<HTML>In a message dated 9/9/02 1:55:27 PM 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">E3           17.5 F#3         16.0 <snip> Back to me... Now, without any inflammatory language, what I see here is a misunderstanding of terms. Ed described, using the the width of Major thirds in cents, a non-standard progression, when comparing the latest published figures for the EBVT.  Bill responded, correctly, that BEATS, not cents, govern what we hear.  However, the above numbers, showing beats/second still show that by using the published numbers, the Emaj third will beat one and a half beats/second faster than the F#maj third.  These numbers still support Ed's position.</BLOCKQUOTE> I thought about this more during my last tuning of the day and tried it.  It is still unclear to me which set of "published figures" you refer to. "Bill Bremmer wrote: Ed Foote lied and tried to escalate a fight on this list as he has done many times in the past by saying: >This doesn't change the fact that the ebvt creates a more tempered E-G# of >17+cents than the F#-A# of 13.7. (snip)" Ed Foote pulled figures from two different analyses, specifically to support the lie he knew he was telling. He knows that and I'm not going to let him get away with it. If you have two contiguous 3rds of the exact same size the way they are supposed to be in ET, it is well known today that the upper 3rd will beat slightly faster than the lower on (the recently and hotly disputed 4:5 ratio of contiguous 3rds).  In my EBVT specifications, I say that you should make A3-C#4 beat exactly the same as Bb3-D4.  In ET, the higher interval would beat just very slightly faster than the lower one.   In order for them to beat the same, you would have to have the lower one be of a slightly larger interval size (which would be neither a numerical nor audible imbalance in this case because the key of A Major has 3 sharps and Bb Major has 2 flats). Therefore, in the example Ed Foote lied about, the E3-G#3 at 17.5 and the F#3-A#3 at 16 (I have *never* measured F#3-A#3 at 13.7 but have measured it as high as 19.5 and felt that was too strong and therefore corrected it), it would seem to me that those two intervals would beat exactly the same, as they usually do. If I make an error and flatten the E3 to make a sweeter C3-E3 3rd, I may well widen the E3-G#4 too much and create a slight imbalance.  This is the kind of error *any* aural tuner can and does make (favoring one interval over the other and not recognizing and/or not compensating the consequences) in ET or any other temperament. Therefore, it is conceivable, possible and probable that you could have what appears on a number list to be a slight interval size imbalance and still have Equal Beating, which is certainly permitted under Werkmeister's Rules.  Moreover, Jorgensen wrote a whole handbook of Temperaments which use Equal Beating as the way to construct the temperament. Even expert, aural ET tuners use a very few of the Equal Beating techniques.  To insure that the A4 matches pitch with the Fork, the F2-A4 test is used.  If both F2-A4 and F2-Fork beat exactly the same, the note is dead on.  Of course, this is still a matter of perception but for a skilled user of this technique, the amount of error can be kept below 1 cent.  4ths and 5ths can be proven to be tempered and *not * pure by the Equal Beating test showing not exactly the same rate of beating.  Tests for the 4:2 and 6:3 octaves also each has there own Equal Beating test. I studied the Equal Beating Temperaments because those were the ones I could be sure I was getting correct with a high degree of confidence.  I designed the EBVT along the same lines.  For the most part, the EBVT comes out about the same each time I tune it.  I have noticed some of the figures to vary somewhat when measured electronically but they are still quite predictable within a certain small range and always have been. One of the variations can be if the initial 6 beats per second is slowed down a bit.  The rest of the steps can be still followed as written and still have no imbalances but the temperament will have a stronger, more unequal sound.  Yes, I do this deliberately at times.  If I take the idea all the way to the point of being a Quasi Equal Temperament with the initial 3rds at 7 beats per second, that is the point at which some slight imbalances can occur, just as they do in the "Best Broadwood" Quasi Equal Temperament. So, there is historical precedent for temperaments which contain imbalances.  Either Ed Foote was lying about that too or he just never read about those temperaments yet.  Let's not forget the most obvious one of them all, the De Morgan Temperament which Ed deliberately chose for Chopin.  I'm sure Ed had his own theory and reasons for doing so.  Even though it was a choice many, including me, thought was very poor, it still does somehow work and most people would never even be aware of what is wrong with it.  That is how tuners get away with tuning Reverse Well every day. While Jason Kanter's Graph has some problems with it, I still like it very much and the basic idea is right.  He was able to show some of the very regular and divisible patterns of 3-6-9 in the Equal Beating Intervals found in it.  There are some corrections which need to be made but in my view, they are not that big of a deal, certainly not enough for me to withdraw it from my website.  When it is corrected, the figures will show even more regularity but not the smooth Bell curve of most other mild Well Tempered Tunings. I'll wait until I am truly satisfied with the correct electronic analyses of the EBVT before I'll ever ask Jason Kanter to rework the graph.  Until then, it stays and I make no apology or other excuse for it. It is Ed Foote who made a big deal out of what he knew were not even the figures from that chart.  Those figures are, in fact, even more imbalanced than the lie he told in his post.  To put it another way, he couldn't even tell the lie as well as it could have been told.  And so, until he admits the truth, the following moniker and signature will stay: "Sideways Well":  the pit Ed Foote dug for himself to wallow in the day he knowingly published false data for the EBVT on Pianotech. Bill Bremmer RPT Madison, Wisconsin <A HREF="http://www.billbremmer.com/">Click here: -=w w w . b i l l b r e m m e r . c o m =-</A> </HTML>