<HTML>List, Ron Koval caught the following error in what I wrote yesterday.  I thank him for his attention and interest.  Unfortunately a simple error like this is easy to make when writing and it can cause lots of confusion. Thanks, Ron. Bill Bremmer RPT Madison, Wisconsin In a message dated 5/11/01 8:34:52 AM Central Daylight Time, drwoodwind@hotmail.com writes: <BLOCKQUOTE TYPE=CITE style="BORDER-LEFT: #0000ff 2px solid; MARGIN-LEFT: 5px; MARGIN-RIGHT: 0px; PADDING-LEFT: 5px">Hi Bill, Thanks for working on this and posting the recipe.  I was zooming through it and I think there is a typo.  When you get to the point of tuning G#3, I think you meant to reference C#4, instead of D#4. (see below) good work Ron Koval (graphman) Date: Thu, 10 May 2001 13:54:56 EDT From: Billbrpt@AOL.COM Subject: Re: HT <<The most important steps in the EBVT are the first ones.  F3-A3, 6 beats. Now tune F3-C4 pure.  Now copy the 6 beats exactly to make C4-E4 beat at 6 beats.  Now make the G3-E4 6th beat a 6 beats.  This will make a G3-C4 tempered 4th.  If this 4th is way too fast, then sharpen G3 until it sounds a little better but not as much as you want, then flatten C4 until the G3-C4 is tolerable.  This will make the C4-E4 3rd faster.  To even out your corrections, flatten E4 just slightly to slow the beat about 1/2 as much as you have increased it, then copy that beat to the F3-A3 3rd by flattening F3 just a little.  Check the F3-C4 5th. It should still sound "pure" to the ear even if it ends up slightly wide or narrow. Doing all of the above will compensate for Inharmonicity.  Now, the G3-B3 3rd can be made by copying the rate of beating established in F3-A3, C4-E4 and G3-E4.  Now tune D4 by making it beat equally between G3 and A3.  Now tune F4 a pure 4th from C4.  The F3-F4 octave should sound pure.  Now tune Bb3 a pure 5th from F4.  The F3-Bb3 4th should sound pure.  Listen to the resultant beat of Bb3-D4.  Now tune C#4 from A3 so that it beats exactly the same as the Bb-D4 3rd.  If this 3rd sounds too fast, you can compromise by flattening C#4 slightly.  If the Bb3-D4 3rd has ended up too fast, sharpen the Bb3 just a bit, which will temper the F3-Bb3 4th and the Bb3-F4 5th just slightly. Now tune F#3 from C#4 a pure 5th.  If the resultant F#3-A#3 3rd seems way too fast, sharpen F#3 just slightly which will make the F#3-C#4 be tempered just <check this following part> slightly. ***Now tune G#3 from D#4 a pure 4th.***</BLOCKQUOTE> ***This should have read:  Now tune G#3 from C#4 a pure 4th.*** <BLOCKQUOTE TYPE=CITE style="BORDER-LEFT: #0000ff 2px solid; MARGIN-LEFT: 5px; MARGIN-RIGHT: 0px; PADDING-LEFT: 5px"> If the resultant Ab3-C4 3rd beats way too fast, then sharpen Ab3 just slightly which will cause the Ab3-C4 to be slightly narrow.  This would be OK however, since the temperament is modeled after the Modified Meantone type, in which slightly wide 5ths and slightly narrow 4ths will occur and are acceptable. Now, there is only one note left to tune, D#4, which you will make beat equally against G#3 and A#3.  This usually ends up being just slightly tempered for both intervals.  Sometimes it sounds virtually pure. Remember that you are trying to make intervals beat within the tolerance your own ear has for what sounds too extreme.  This is why I say that when an interval beats "way too fast", use your musical judgment to make a compromise but be aware of the consequences of that compromise.  This means that you can create an even milder form of the EBVT if you wish but the more you compromise from the basic formula, the more you risk losing the Equal Beating effects and the effects of having 4 pure 5ths within the temperament. I hope these comments have been helpful.>> Bill Bremmer RPT Madison, Wisconsin</BLOCKQUOTE> </HTML>