(Sorry about the "mis-fire" of this post before.) pianoman wrote: >Dear list, >With the process of doing the perfect fifths tunings on the SAT, questions. > >1. Are the perfect fifths used only as a way to stretch the octaves further >or is it just as important that the fifths be perfect as well as the >octaves stretched further. Wide tunings are desirable for a number of reasons, including the fact that melody notes of octave 6 and thereabouts just sound so wonderfully "in-tune" for whatever reason when the tunings are wide. >2. In using the RCT, since there is a choice of 10 different octave >stretch choices, is there on of them that comes closest to the perfect >fifth results of the SAT? No. This will vary from piano to piano. Pianos vary in both general level of inharmonicity and in the inharmonicity curves throughout the scales. If piano tuners put a more-or-less uniform amount of stretch in the A3-A4 octave, say 1/3 beat per second at the 4:2, then the width of the fifths in pianos will vary. This means that Jim Coleman's suggestion of adding an extra 1.5 cents to the reading for the A in FAC will have a different effect on different pianos. Caution is in order. That same extra 1.5 cents will be conservative on some pianos and extreme on others. Kent Swafford I posted the following to some of the RCT users on September 1. The other RCT users seemed to agree. I have experimented with some wider tunings during the time that these tunings have been under discussion on the lists. My conclusion is that there are very good reasons for the standard practices that we employ. A pure fifths temperament may be an "extreme" tuning unsuitable for everyday use. On pianos that are in use by a given pianist day in and day out, I think those wide octaves and fast fourths are going to become excruciating. And if, as happened on a B that I tuned wide, the tenor drops, the octaves will simply be over-the-line and unacceptable. 12-tone equal temperament has a built-in safety factor that you will surely lose with wide tunings. Now, having said that, I do think that there is a place for some wide tunings on concert instruments that will have little opportunity for drift between tuning and concert. A tuning done up somewhat differently from an artist's everyday piano might be just the thing to inspire the pianist into a transcendent performance. Now, wide tunings and calculating them: As I have said, a pure fifths equal temperament is an extreme temperament. Instead of being a tuning based on the 12th root of 2 as is 12-tone to the octave equal temperament, 7-tone to the pure perfect fifth equal temperament would be based on the 7th root of 1.5. The difference between the two is not minor; pure fifths equal temperament is a _different_ tuning and and we should not necessarily expect our VTD's to calculate them. Based on looking at the 3:2 5ths that Ch2 calculates directly, and assuming that Ch2 is calculating high quality equal temperament, and seeing that the fifths are often still 2 cents contracted at the same time the octave is expanded 2/3 cents at the 4:2, I am extremely skeptical that an FAC tuning with an extra cent in the A number will result in pure fifths, although they may _sound_ aurally mostly pure. Theoretically, it would take well over 3 cents expansion in the octave to result in pure 5ths. In other words I think Jim Coleman, Sr. isn't _really_ tuning pure 5th equal temperament, but more like 1 cent contracted 5ths equal temperament, which I have found to be plenty extreme in itself, at least on some pianos. You know, since Jim Coleman, Sr. has been talking about all this, some things have been made clear: There is a clear discrepancy between one thing tuners _believe_ and what appears to be the _reality_ of piano beat rates. Dr. Sanderson always said that pianos are scaled so that their beat rates can resemble those of the mathematical model. Tuners often repeat that piano 5ths are tuned at 1 cent contracted instead of 2 as a part of normal stretching. Based on what I have seen in Ch2 and my experiences trying out some wide tunings that I found to be way too extreme, I would say Dr. Sanderson was absolutely right -- we tune pianos with 2 cent contracted 5ths, and the oft-repeated tale of 1 cent fifths is, mostly, a simple myth. Kent
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