<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<HTML><HEAD>
<META http-equiv=Content-Type content="text/html; =
charset=iso-8859-1">
<META content="MSHTML 6.00.2800.1264" name=GENERATOR>
<STYLE></STYLE>
</HEAD>
<BODY bgColor=#ffffff>
<DIV><SPAN class=613325620-20102003><FONT face=Arial color=#0000ff =
size=2>Michael,</FONT></SPAN></DIV>
<DIV><SPAN class=613325620-20102003><FONT face=Arial color=#0000ff =
size=2></FONT></SPAN> </DIV>
<DIV><SPAN class=613325620-20102003><FONT face=Arial color=#0000ff =
size=2>out of
any computation, the most universal admitted ratio that works in the =
piano is
the 4/5 ratio for 2 contigous major thirds.</FONT></SPAN></DIV>
<DIV><SPAN class=613325620-20102003><FONT face=Arial color=#0000ff =
size=2></FONT></SPAN> </DIV>
<DIV><SPAN class=613325620-20102003><FONT face=Arial color=#0000ff =
size=2>All
these beat rates computed, does not have to do much with the beat rates =
in the
piano (while being near)</FONT></SPAN></DIV>
<DIV><SPAN class=613325620-20102003><FONT face=Arial color=#0000ff =
size=2></FONT></SPAN> </DIV>
<DIV><SPAN class=613325620-20102003><FONT face=Arial color=#0000ff =
size=2>On
some pianos the FA major 3d is as fast as 7.3 and on others it can't be
even 6.8 bps.</FONT></SPAN></DIV>
<DIV><SPAN class=613325620-20102003><FONT face=Arial color=#0000ff =
size=2></FONT></SPAN> </DIV>
<DIV><SPAN class=613325620-20102003><FONT =
size=2>Regards</FONT></SPAN></DIV>
<DIV><FONT size=2></FONT> </DIV>
<DIV><FONT size=2>Isaac OLEG<BR><BR>Entretien et réparation de
pianos.<BR><BR>PianoTech<BR>17 rue de Choisy<BR>94400 VITRY sur
SEINE<BR>FRANCE<BR>tel : 033 01 47 18 06 98<BR>fax : 033 01 47 18 06 =
90<BR>cell:
06 60 42 58 77 </FONT></DIV>
<BLOCKQUOTE dir=ltr
style="PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: #0000ff 2px =
solid; MARGIN-RIGHT: 0px">
<DIV class=OutlookMessageHeader dir=ltr align=left><FONT =
face=Tahoma
size=2>-----Message d'origine-----<BR><B>De :</B>
pianotech-bounces@ptg.org [mailto:pianotech-bounces@ptg.org]<B>De la =
part
de</B> Michael Gamble<BR><B>Envoyé :</B> lundi 20 octobre 2003
17:27<BR><B>À :</B> pianotech@ptg.org<BR><B>Objet :</B> =
"The
Invisible Tool"/beat rates - and where they come =
from<BR><BR></FONT></DIV>
<DIV><FONT face=Arial size=2>Hello list</FONT></DIV>
<DIV><FONT face=Arial size=2>Like all of you, I imagine, I was =
first made
aware of these beats when listening to a piano (in my case pipe organ) =
being
tuned. My curiosity led me to analyse the reason and I turned to =
simple
mathematics for the answer. Enter my "small equation" where the =
fundamental
(1st.Harm.) is multiplied by the 12th. root of 2 to derive the next
fundamental in the ascending equal tempered chromatic scale. =
(Simply
devide if you want to go down chromatically). In every case the =
resultant
becomes a Fundamental Note - or 1st.Harmonic. I know this is all "old =
hat" but
there's probably some meat in it to be chewed over just the same. Now =
taking
the Fundamental and multiplying by "Two" one gets the second harmonic. =
Multiplying by "Three" gets the third harmonic ad. inf. The really =
interesting
point now comes... 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
=
F =2793.8259...... There we =
have a
difference of 3.1567..... Hz which is the beat you hear. The same =
applies, of
course, to any and all intervals in the equal tempered scale, be they =
M3,M4,M5
- whatever.</FONT></DIV>
<DIV><FONT face=Arial size=2>It is interesting to apply that =
"small formula"
to log all the notes of the equal tempered scale on a mathematical =
basis and
thereby to extract the "Beat-rate" information whole-sale. To me this
information is "an invisible tool" - and I use it - as do you. But =
it's nice
to <EM>see</EM> an invisible friend sometimes! </FONT></DIV>
<DIV><FONT face=Arial size=2>Of course! There are many pitfalls! =
Many pianos
do not produce the exact mathematical frequencies according to my =
table. Those
times when the first covered (wrapped) Bass string are played with =
their M10 -
and the beat rate does not conform to the mathematical progression of =
the
tables as produced in the "metals" section of the piano. Well..., =
That's life
:-) I find the "scientific calculator on the PC best as it =
produces so
many decimal places! In using such a calculator you can go =
right up the
scale and land up, an 8ve later with exactly twice the number you =
started out
with. Now that's Magic! </FONT></DIV>
<DIV><FONT face=Arial size=2>Regards</FONT></DIV>
<DIV><FONT face=Arial size=2>Michael G
(UK)</FONT></DIV></BLOCKQUOTE></BODY></HTML>