On Apr 13, 2010, at 11:22 AM, Laurence Libin wrote: > Fred, Rameau's remarks from 1737 might or might not indicate equal > temperament as we understand it (he might have had in mind a > circulating temperament that approximates equal), Here I am going to disagree. Rameau is very clear in laying out his arguments for ET, calling it the natural tuning for the rational system of harmony he was espousing. The fifth being more basic than the third, it should be as pure as possible. His practical instructions are crude: a circle of fifths upward from C, each "un petit peu" (a very little bit) narrow, with the proof being FC at the end also being a little narrow. But there is no evidence that I know of to suggest any other alternate circulating temperament (for Rameau and for France of that period) than a flavor of modified mean tone we know today as French Ordinaire. > but a character piece like L'Enharmonique from the ca. 1728 > Nouvelles suites kind of misses its point in ET. The chords under > the fermata in bar 12 of the reprise, in the midst of the descending > bass line g-f-e-d-c#-b-b flat-a flat-g, are all about cringe, it > seems to me. No argument there. Rameau changed his mind. He wrote quite eloquently in the 1720s about unequal temperament, and its expressive qualities. Rousseau later threw those writings back in his face, saying Rameau got it right the first time, and his ET proposal lost all that expressiveness inherent in UET. But the point I was trying to make is that what is expressive in one context can be painfully "out of tune" in another. To take a more modern example, jazz musicians often bend pitch in a "blue note." Suppose we tune that note on a piano to a "blue" pitch, say B flat in the key of C. Nice and expressive in that context. Now we want to play in the key of B flat. All of a sudden, what was expressive has become unbearable. It's just the centuries old conundrum of fixed pitch. What is given in one place is taken away in another. For a style of music which is written with a tuning pattern in mind, well and good. When we try to impose that tuning pattern on another body of music, it may be very inappropriate. Some of the 20th/21st century experimentation with UETs has been aimed seemingly at a compromise that will cover all bases. My question (which I doubt can be answered definitively) concerns where the boundary lies between enhancement and detriment, between significant and insignificant. When we arrive at something like the Di Veroli "almost-equal" pattern, with offsets from ET of 0.27, 0.54, 0.81, 1.08 plus and minus, we are probably in the realm where belief trumps ears, in my practical opinion (I like it fine as a theoretical model). Partly, this opinion is based on the inevitable accumulation of error in actually tuning instruments. It is rare to tune with more refinement than unisons within a range of 0.5 cents, let alone the precision with which the pitch of any given note is placed. Fine differences disappear in the chatter of random error. But perhaps there are people with more acute hearing than I have (and with better tuning chops, capable of achieving these niceties with precision), who can tell the difference between that pattern and ET, without carefully listening to beat rates of thirds in isolation. Regards, Fred Sturm University of New Mexico fssturm at unm.edu -------------- next part -------------- An HTML attachment was scrubbed... URL: <http://ptg.org/pipermail/caut.php/attachments/20100413/f4db1483/attachment-0001.htm>
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