In a message dated 7/14/98 4:23:21 PM Central Daylight Time, rscott@wwnet.net writes: << What is involved in creating a "cents offset from ET" program for tuning an historical temperament? This is what people want to know if they are going to tune an historical temperament by means of a visual tuning aid. But it may not always be possible to come up with such a program. >> etc. (snip) My hat is off to you on this post, colleague. You are the very first person who seems to understand what I've been saying for a long while. While I know very well that many HT tuners use the FAC/Cents Deviation Program (FAC/CDP) and have good artistic results, I have never trusted nor even tried (because of my mistrust) it. To use it, you have to assume that both sets of calculations are correct, without error (or reasonably so) and that the amount of octave stretching is appropriate for the situation. I believe that you are correct when you assume that Jorgensen's figures are for zero inharmonicity. He was more or less required to calculate them that way. (You have to start somewhere.) If however, you create an FAC (or RCT) program that deviates theoretical ET into an artistically good and musical interpretation of ET as would be appropriate for the modern piano, then deviate each of its pitches by the theoretical values that Jorgensen has computed, you will get a reasonable approximation of the desired temperament. Just as with ET, you can get a certain range of interpretations of the same idea and still consider that they all qualify as one single kind of temperament. The idea I have at present to come up with the deviations for the EB Vic is to take a good program such as the one I did for the Walter Grand and "back the FAC program out" of them. That is to say, subtract each FAC value from the actual value. The remainder would be the Cents Deviation Program (CDP). This might be done with several different tunings of different pianos and a comparison be made to see how much consistency there is. If one could get reasonably consistent results when comparing a Steinway, a Yamaha then a Kawai, for example, you might conclude that a single set of deviations would apply to any appropriate FAC program. If you get different results each time, you might conclude (as I have), that you need to think in terms of the piano being a *High*, *Medium* or *Low* inharmonicity piano and produce an appropriate CDP for each. >From what I have heard, both Reyburn and Sanderson have incorporated increased octave stretching into their program capabilities. I assume however, that the stretching would always follow a smooth curve, which would indeed be appropriate for ET. The kind of *tempered octaves* that I came to discover and use, however, vary in size from note to note. I do not think either the RCT nor the SAT can do this. I must add however, that the difference between what I do with the *Equal Beating* method, where the beats are not quantified, merely *reproduced exactly*, and the scientific, mathematically calculated method of Sanderson and Reyburn, may be aurally insignificant. The more these ideas are explored, the more questions will be raised. I hope this thread will continue and that we can really accomplish something here. The questions you raised were the very reason that I developed an Equal Beating (EB) method for a Victorian Temperament (VT). None of the VT's in the book, Tuning, are of the EB method. They all have irrational, theoretical beat specifications. The best one can do is to use the FAC/CDP. Skip Becker RPT, the host of the Temperament Festival at the Convention does the Usual Broadwood Temperament this way as a normal part of his practice. Although I have not heard one of his pianos tuned this way, I have no reason to doubt that it produces a very fine and distinct kind of character for his pianos. Our colleague on the List, Paul Bailey RPT does all of his temperaments this way, including the Meantone type which he generated on computer. His tunings are no less than superb. There is only really one thing we can all agree upon. When we manipulate the temperament and the octaves, we alter the way the music sounds when performed on the piano. We can be very precise about what we do or we can choose to accept a broad tolerance. We can choose to practice what is considered standard or we can choose to take the riskier route of innovation. It will still always be a practice of art: good, sometimes bad, but hopefully not too often mediocre. Bill Bremmer RPT Madison, Wisconsin
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