understand it. As long as I hear a wa=
h
wah, I know my piano is in tune. I guess I shouldn't have asked the question=
in
the first place. Sorry. </DIV>
<DIV> </DIV>
<DIV>Wim </DIV></FONT></BODY></HTML>