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<DIV><FONT face=Arial size=2>Ric, Duh, so al' I gotta do is =
stop da little
lights, right? (grin)</FONT></DIV>
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style="PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; =
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<DIV style="FONT: 10pt arial">----- Original Message ----- </DIV>
<DIV
style="BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: =
black"><B>From:</B>
<A title=Richard.Brekne@grieg.uib.no
href="mailto:Richard.Brekne@grieg.uib.no">Richard Brekne</A> </DIV>
<DIV style="FONT: 10pt arial"><B>To:</B> <A =
title=pianotech@ptg.org
href="mailto:pianotech@ptg.org">PTG</A> </DIV>
<DIV style="FONT: 10pt arial"><B>Sent:</B> Saturday, August 17, 2002 =
8:47
AM</DIV>
<DIV style="FONT: 10pt arial"><B>Subject:</B> May the 4ths be with =
you</DIV>
<DIV><BR></DIV>List. <BR><BR>The following is an except from appendix =
F of the
SAT<BR>manual. It gives an explanation by Dr Sanderson that =
shows<BR>why David
Anderson was "correct" about 4ths having the same<BR>slow beat rates, =
and why
I was "correct" in stating that<BR>4ths should have a contiguous =
relationship
as 3rds do.<BR><BR>"Two contiguous musical intervals are intervals =
that
touch<BR>each other, in other words, share the note in the middle. =
<BR>Tests
that use contiguous intervals are easy to learn and<BR>use, and tell =
the tuner
explicitly which notes are at fault<BR>and what to do to correct
them.<BR>Contiguous major thirds will beat in the ratio of four =
to<BR>five
because the major third itself consists of two notes<BR>whose =
frequencies are
in the ratio of four to five. <BR>Displacing any interval up the =
keyboard will
speed it up<BR>theoretically in the ratio of the frequencies of the
two<BR>root notes involved. Therefore two contiguous major
thirds<BR>should beat in the ratio of four to five, two =
contiguous<BR>minor
thirds in the ratio of five to six.Similarly, two<BR>contiguous =
fourths should
beat in the ratio of three to four<BR>and two contiguous fifths in
the<BR>ratio of two to three. However, on the piano =
this<BR>theoretical
relationship holds well only for the major and<BR>minor
thirds. The fourths and =
fifths
are so <BR>strongly affected by =
inharmonicity
that these <BR>contiguous intervals beat at almost the same
speeds"<BR><BR><BR>Cheers !<BR><BR>Ricb</BLOCKQUOTE></BODY></HTML>