<HTML><FONT FACE=arial,helvetica><FONT SIZE=2>In a message dated 5/10/01 12:40:25 PM Central Daylight Time, :
<BR>tunenbww@clear.lakes.com (Paul) writes:
<BR>
<BR><BLOCKQUOTE TYPE=CITE style="BORDER-LEFT: #0000ff 2px solid; MARGIN-LEFT: 5px; MARGIN-RIGHT: 0px; PADDING-LEFT: 5px">Also, I followed Bill Bremmer's instructions for EBVT. The test piano was a
<BR>small grand I've just restrung,etc. It sounds better than the ET I had
<BR>initially tuned it to. There is a chapter meeting at my shop this week end,
<BR>and we'll scrutinize the tuning. Several of the members are accomplished
<BR>musicians. I'm anxious to hear their reactions. I must say it takes me
<BR>awhile to get the temperaments set (aural tuning only). The EBVT took me
<BR>about an hour, but the others take me about 15-20 minutes. The practice is
<BR>helping. All in all, thanks to all who have contributed and encouraged me
<BR>and others to try. It's very enjoyable!
<BR>
<BR>Paul Chick</FONT><FONT COLOR="#0f0f0f" SIZE=2 FAMILY="SANSSERIF" FACE="Arial" LANG="0"></BLOCKQUOTE>
<BR></FONT></FONT><FONT COLOR="#000000" SIZE=2 FAMILY="SANSSERIF" FACE="Arial" LANG="0">
<BR>Thanks for you comments, Paul. I am currently reworking the temperament
<BR>sequence to make it easier to understand and follow. It only takes me a few
<BR>minutes to run through but I understand that it is foreign to all others.
<BR>Recently, I wrote to Ola of Norway the following remarks. Maybe they can
<BR>help you understand what I do a little better until I get the whole thing
<BR>rewritten.
<BR>
<BR>(The new version will start with F3-A3 as the first interval to tune at 6
<BR>beats per second and will be the only estimate you have to make. All other
<BR>intervals are either pure or Equal Beating).
<BR>
<BR><<The most important steps in the EBVT are the first ones. F3-A3, 6 beats.
<BR>Now tune F3-C4 pure. Now copy the 6 beats exactly to make C4-E4 beat at 6
<BR>beats. Now make the G3-E4 6th beat a 6 beats. This will make a G3-C4
<BR>tempered 4th. If this 4th is way too fast, then sharpen G3 until it sounds a
<BR>little better but not as much as you want, then flatten C4 until the G3-C4 is
<BR>tolerable. This will make the C4-E4 3rd faster. To even out your
<BR>corrections, flatten E4 just slightly to slow the beat about 1/2 as much as
<BR>you have increased it, then copy that beat to the F3-A3 3rd by flattening F3
<BR>just a little. Check the F3-C4 5th. It should still sound "pure" to the ear
<BR>even if it ends up slightly wide or narrow.
<BR>
<BR>Doing all of the above will compensate for Inharmonicity. Now, the G3-B3 3rd
<BR>can be made by copying the rate of beating established in F3-A3, C4-E4 and
<BR>G3-E4. Now tune D4 by making it beat equally between G3 and A3. Now tune F4
<BR>a pure 4th from C4. The F3-F4 octave should sound pure. Now tune Bb3 a pure
<BR>5th from F4. The F3-Bb3 4th should sound pure. Listen to the resultant beat
<BR>of Bb3-D4. Now tune C#4 from A3 so that it beats exactly the same as the
<BR>Bb-D4 3rd. If this 3rd sounds too fast, you can compromise by flattening C#4
<BR>slightly. If the Bb3-D4 3rd has ended up too fast, sharpen the Bb3 just a
<BR>bit, which will temper the F3-Bb3 4th and the Bb3-F4 5th just slightly.
<BR>
<BR>Now tune F#3 from C#4 a pure 5th. If the resultant F#3-A#3 3rd seems way too
<BR>fast, sharpen F#3 just slightly which will make the F#3-C#4 be tempered just
<BR>slightly. Now tune G#3 from D#4 a pure 4th. If the resultant Ab3-C4 3rd
<BR>beats way too fast, then sharpen Ab3 just slightly which will cause the
<BR>Ab3-C4 to be slightly narrow. This would be OK however, since the
<BR>temperament is modeled after the Modified Meantone type, in which slightly
<BR>wide 5ths and slightly narrow 4ths will occur and are acceptable.
<BR>
<BR>Now, there is only one note left to tune, D#4, which you will make beat
<BR>equally against G#3 and A#3. This usually ends up being just slightly
<BR>tempered for both intervals. Sometimes it sounds virtually pure.
<BR>
<BR>Remember that you are trying to make intervals beat within the tolerance your
<BR>own ear has for what sounds too extreme. This is why I say that when an
<BR>interval beats "way too fast", use your musical judgment to make a compromise
<BR>but be aware of the consequences of that compromise. This means that you can
<BR>create an even milder form of the EBVT if you wish but the more you
<BR>compromise from the basic formula, the more you risk losing the Equal Beating
<BR>effects and the effects of having 4 pure 5ths within the temperament.
<BR>
<BR>I hope these comments have been helpful.>>
<BR>
<BR>
<BR>Bill Bremmer RPT
<BR>Madison, Wisconsin
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