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<DIV><FONT face=Arial size=2>Hi Bill and everybody</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>I've missed some test intervals on the =
EBVT so
</FONT><FONT face=Arial size=2>from Robert Scotts EBVT calculation I =
got those
beats (hope I got it right)</FONT></DIV>
<DIV> </DIV>
<DIV><FONT face=Arial size=2>D3-B3=6,1</FONT></DIV>
<DIV><FONT face=Arial size=2>E3-G#3=8,1</FONT></DIV>
<DIV><FONT face=Arial size=2>F3-A3=5,4bps</FONT></DIV>
<DIV><FONT face=Arial size=2>F3-C4=0bps</FONT></DIV>
<DIV><FONT face=Arial size=2>F3-A#3=0bps </FONT></DIV>
<DIV><FONT face=Arial size=2>F3-D4=7,3bps</FONT></DIV>
<DIV><FONT face=Arial size=2>F#3-C#3=0bps =
</FONT></DIV>
<DIV><FONT face=Arial size=2>F#3-B3=1,6bps</FONT></DIV>
<DIV><FONT face=Arial size=2>F#3-A#3=8,9bps</FONT></DIV>
<DIV><FONT face=Arial size=2>F#3-</FONT><FONT face=Arial
size=2>D#4=10,2bps</FONT></DIV>
<DIV><FONT face=Arial size=2>G3-D4=1,5bps</FONT></DIV>
<DIV><FONT face=Arial size=2>G3-C4=1,5bps</FONT></DIV>
<DIV><FONT face=Arial size=2>G3-B3=5,7bps</FONT></DIV>
<DIV><FONT face=Arial size=2>G3-E4=6,1bps</FONT></DIV>
<DIV><FONT face=Arial size=2>G#3-D#4=0,9</FONT></DIV>
<DIV><FONT face=Arial size=2>G#3-C#4=0bps </FONT></DIV>
<DIV><FONT face=Arial size=2>G#3-C4=9,9bps</FONT></DIV>
<DIV><FONT face=Arial size=2>G#3-F4=9,7bps</FONT></DIV>
<DIV><FONT face=Arial size=2>A3-E4=1,1bps</FONT></DIV>
<DIV><FONT face=Arial size=2>A3-D4=1,9bps</FONT></DIV>
<DIV><FONT face=Arial size=2>A3-C#4=9,4bps</FONT></DIV>
<DIV><FONT face=Arial size=2>A3-F#4=9.2bps</FONT></DIV>
<DIV><FONT face=Arial size=2>A#3-F4=0bps </FONT></DIV>
<DIV><FONT face=Arial size=2>A#3-D#4=1,3bps</FONT></DIV>
<DIV><FONT face=Arial size=2>A#3-D4=9,4bps</FONT></DIV>
<DIV><FONT face=Arial size=2>A#3-G4=12,2bps</FONT></DIV>
<DIV><FONT face=Arial size=2>B3-F#4=1,6bps</FONT></DIV>
<DIV><FONT face=Arial size=2>B3-E4=0,3bps</FONT></DIV>
<DIV><FONT face=Arial size=2>B3-D#4=10,9bps</FONT></DIV>
<DIV><FONT face=Arial size=2>B3-G#4=12,6bps</FONT></DIV>
<DIV><FONT face=Arial size=2>C4-G4=1,5bps</FONT></DIV>
<DIV><FONT face=Arial size=2>C4-F4=0bps =
</FONT></DIV>
<DIV><FONT face=Arial size=2>C4-E4=5,7bps</FONT></DIV>
<DIV><FONT face=Arial size=2>C4-A4=7,8bps</FONT></DIV>
<DIV><FONT face=Arial size=2>C#4-G#4=0bps =
</FONT></DIV>
<DIV><FONT face=Arial size=2>C#4-F#4=0bps =
</FONT></DIV>
<DIV><FONT face=Arial size=2>C#4-F4=12,6bps</FONT></DIV>
<DIV><FONT face=Arial size=2>C#4-A#4=13,2bps</FONT></DIV>
<DIV><FONT face=Arial size=2>D4-A4=1,9bps</FONT></DIV>
<DIV><FONT face=Arial size=2>D4-G4=2,8bps</FONT></DIV>
<DIV><FONT face=Arial size=2>D4-F#4=9bps</FONT></DIV>
<DIV><FONT face=Arial size=2>D#4-G#4=1,7bps</FONT></DIV>
<DIV><FONT face=Arial size=2>D#4-G4=14,2bps</FONT></DIV>
<DIV><FONT face=Arial size=2>E4-A4=2,1bps</FONT></DIV>
<DIV><FONT face=Arial size=2>E4-G#4=16,3bps</FONT></DIV>
<DIV><FONT face=Arial size=2>F4-A4=10,8bps</FONT></DIV>
<DIV> </DIV>
<DIV><FONT face=Arial size=2>Is this what you mean?</FONT></DIV>
<DIV><FONT face=Arial size=2>Do you want to change =
anything?</FONT></DIV>
<DIV> </DIV>
<DIV><FONT face=Arial size=2>A question</FONT></DIV>
<DIV> </DIV>
<DIV><FONT face=Arial size=2>I can't understand why you after tuning =
A4 and A3
want to tune</FONT></DIV>
<DIV><FONT face=Arial size=2>E4-C4-G3-B3-D4-F4-F3</FONT></DIV>
<DIV> </DIV>
<DIV><FONT face=Arial size=2>Why not take the short cut</FONT></DIV>
<DIV><FONT face=Arial size=2>F3-C4-E4 to see how the thirds of F3-A3 =
and C4-E4
beat the same, retune(?) and then take the rest of the =
whites</FONT></DIV>
<DIV> </DIV>
<DIV><FONT face=Arial size=2>Please tell me:-)</FONT></DIV>
<DIV> </DIV>
<DIV> </DIV>
<DIV><FONT face=Arial size=2>Ola Andersson</FONT></DIV>
<DIV><FONT face=Arial size=2>Bergen Norway</FONT></DIV>
<DIV> </DIV>
<DIV> </DIV>
<BLOCKQUOTE
style="BORDER-LEFT: #000000 2px solid; MARGIN-LEFT: 5px; MARGIN-RIGHT: =
0px; PADDING-LEFT: 5px; PADDING-RIGHT: 0px">
<DIV style="FONT: 10pt arial">----- Original Message ----- </DIV>
<DIV
style="BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: =
black"><B>From:</B>
<A href="mailto:Billbrpt@AOL.COM" =
title=Billbrpt@AOL.COM>Billbrpt@AOL.COM</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> Saturday, April 07, 2001 =
7:31
PM</DIV>
<DIV style="FONT: 10pt arial"><B>Subject:</B> Re: alternative
temperaments</DIV>
<DIV><BR></DIV><FONT face=arial,helvetica><FONT size=2>In a =
message dated
4/7/01 11:28:35 AM Central Daylight Time, <BR><A
href="mailto:tunenbww@clear.lakes.com">tunenbww@clear.lakes.com</A> =
(Paul)
writes: <BR><BR>
<BLOCKQUOTE
style="BORDER-LEFT: #0000ff 2px solid; MARGIN-LEFT: 5px; =
MARGIN-RIGHT: 0px; PADDING-LEFT: 5px"
TYPE="CITE">I'm an aural tuner, so setting this temperament was a =
bit of a
struggle. It <BR>did work out. All of the checks proofed correct. I =
had
several people try <BR>the piano. Their reactions is another story.
</FONT><FONT color=#000000 face=Arial lang=0 size=3
FAMILY="SANSSERIF"></BLOCKQUOTE><BR></FONT><FONT color=#000000 =
face=Arial
lang=0 size=2 FAMILY="SANSSERIF"><BR>I'm glad that you are an =
aural tuner
because I have the ideal temperament for <BR>you to try. It will =
be in
the same general area as Jim Coleman's #11, yet <BR>different enough =
to be
quite significantly different in the overall effects <BR>it produces =
when
actual music is played. The difference is in the effects =
<BR>that Equal
Beating (EB) produces. <BR><BR>While not attempting to say anything =
negative
about Jim Coleman's idea, it <BR>was formed simply by meting out =
certain
proportions for various intervals, <BR>giving up purity at the top of =
the
Cycle of 5ths in order to avoid harshness <BR>at the bottom. =
Mine does
essentially the same thing but because of the EB <BR>effect, you can =
play
early music with it and have it mimic the sound of a <BR>much earlier
temperament which would have uncalled for harshness in the <BR>remote =
keys
when trying to play music from the 19th or 20th Centuries. =
<BR><BR>What
happens is a canceling out effect in the Rapidly Beating Intervals =
<BR>(RBI),
e.g., 3rds, 6ths, 10ths & 17ths that make them sound much purer =
than
<BR>they really are. This is not an imaginary effect. It =
is the
same effect <BR>found in such acoustical tricks as Noise Cancellation =
Systems
and Beat <BR>Eliminators. The gist of it is that when there are =
two sets
of beats <BR>occurring at the same time, they phase each other out so =
that
they are not <BR>perceived by the ear. <BR><BR>This gives you an =
advantage in
that you can have a true, Cycle of 5ths based <BR>temperament that can =
and
does work well with virtually any kind of music, the <BR>way only ET =
is
believed to be able to do. There are many myths about ET and =
<BR>one of
them is that it is "Universally" practiced. In fact, most aural
<BR>tuners cannot really produce a true ET. There is always some =
error
and that <BR>error does produce an effect or "color", as it is called =
in the
music. <BR><BR>The Equal Beating Victorian Temperament (EBVT) that I =
designed
stays well <BR>within the bounds of deviation (or "error") in ET that =
most
aural tuners <BR>produce. Therefore, it produces no sound so =
extreme
(either too pure or too <BR>harsh) that the *contemporary* ear will =
reject it.
I designed and <BR>implemented this temperament in 1992 and have =
used it
ever since as my own <BR>personal replacement for ET. I have, in =
fact,
tuned no pianos in ET since <BR>1989. I tune all kinds of =
pianos, in
homes, schools, churches, concert <BR>halls, restaurants, hotels, etc. =
I
have a very loyal and devoted following <BR>that really likes the way =
I make
my pianos sound. <BR><BR>Ed Foote's latest essay found in the liner =
notes of
his new CD is quite <BR>impressive. But I find a couple of areas =
of
temperament research lacking in <BR>his study that I usually find, =
even among
the most knowledgeable alternative <BR>temperament practitioners. =
There
seems to be only one "Meantone", the most <BR>extreme form, the one =
that makes
the modern piano sound like an antique one <BR>with virtually none of =
the
resonance we expect to hear. There are whole <BR>classes of =
temperaments
that remain ignored and unexplored, the Modified <BR>Meantones (not =
the same
kind of temperament as a "Meantone") and the Quasi <BR>Equal =
Temperaments.
The EBVT is, in fact a Modified Meantone Temperament =
<BR>although it
also just barely satisfies the Rules for Well-Tempered Tuning as =
<BR>written
by Andreas Werkmeister in the 17th Century. <BR><BR>Ed mentioned in a =
recent
post that a Gershwin piece in Db would have sounded <BR>"better" in =
ET.
I've seen him say the same about Chopin and Debussy. I
<BR>respectfully disagree. There is a reason that these =
composers chose
a remote <BR>key, the challenge is to find the exact combinations that =
make it
sound <BR>vibrant and singing but not harsh. ET is merely the =
default
choice for those <BR>who do not have the answer. It neutralizes =
the
piano to the point where it <BR>would make no difference at all which =
key is
chosen to play in. I hardly <BR>think anyone would choose ET if =
they
really knew how much better music could <BR>sound with a more advanced =
approach to tuning. <BR><BR>Below are the basic instructions for the =
EBVT.
It cannot be tuned the way <BR>most people are trying to attempt =
alternative temperaments, by imposing a set <BR>of "Correction =
Figures" to a
smooth curve calculation for ET using an <BR>Electronic Tuning Device =
(ETD).
If you tune the octaves the way I have <BR>indicated in a very =
brief
description, they will naturally be of different <BR>sizes as you =
ascend and
descend the scale. No smooth curve calculation can <BR>produce =
this.
They are known as "Tempered Octaves". <BR><BR>If you or anyone =
is
interested in reading a background article I have written <BR>to =
support my
ideas called "Key Color", please request it privately. It is =
<BR>too
long to post on Pianotech. Also, please inquire if you need =
further
<BR>explanation of how to tune the octaves. It is really quite =
easy and
simple <BR>but not the way you have probably been taught. <BR><BR>Good =
luck
with this and let me and/or the List know of your own reaction and =
<BR>those
of your customers. <BR><BR>Regards, <BR><BR>Bill Bremmer RPT =
<BR>Madison,
Wisconsin
=
<BR><BR>  =
; EBVT
Aural Tuning Instructions: Introduction <BR><BR>Below are the =
line by
line instructions for tuning the EBVT. You will begin <BR>by =
estimating
just 2 intervals, a 5th which you will temper just slightly <BR>more =
than you
would for ET and a 3rd which you will temper about half as much <BR>as =
you
would for ET. Thereafter, all you will need to do is either tune =
an
<BR>interval perfectly pure or make it beat exactly the same as =
another.
In <BR>short, the temperament sequence itself provides you with =
the
exact <BR>information you need. <BR><BR>The instructions include the =
aural way
of proving your pure 4ths and 5ths. <BR>When doing an initial =
first
rough pass, it is not necessary to prove these <BR>intervals so =
exactly.
Also, the instructions have several places where they <BR>tell =
you to
"temporarily tune...etc". These are for people who are just
<BR>beginning to learn the temperament sequence. <BR><BR>With =
experience and
during the fine tuning of the temperament, you may skip <BR>the =
"temporary"
part the same way you learn to skip elementary steps in <BR>Algebra. =
You
simply learn how to make 2 intervals beat exactly the same as <BR>each =
other
by placing the note to be tuned at point where it creates 2 =
<BR>equally
beating intervals. This is also called "Meantone tuning". =
<BR><BR>The
following is the way the 3rds played chromatically will sound from =
F3-F4.
<BR> Just imagine all values inverted and you have the most =
commonly made
error <BR>in tuning today which is known as "Reverse Well". =
<BR><BR>F3-A3:
slow <BR>F#3-A#3: fast <BR>G3-B3: slow <BR>Ab3-C4: quite fast =
<BR>A3-C#4:
moderate, about the same as ET <BR>Bb-D4: moderate <BR>B3-D#4: very =
fast
<BR>C4-E4: slow, half the speed of ET <BR>C#4-F4: very fast
=
<BR><BR><BR> &=
nbsp; Equal
Beating Victorian Temperament =
<BR><BR> (Equal
Beating Victorianized Modified Meantone Temperament)
=
<BR><BR>  =
; Instructions=
for Aural Tuning
=
<BR> &nb=
sp; &nbs=
p;(With
Tempered Octaves) <BR><BR><BR>1. Tune A4 to A-440 pitch source. =
<BR>2.
Tune A3 to A4, stretching the octave to a a 6:3 type. <BR>3.
Temper E4 from A3, a narrow 5th, a little more than an Equal
<BR> Temperament (ET) 5th but still slightly less =
than 1 beat
per second. <BR> This is an estimate and may be =
checked or
adjusted later, if <BR> necessary. <BR>4. =
Listen to the
4th, E4-A4. It should beat faster than the 5th, A3-E4
<BR> but should not be faster than 2 beats per =
second. <BR>5.
Temper C4 from E4, a wide Major 3rd to beat approximately 6 =
beats per
<BR> second. (Half the speed of the same interval in =
ET.)
<BR>6. Temper G3 from E4, a wide Major 6th so that it beats =
exactly the
same <BR> as the C4-E4 3rd. (Approximately 6 beats =
per
second). <BR>7. Temper B3 from G3, a wide Major 3rd so that it =
beats
exactly the same <BR> as both the C4-E4 3rd and the =
G3-E4
6th. (Approximately 6 beats per <BR> second). <BR>8.
Temporarily tune D4 a pure 4th from A4 then notice the strong =
beat
<BR> in the 5th G3-D4 and sharpen D4 until the beat =
is
exactly the same <BR> in both the G3-D4 5th and the =
A3-D4
4th. (Faster than the same <BR> interval in ET.) =
<BR>9.
Tune F3 a pure 5th from C4. To check this interval, use =
G#2 as the
<BR> test note and prove that the Ab2-F3 6th beats =
exactly
the same as <BR> the Ab2-C4 10th. <BR>10. Tune =
F4 a
pure 4th from C4. To check this interval, use G#3 as the
<BR> test note and prove that the 3rd Ab3-C4 beats =
exactly
the same as the <BR> Ab3-F4 6th. <BR>11. Verify the =
F3-F4
octave. Using the test for a pure 5th which chooses
<BR> the lowest coincident partial of F3 & C4 and =
the
test for the pure 4th <BR> C4-F4 will yield a =
properly
stretched octave, usually a compromise <BR> between a =
4:2
& 6:3 type. <BR>12. Check the speed of the 3rd, F3-A3. It =
should
beat exactly the same <BR> or very similarly to the =
3rds
G3-B3 and C4-E4. If it is too slow, <BR> adjust =
the
note, E4 slightly flatter and begin the sequence again.
<BR> If too fast, adjust E4 slightly sharper and =
restart the
sequence. <BR>13. Tune Bb3 a pure 5th from F4. Use the test note =
C#3 to
prove that the <BR> Db3-Bb3 6th beats exactly the =
same as the
Db3-F4 10th. <BR>14. Listen to the resultant 3rd, Bb3-D4. Temper =
C#4 so
that the A3-C#4 <BR> 3rd beats exactly the same as =
the Bb3-D4
3rd. <BR>15. Tune F#3 a pure 5th from C#4. Use the test note A2 =
to prove
that the <BR> A2-F#3 6th beats exactly the same as =
the A2-C#4
10th. <BR>16. Tune G#3 a pure 4th from C#4. Use the test note E3 =
to
prove that the <BR> E3-G#3 3rd beats exactly the same =
as the
E3-C#4 6th. The Ab3-C4 3rd <BR> will beat =
exactly the
same as the F#3-A#3 3rd. <BR>17. Temporarily tune D#4 a pure 5th from =
G#3 then
notice the slight beat <BR> between D#4 & A#3 and =
flatten
D#4 until the G#3-D#4 5th beats exactly <BR> the same =
as the
A#3-D#4 4th. It will be a very slight beat, less than
<BR> the same interval in ET. The B3-D#4 3rd will =
beat very
rapidly, at <BR> least as fast as the F#3-A#3 & =
Ab3-C4
3rds below and similar to but <BR> perhaps not quite =
as fast
as the C#4-F4 3rd above. <BR>18. When expanding the octaves do so in a =
manner
which will cause the <BR> 2nd inversion major triads =
of C, G,
D, A, E, & B to have the 3rd & 6th <BR> beat =
exactly
the same. The octave should be stretched enough so that
<BR> there is a very slight beat in the single octave =
(approximately 1/2 <BR> beat per second) and that the =
tempered 5th will beat slower than the <BR> 4th. When =
both
the 4th and the 5th were pure in the temperament, the
<BR> octave will naturally be stretched a little less =
than an
octave <BR> whose 4th and 5th are tempered. <BR>19. =
When
expanding the outer octaves, try to reconcile the double octave
<BR> and the octave and a 5th (12th) so that the =
double
octave and the 12th <BR> beat exactly the same. (A =
very
slight beat, almost inaudible). This <BR> will =
naturally
result in octaves which vary slightly in size up and
<BR> down the keyboard. These will quite effectively =
be
"tempered <BR> octaves". <BR><BR>Bill Bremmer RPT
<BR>Madison, Wisconsin <BR>April, 2000
<BR><BR><BR></BLOCKQUOTE></FONT></FONT></BODY></HTML>