Richard, I applaud your approach. I think that we are all too much affected by the almost anal precision that has become associated with Equal Temperament tuning, which is after all a strictly mathematical concept, not based on any acoustical phenomenon, but rather on the square root of twelve - which is a fictitious number that cannot be expressed by a ratio (which, after all is what forms intervals). Well temperaments do not require the same sort of mathematical precision - they are after all calculated to achieve a specific aural effect of perhaps differentiating between keys and perhaps (in the earlier ones) creating a more "leading" affect in leading tones. Scientifically and mathematically inclined persons attempt to express these tuning systems in mathematical terms, and designers and marketers of tuning devices attempt to express them in terms that work on their machines. But the bottom line is, if you know what it is supposed to sound like, and you know the technique of achieving it, then you can do it - regardless of whatever mathematical or technological terms have been devised to express it or how closely your results accord with them. Are you familiar with the brochure on how to tune various temperaments using equal-beating intervals?(I believe it's Jorgensen's..) It involves some retuning of previously tuned intervals to avoid counting beats, but the result is the affect that the given temperament is supposed to achieve. It would help to remember that published temperaments (e.g. Werkmeister, Kirnberger and such) are attempts to describe actual practices by myriads of musicians - each with their own "wrinkles" - which probably precede their publication by decades if not centuries - and are not to be confused with an authoritative prescription. They are just one person's interpretation of what many others have been doing for a long time. So the final arbiter has to be one's own ear rather than a set of numbers... Israel Stein > Message: 5 > Date: Sat, 31 Jan 2009 09:27:15 -0600 > From: "rwest1 at unl.edu" <rwest1 at unl.edu> > Subject: Re: [CAUT] Claudio Di Veroli & Equal Temperament > To: caut at ptg.org > Message-ID: <D91F0E31-9BAD-41F8-A53E-77D6A50B6AB6 at unl.edu> > Content-Type: text/plain; charset=US-ASCII; delsp=yes; format=flowed > > 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 >
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