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<DIV><FONT face=Arial size=2>Hello Isaac</FONT></DIV>
<DIV><FONT face=Arial size=2>Thanks for your reply, the most =
interesting part of
which was in the final para: "BTW, my favourite first octave test =
(temperament)
is to have the 3 major thirds (FA - AC# - C#F) sounding together.." =
Actually
Isaac, this is the very basis of my so called "Quadrant System" both in =
tuning
and its utilisation in raising the pitch of a piano. And it sounds nice
too! I have never (in memory) used a 17th. interval at the top end =
of the
piano, only 15ths. I can stretch to play and tune while holding =
down
10ths. Very useful - but that's in the Bass where the beats are more =
prominent
for that interval. Nothing much can be done with the very bottom 8ve. =
the notes
seem reluctant to produce beats with any interval.I only use the =
TLA for
the middle twelve notes (checking as soon as possible with M3) Having
laid the bearings I then play the bearings chromatically in M3 =
and
listen to the smoothe change in beat-rate. I go throught the whole =
tuning
process going down in M3, 4ths, 5ths, 8ves and 10ths. And up to the top =
using
4ths, 5ths, 8ves and 15ths. I start using the 15ths right at the outset. =
It's a
pretty rapid system. I find that this works wonderfully in =
Harpsichords -
it very quickly discloses the maverick tunings!</FONT></DIV>
<DIV><FONT face=Arial size=2>I agree with the lively colouration of =
a modified
equal temperament...!! Dare I call it that? That the tone dies away =
sooner is, I
think, due to lack of sympathetic harmonics. String players love to hear =
the
pure 4ths and 5ths .... and so we go full circle and realise we are, at =
best,
making a compromise in any setting of the scale! I am sure M.Pythagoras =
went
through all this mental anguish when he discovered (in sand) his =
wretched
interval. The bane of our lives and reason for our =
existance!</FONT></DIV>
<DIV><FONT face=Arial size=2>Regards</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=oleg-i@noos.fr href="mailto:oleg-i@noos.fr">Isaac sur Noos</A> =
</DIV>
<DIV><B>To:</B> <A title=pianotech@ptg.org
href="mailto:pianotech@ptg.org">Pianotech</A> </DIV>
<DIV><B>Sent:</B> Tuesday, October 21, 2003 6:00 AM</DIV>
<DIV><B>Subject:</B> RE: "The Invisible Tool"/beat rates - and where =
they come
from</DIV></DIV>
<DIV><BR></DIV>
<DIV><SPAN class=308184003-21102003><FONT face=Arial color=#0000ff =
size=2>Michiel,</FONT></SPAN></DIV>
<DIV><SPAN class=308184003-21102003><FONT face=Arial color=#0000ff =
size=2></FONT></SPAN> </DIV>
<DIV><SPAN class=308184003-21102003><FONT face=Arial color=#0000ff =
size=2>I see
what you mean ,I have computed all beat rates for 3 octaves and all =
intervals
once, and I remeber using a little metronome to learn to count =
beats (just
insist, and you'll know how to tune someday :>)!</FONT></SPAN></DIV>
<DIV><SPAN class=308184003-21102003><FONT face=Arial color=#0000ff =
size=2></FONT></SPAN> </DIV>
<DIV><SPAN class=308184003-21102003></SPAN><SPAN =
class=308184003-21102003><FONT
face=Arial color=#0000ff size=2></FONT></SPAN> </DIV>
<DIV><SPAN class=308184003-21102003><FONT face=Arial color=#0000ff =
size=2>As
understand it you tune by fast intervals mostly. Indeed one can train to =
get a good interval color for the fast beatings, and get a =
feel for it
.One can even consider the fast beating as if they where octaves or =
fiths, and
tune unissons while correcting their speed. I've done it but have find =
it to be
too tiring for the ears. (But I remember a Balwin spinet, the only one I =
tuned I
guess, and it was easier to tune without any muting, mutes gave a so =
unfocused
tone that it was an horror to try to hear beats, while they appear more =
clearly
in the full garbage ;>)</FONT></SPAN></DIV>
<DIV><SPAN class=308184003-21102003><FONT face=Arial color=#0000ff =
size=2></FONT></SPAN> </DIV>
<DIV><SPAN class=308184003-21102003><FONT face=Arial color=#0000ff =
size=2>But as
the 10th and 17th beat rate progression slow on most pianos in the =
treble,
if we follow the inharmonicity of the instrument.</FONT></SPAN></DIV>
<DIV><SPAN class=308184003-21102003><FONT face=Arial color=#0000ff =
size=2>If we
follow beat rate progression , the treble scream a bit , (is an =
advantage for
some situation).</FONT></SPAN></DIV>
<DIV><SPAN class=308184003-21102003><FONT face=Arial color=#0000ff =
size=2></FONT></SPAN> </DIV>
<DIV><SPAN class=308184003-21102003><FONT face=Arial color=#0000ff =
size=2>I use
the 17 th's in the treble but mostly if I am lost with a high =
treble note,
to check my double octave.</FONT></SPAN></DIV>
<DIV><SPAN class=308184003-21102003><FONT face=Arial color=#0000ff =
size=2></FONT></SPAN> </DIV>
<DIV><SPAN class=308184003-21102003><FONT face=Arial color=#0000ff =
size=2>And I
use to check the progression of course, but is enough to tune by octave =
(the
worst interval for tuning !) to me .</FONT></SPAN></DIV>
<DIV><SPAN class=308184003-21102003><FONT face=Arial color=#0000ff =
size=2></FONT></SPAN> </DIV>
<DIV><SPAN class=308184003-21102003><FONT face=Arial color=#0000ff =
size=2>Nowadays any focused tuning is musical, for instance a fourth =
based, even
a fiths based tuning, </FONT></SPAN></DIV>
<DIV><SPAN class=308184003-21102003></SPAN><SPAN =
class=308184003-21102003><FONT
face=Arial color=#0000ff size=2></FONT></SPAN> </DIV>
<DIV><SPAN class=308184003-21102003><FONT face=Arial color=#0000ff =
size=2>Just
that some tunings are more in the iH of the piano and others more in the =
mood of
the tuner.!</FONT></SPAN></DIV>
<DIV><SPAN class=308184003-21102003><FONT face=Arial color=#0000ff =
size=2></FONT></SPAN> </DIV>
<DIV><SPAN class=308184003-21102003><FONT face=Arial color=#0000ff =
size=2>I mean
that even a pure ffith tuning does not sound false to the player, while =
the
octaves beat as hell, but when chords are leaved sustaining, the more =
the tuning
respect the piano Iharmonicity, the more sustain you get, and in Western =
harmony
you have more immediate tone in harmony because of the reinforcement of =
the
partials. </FONT></SPAN></DIV>
<DIV><SPAN class=308184003-21102003><FONT face=Arial color=#0000ff =
size=2></FONT></SPAN> </DIV>
<DIV><SPAN class=308184003-21102003><FONT face=Arial color=#0000ff =
size=2>Indeed
Il like the lively coloration of a little untempered tuning when =
large
chords are sustained (leaved sounding), you have more move and partial =
rubbing,
that gives a "singing" quality, but the tone extinct sooner I have =
seen
(why ?). The tunings computed by the VT, when you hold the sustain pedal =
with a
large chord, the tone does not seem to want to end. </FONT></SPAN></DIV>
<DIV><SPAN class=308184003-21102003><FONT face=Arial color=#0000ff =
size=2>Then
my I deduction is that there is a more lively tone in this =
situation, while
I understand it is difficult to ascertain for sure =
!</FONT></SPAN></DIV>
<DIV><SPAN class=308184003-21102003><FONT face=Arial color=#0000ff =
size=2></FONT></SPAN> </DIV>
<DIV><SPAN class=308184003-21102003><FONT face=Arial color=#0000ff =
size=2>BTW,
my favourite first octave test (temperament) is to have the 3 major =
thirds (FA -
A C# - C#F) sounding together, no third may be heard more than others, =
thats a
neat test !</FONT></SPAN></DIV>
<DIV><SPAN class=308184003-21102003></SPAN> </DIV>
<DIV><SPAN class=308184003-21102003><FONT face=Arial color=#0000ff =
size=2>My
best to </FONT></SPAN><SPAN class=308184003-21102003><FONT =
face=Arial
color=#0000ff size=2>you all !</FONT></SPAN></DIV>
<DIV><SPAN class=308184003-21102003><FONT face=Arial color=#0000ff =
size=2></FONT></SPAN> </DIV>
<DIV><SPAN class=308184003-21102003><FONT face=Arial color=#0000ff =
size=2>Isaac
OLEG</FONT></SPAN></DIV>
<DIV><SPAN class=308184003-21102003><FONT face=Arial color=#0000ff =
size=2></FONT></SPAN> </DIV>
<DIV><SPAN class=308184003-21102003><FONT face=Arial color=#0000ff =
size=2></FONT></SPAN> </DIV>
<DIV><SPAN class=308184003-21102003><FONT face=Arial color=#0000ff =
size=2></FONT></SPAN> </DIV>
<DIV><SPAN class=308184003-21102003><FONT face=Arial color=#0000ff =
size=2></FONT></SPAN> </DIV>
<DIV><SPAN class=308184003-21102003><FONT face=Arial color=#0000ff =
size=2></FONT></SPAN> </DIV>
<DIV><SPAN class=308184003-21102003><FONT face=Arial color=#0000ff =
size=2>Best</FONT></SPAN></DIV>
<DIV><SPAN class=308184003-21102003><FONT face=Arial color=#0000ff =
size=2></FONT></SPAN> </DIV>
<DIV><SPAN class=308184003-21102003><FONT face=Arial color=#0000ff =
size=2></FONT></SPAN> </DIV>
<DIV> </DIV>
<P><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></P>
<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> mardi 21 octobre 2003
01:23<BR><B>À :</B> pianotech@ptg.org<BR><B>Objet :</B> =
Fw: "The
Invisible Tool"/beat rates - and where they come =
from<BR><BR></FONT></DIV>
<DIV><FONT face=Arial size=2>Hello Isaac</FONT></DIV>
<DIV><FONT face=Arial color=#0000ff size=2>(while being near) =
you said. In
this I am very happy. At least the concept even if not completely =
accurate,
gives a working knowledge of the system. :-)</FONT></DIV>
<DIV><FONT face=Arial color=#0000ff size=2>You'll notice I =
extracted a bit
from your message and stuck it on my reply - I'm finding out how these =
new
fangled computer thingys work.</FONT></DIV>
<DIV><FONT face=Arial color=#0000ff size=2>Kindest =
regards</FONT></DIV>
<DIV><FONT face=Arial color=#0000ff size=2>Michael G (UK across =
the
Chanel) <- ;-)</FONT></DIV>
<DIV style="FONT: 10pt arial">----- Original Message -----
<DIV style="BACKGROUND: #e4e4e4; font-color: black"><B>From:</B> <A
title=oleg-i@noos.fr href="mailto:oleg-i@noos.fr">Isaac sur =
Noos</A> </DIV>
<DIV><B>To:</B> <A title=pianotech@ptg.org
href="mailto:pianotech@ptg.org">Pianotech</A> </DIV>
<DIV><B>Sent:</B> Monday, October 20, 2003 10:02 PM</DIV>
<DIV><B>Subject:</B> RE: "The Invisible Tool"/beat rates - and where =
they come
from</DIV></DIV>
<DIV><BR></DIV>
<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 </FONT></SPAN><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></BLOCKQUOTE></BODY></HTML>