<HTML><FONT FACE=arial,helvetica><FONT SIZE=2>In a message dated 6/7/01 6:42:25 AM Central Daylight Time,
<BR>mjbkspal@execpc.com (Mike and Jane Spalding) writes:
<BR>
<BR>
<BR><BLOCKQUOTE TYPE=CITE style="BORDER-LEFT: #0000ff 2px solid; MARGIN-LEFT: 5px; MARGIN-RIGHT: 0px; PADDING-LEFT: 5px">please try to include tests and troubleshooting, for example "if the A#-D#
<BR>4th and G#-D# 5th beat too fast, then..... ". </FONT><FONT COLOR="#000000" SIZE=3 FAMILY="SANSSERIF" FACE="Arial" LANG="0"></BLOCKQUOTE>
<BR>
<BR>These intervals are tuned pure in EBVT. They don't beat at all. To test the
<BR>purity of a 5th, find the note which would make a minor chord, drop it down
<BR>an octave. Play that note against the bottom note of the interval, then
<BR>against the top. If both intervals beat exactly the same, the 5th is pure.
<BR>
<BR>To test for a pure 4th, find the note a major 3rd below the bottom note of
<BR>the interval. Play it against the bottom note, then against the top note.
<BR>When both intervals beat exactly the same, the 4th is pure.
<BR>
<BR></FONT><FONT COLOR="#000000" SIZE=2 FAMILY="SANSSERIF" FACE="Arial" LANG="0">
<BR>I<BLOCKQUOTE TYPE=CITE style="BORDER-LEFT: #0000ff 2px solid; MARGIN-LEFT: 5px; MARGIN-RIGHT: 0px; PADDING-LEFT: 5px">n past posts, you've referred to "reverse well temperament, the most common
<BR>error made by aural tuners attempting equal temperament"? What is reverse
<BR>well? How can I watch out for, and avoid or correct it as I'm setting an
<BR>equal temperament?</BLOCKQUOTE>
<BR>
<BR>In any Well Tempered tuning, the chromatic 3rds will have a markedly uneven
<BR>pattern of beating which is in alignment with the cycle of 5ths: slow for no
<BR>or few sharps or flats, faster for 3 or 4 sharps or flats and very fast for 5
<BR>or 6. Equal Temperament is very difficult to get exactly equal if only 4ths
<BR>and 5ths are used to tune. Most people will make some kind of error and thus
<BR>produce uneven 3rds.
<BR>
<BR>The most common mistake is to make the 4ths and 5ths among the white keys too
<BR>pure which will cause the 3rds to be uneven but in *opposition* to the cycle
<BR>of 5ths. This will make virtually all music played have an out of focus,
<BR>unbalanced sound to it. I've encountered this kind of error everywhere I've
<BR>gone, north, south, east, west, at Steinway Hall, other piano stores,
<BR>schools, theaters, at the PTG Convention, everywhere.
<BR>
<BR>I'll be in Los Angeles for the weekend, returning Monday night.
<BR>Bill Bremmer RPT
<BR>Madison, Wisconsin</FONT></HTML>