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<DIV><FONT face=Arial size=2>"If you have not read my essay on =
Tempered Octaves,
please request it, I will send it in a separate post." <BR></FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Hello, I'm fairly new to the list and =
would like to
see the above mentioned essay if you don't mind submitting it
again.</FONT></DIV>
<DIV> </DIV>
<DIV><FONT face=Arial size=2>Thank you,</FONT></DIV>
<DIV><FONT face=Arial size=2> </DIV></FONT>
<DIV><FONT face=Arial size=2>Bobby Sims<BR></FONT>----- Original =
Message -----
</DIV>
<BLOCKQUOTE
style="BORDER-LEFT: #000000 2px solid; MARGIN-LEFT: 5px; MARGIN-RIGHT: =
0px; PADDING-LEFT: 5px; PADDING-RIGHT: 0px">
<DIV
style="BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: =
black"><B>From:</B>
<A href="mailto:tunenbww@clear.lakes.com"
title=tunenbww@clear.lakes.com>Paul</A> </DIV>
<DIV style="FONT: 10pt arial"><B>To:</B> <A =
href="mailto:pianotech@ptg.org"
title=pianotech@ptg.org>pianotech@ptg.org</A> </DIV>
<DIV style="FONT: 10pt arial"><B>Sent:</B> Friday, October 19, 2001 =
8:44
AM</DIV>
<DIV style="FONT: 10pt arial"><B>Subject:</B> Fw: Quasi ET</DIV>
<DIV><BR></DIV>
<DIV> </DIV>
<DIV style="FONT: 10pt arial">----- Original Message -----
<DIV style="BACKGROUND: #e4e4e4; font-color: black"><B>From:</B> <A
href="mailto:Billbrpt@aol.com" =
title=Billbrpt@aol.com>Billbrpt@aol.com</A>
</DIV>
<DIV><B>To:</B> <A href="mailto:tunenbww@clear.lakes.com"
title=tunenbww@clear.lakes.com>tunenbww@clear.lakes.com</A> </DIV>
<DIV><B>Sent:</B> Saturday, October 13, 2001 10:27 AM</DIV>
<DIV><B>Subject:</B> Re: Quasi ET</DIV></DIV>
<DIV><BR></DIV><FONT face=arial,helvetica><FONT size=2>In a =
message dated
10/13/01 9:04:55 AM Central Daylight Time, <A
href="mailto:tunenbww@clear.lakes.com">tunenbww@clear.lakes.com</A> =
writes:
<BR><BR><BR>
<BLOCKQUOTE
style="BORDER-LEFT: #0000ff 2px solid; MARGIN-LEFT: 5px; =
MARGIN-RIGHT: 0px; PADDING-LEFT: 5px"
TYPE="CITE">Bill <BR>Sometime ago you responded to the list with a
temperament as I recall you stating being used by Horace Greeley and =
others
as an alternative to ET. I should have brought the description with =
me, but
anyway, I've been trying it and it does have a nice openness to the =
sound.
My difficulty is setting the F3 to a good Major 3rd below the A3. I =
haven't
figured out a reliable method. I was wondering if you have a =
technique I
could try. <BR><BR>Thanks for your time and considerations. =
<BR><BR>Paul
Chick</BLOCKQUOTE><BR><BR>The 3 contiguous 3rds, F3-A3, A3-C#4 and =
Db4(C#4)-F4
are *exactly* the same as in regular ET. Therefore, set your =
F3-A3
*exactly the same* as you would when tuning ET, whatever your =
technique may be
is. Aurally, you would estimate 7 beats per second, then tune =
the F3-F4
octave and fill in C#4. Adjust all intervals until you get the =
proper
4:5 ratio of contiguous 3rds and a good sounding stretched octave. =
<BR><BR>The
F3-F4 octave is usually best as a compromise between a 4:2 and 6:3 =
octave. To
get that, use the test for 4:2 which is Db3(C#3)-F3 then Db3(C#3)-F4. =
If
they are exactly the same, you have 4:2 octave. If the upper =
interval is
*slightly* faster, the octave is stretched more than a 4:2. Now =
test for
6:3. Play F3-Ab3(G#3) and Ab3(G#3)-F4. If both are exactly =
the
same, you have a 6:3 octave. If the upper interval is *slightly* =
slower,
you have the octave stretched less than 6:3. Try to find the =
spot where
the 4:2 tests a little wide and the 6:3 a little narrow. <BR><BR>This =
is a
very fine distinction. Electronically, it would probably be less =
than 2
cents. A piano with low inharmonicity (such as most Kawai, =
M&H,
Baldwin Concert Grands) would reveal practically no distinction =
between the
two. A piano with high inharmonicity (such as a Steinway) would =
provide
an easily audible distinction. Yamahas are usually in the =
middle.
<BR><BR>If you use and electronic program such as the FAC, simply tune =
the
notes F3-A3-C#4-F4 according to the program and use the above aural =
tests to
make any adjustment if necessary. <BR><BR>After tuning F3-A3-C#4-F4, =
simply
tune a pure 4th and 5th from each of these notes. Use the test =
for a
pure 4th or 5th to prove. I use the SAT in the Direct Interval =
mode to
prove. With practice and good understanding, it is quickly and =
easily
done. After that, place the note G3 so that it beats exactly the =
same
between C4 and D4. Place the note B3 so that it beats exactly =
the same
between F#3 and E4. Finally, place the note Eb4(D#4) so that it =
beats
exactly the same between Ab3(G#3) and Bb3(A#3). <BR><BR>This will =
produce 3rds
and 6ths which will sound identical to those in ET. Most of the =
4ths and
5ths will sound really good because they are pure. You will have =
just a
few "wobbly" ones. (Now ask yourself, who's aural attempt at ET
doesn't?). In my opinion based on many years of observation, =
very few
aural attempts at ET are clinically perfect. They are almost =
always a
*Quasi* ET. (Quasi means "almost"). <BR><BR>I strongly suggest =
you use
my Tempered Octaves method for tuning the octaves. This will give your =
piano a
"crystal clear" sound and will make the "wobbly" 4ths and 5ths in the
temperament octave range become inaudible in the outer octaves. =
If you
have not read my essay on Tempered Octaves, please request it, I will =
send it
in a separate post. <BR><BR>If you feel this answer to you would be =
useful to
the List in general, please feel free to forward it. There are =
always
new subscribers who have not read of this idea before. By the =
way, it is
properly known as the "Marpurg-Neidhardt Composite Quasi Equal =
Temperament".
It is close enough to regular ET to fall within the tolerances =
of the
PTG Tuning Exam. In my opinion, it could be freely substituted =
for ET
under any tuning circumstances, including high level concert tuning =
without
the technicians feeling an ethical need to disclose any techniques =
whatsoever.
<BR><BR>Please let me know of your experience using it. <BR><BR>Bill =
Bremmer
RPT <BR>Madison, Wisconsin</FONT> </FONT></BLOCKQUOTE></BODY></HTML>