Fred writes: << Where I lose Lehman is in his second article, with all the "proof" having to do with things like size of EG# M3 and the like. I have my doubts that there was ever that degree of hyper-sensitivity to minute shadings on the part of composers. Not impossible, but unlikely IMO. I think the general shape is what mattered, when it mattered (which certainly isn't all the time). >> I agree. It is very plausible that musicians were using Werckmiester's general instruction to stagger the sizes of the tonic thirds from the key of C around the circle. This is the near universal form of tuning that Jorgensen documents through many, many theorists and writers from 1681 through 1885. There is a finite amount of tempering that must be spread among the 12 keys, and how it was historically done was near constant. The main differences in temperaments is how gradual the changes were, and how extreme the range. By range, I mean the distance between the tempering of C-E and the tempering of F#-A#. If you want a pure C-E, you are going to have to put a lot of tempering somewhere else, usually in the thirds of B, C# and F#. The Kirnberger tunings have a Just C-E, and three 21 cent thirds to accomodate the left-over dissonance. If you compromise C-E by 5 cents, you can soften up the higher keys a great deal. Or, as Young does, temper C-E by about 6 cents and have only one third that carries a full syntonic comma (F#-A#). Any musician that was tempering their own keyboard might very well have allowed any key higher than they would use to absorb a lot more tempering, the modified meantones show how far this could be taken. It would even be plausible that many keyboardists would tune only what they needed for a given performance, doing the extra work to spread the comma farther only when they had to modulate farther. Today? The 21st century ears are tender, indeed. If hit with a lot of 21 cent thirds, many modern musicians recoil. This is not only due to the width of the third, but the manner of playing them! Enid Katahn has clearly demonstrated that music in very remote keys can be played harshly or expressively. The quality of the sound is not totally a function of how tempered the intervals are, but rather, how well the performer can use the greatly expanded resources. Regards, Ed Foote RPT http://www.uk-piano.org/edfoote/index.html www.uk-piano.org/edfoote/well_tempered_piano.html <BR><BR><BR>**************<BR>Create a Home Theater Like the Pros. Watch the video on AOL Home.<BR> (http://home.aol.com/diy/home-improvement-eric-stromer?video=15?ncid=aolhom00030000000001)</HTML>
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