<HTML>In a message dated 1/14/02 10:35:17 PM Central Standard Time, From:    davidlovepianos@earthlink.net (David Love) writes: <BLOCKQUOTE TYPE=CITE style="BORDER-LEFT: #0000ff 2px solid; MARGIN-LEFT: 5px; MARGIN-RIGHT: 0px; PADDING-LEFT: 5px">Thanks Ed.  This is a terrific way to visualize it.  I am curious what Bill Bremmers EBVT looks like. David Love </BLOCKQUOTE> The graph would look similar to the Best Broadwood.  Nominally, the EBVT ranges from 7 to 18 cents just as the Broadwood does.  However, the piano's Inharmonicity does play a factor.  I first set a series of intervals to all beat at 6 per second.  It is and easy pulse to hear.  (According to Dr. H. A. Kellner, it is nothing short of *divine*). Two things can happen, however.  That rate can be just a little faster or slower and the intervals that follow will still work.  Also, Inharmonicity affects what would be the deviation from ET to make the 4 pure 4ths and 5ths which are part of the temperament. These "correction figures" are often given in whole cents.  A piano with a "poor" scale design will most definitely yield skewed results.  Even among well scaled pianos, such as a Steinway with high Inharmonicity, a Yamaha with moderate and a Kawai or M&H with low, for example, I can't imagine a single set of deviations producing the same results or even the desired results. I still encourage those who are interested in the EBVT to learn to do it aurally.  There are far more Equal Beating (EB) intervals which can be tuned than in just the F3-F4 octave.  That is the goal:  the most EB possible.  Plus, the unique Tempered Octave method I use is essentially an EB way of tuning which the smooth FAC curve will not quite match. When I look at those graphs, the most "well proportioned" one appears to be the Thomas Young.  While it is good, sound theoretical thinking, I almost never choose it because I have found many other little known ideas that simply sound more appealing.  I have heard the opinion of many fine technicians and pianists who still maintain that the Thomas Young sounds unacceptably out of tune and is thus not an option.  Others who can tolerate what it has to offer find it to be too bland and uninteresting.  That is my opinion of it. The EBVT is in fact, from a little known or used class of Temperaments called the *Modified* Meantones.  Only Jorgensen ever wrote about these.  You never see them written about in books or articles or talked about in HT lectures.  Yet, that is where I found my magic.  By its very nature, a Modified Meantone Temperament (MMT) *breaks* Werkmeister's Rules for Well Tempered Tuning.  (See my website for these rules). It has what are known as "imbalances" which mean 3rds which do not progress in beat speed according to his rules, that is, in a strict alignment with the cycle of 5ths. Yet these temperaments can produce strikingly beautiful sounds, mellow and harmonious and Equal Beating among the white keys and electrifying brilliance among the flat keys.  There are actually 5ths which are slightly wide rather than tempered narrow.  This is a flagrant violation of Werkmeister's rules but which actuall produce a very appealing sound. The EBVT however, in order to move into the mild, Victorian category, just *barely* meets Werkmeister's rules.  The intervals do beat correctly according to his rules but when they are analyzed as Interval Sizes, that is, Cents Deviation from pure or Just Intonation, a true graph of the way I tune the EBVT would show a little irregularity and slight imbalances. Therein lies the *difference* between the EBVT and all others, the Coleman 11, the Best Broadwood or any other mild design.  Long ago, I began to realize in temperament study that it was often the *irregular* temperaments which sounded best over the ones which looked or seemed to be more logically and symmetrically constructed. 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>