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<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></BODY></HTML>