I can't argue against your reply. But I'm not purporting to be the scholar; I'm just trying to benefit from what "scholars" are publishing. When a web site or book states that a particular third in a particular temperament is supposed to be tuned at 3 beats per second, I accept that research has determined the author's published size of the interval. That is, if Werckmeister is an acknowledged temperament, scholars have come to some agreement about the size of the intervals in that temperament based on Werckmeister's own writings. But over the years I've seen different offset numbers for the same temperament, so my inclination is to go back to the calculated interval sizes to aurally confirm any set of offsets. Yes, I can go back to the original sources, build a monochord, and put on my scholar's thinking cap. But I can say with some assurance that I probably won't be doing that. I'm no scholar. I accept the scholarly work and remain open to what new research is finding. There will be disputed areas; there will be some agreement. I will approach the work with some healthy skepticism, but I'm ultimately going to accept some version of what the experts are telling me and use that as a basis to set a temperament. Perhaps what I'm saying is that given the research that's out there, and my inclination to trust my ears more than a set of numbers, I tend to favor aural descriptions of interval sizes rather than ETD numbers. Does trying to duplicate a historical temperament by using contemporary methods automatically disqualify the result? If so ETD numbers are suspect as well as using beats. The practical business of tuning a temperament comes down to what method you prefer to achieve a sound that may only truly exist in history. Richard West On Jan 30, 2009, at 9:10 PM, Fred Sturm wrote: > On Jan 30, 2009, at 12:20 PM, rwest1 at unl.edu wrote: > >> I've never tuned an unequal temperament without first >> investigating what it's supposed to sound like aurally. Going >> strictly by the numbers does not guarantee that the numbers >> actually are correct or that the technician has produced a correct >> temperament. Only by knowing, for example, that a particular >> third is supposed to be 3 beats, or no beats does a person know >> that the temperament is properly rendered. In other words, it may >> look like a duck and it may walk like a duck, but it may not sound >> like a duck. > > Well, actually the historical tuner tuning the historical > temperament didn't have access to Jorgensen's table of beat rates, > and didn't tune in accordance with beat rates. And Jorgensen based > his beat rates on the same information used to generate the cents > offsets, a calculation based on an interpretation of the historical > data. Knowing and matching the beat rates he calculated is no more > authentic than using the cents offsets. > If you really want to do an aural emulation, you need to go back > to the source. Sometimes the source is a theoretician, in which > case the information usually has to do with proportions of commas > and where they are distributed. So the calculated tuning is > probably the best emulation you can come up with, as there often > isn't a practical method for achieving the result (no series of > steps and proofs for the aural tuner. Instead, one was to match > pitch with a monochord). > If the source is one based on practical tuning instructions, the > cents and beats given by Jorgensen are his own interpretation of > what is usually a very nebulous set of instructions. Take Prelleur, > for example. Read literally, he is giving instructions for ET, > though there aren't adequate tests/proofs to do a creditable job of > it. Jorgensen comes up with a set of cents offsets and beats based > on some historical interpretation and his own notions. > All this said, in my experience a cents offset tables work just > fine to produce as good a replication as we can of the historical > tuning, based on the available evidence. > Regards, > Fred Sturm > University of New Mexico > fssturm at unm.edu > >
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