source file: mills2.txt Date: Mon, 14 Jul 1997 13:20:54 +0200 Subject: Historical Temperaments From: A440A@aol.com Ed Remler writes: >Prior to the publication by Mersenne of the correct frequency ratios >for ET in 1636 it would have been practically impossible to tune in ET. >Subsequent to that time it spread through continental Europe. the history >of the use of beats to tune in ET is >unknown to me, but exact rules for ET tuning are relatively unimportant. I must respectfully disagree. ET is an exact placement of the pitches, and getting there accurately enough to distinguish ones tuning from the late well-temperaments requires aural measurements that must be exact. As the temperament wars of the early 1800's raged, ( Stanhope, Farey, see Jorgensen, "Tuning" pg 295), nothing was said about these techniques. Beats were used for the many equal beating temperaments, true, but that is setting intervals directly, not using the beats caused by test notes (for the maj3rd/min3rd fifth test, or the maj3rd/sixth test for fourths). Without the use of these tests, I will defy anybody to tune an acceptable ET on a piano, and there will be darn few that can do it on a harpsichord. A clavichord has so much "bebung" variability, I would hesitate to draw any conclusions from what the players said about their tuning at all. Montal gives a set of instructions for tuning a temperament that, according to Bill Garlick, results in a very good to excellent ET. These were published in 1836, which to my knowledge is the earliest date assigned a written bearing plan that actually worked. We do see that Hipkins documented the Broadwood tuners use of non-equal temperament ca.1848 Also: > von Helmholtz (p.321 of >Dover Edition) quotes Marpurg who quotes Kirnberger, a pupil of J.S. >Bach, that he required all major Thirds to be sharpened, and this can >only mean sharpened with respect to MT which is 14 cents flatter the ET. >This is important not only to show Bach's preferences, but to indicate >how clavier tuners probably tuned in ET as a practical matter at that >time (pre 1750). Requiring that "all thirds be tuned sharp" is not saying that they are all tuned equally sharp. Sharpening a third slightly from pure lets the tuner know two things, how tempered the interval is, and on which side of pure. It makes for easier tuning, but there is considerable difficulty in getting them all the same. There is little evidence that Bach wanted all keys identical. > There is no doubt that all the great masters of the classical period >considered ET to be the ideal. There is considerable doubt. Especially among those that tune professionally. The distinctions between irregular and regular circulating temperaments must be appreciated. This is important, because the greatest keyboard works composed so far seem to have come from the period in which the tuning underwent its most rapid changes. Can any list of composers compare with those that worked between 1700 and 1850? This whole era was concerned with tonality, the plausibility of an atonal tuning being popular is (IMHO) thin. > I am also happy to stand with them in disagreeing with the remark often >made here and elsewhere that ET is some sort of a 'compromise' system of >tuning. ET is certainly not and should not be considered in the same >league as MT which is a compromise. ET was a great discovery-both >aesthetic and scientific-and without it, Western music could not have >achieved its unique glory. Hmmm. I tune equal temperaments for a living. I think I know the relationships in a 12TET backwards and forwards on at least a hundred different pianos, ( yes, the aural sizes of the thirds are different on different sizes of instruments, 9' pianos beat faster than spinets). I consider ET to be a compromise, because there is something lacking. That something is the pure interval. There is something physiologically important about being subjected to pure intervals, and the dissonance of the tempered intervals is useful in providing a context for this appreciation. With 12TET, there is no textural difference, and the context must come from without. ET is a great developement, but the unique glory of Western Music was formed before it was firmly in place. I personally see ET as more of an entropic, dead-end detour, than a realized ideal of musical perfection. As to the temperaments used by the past? In 1780, a piano performance would have been followed by a discussion on the tuning, comparing the beauty of certain keys with the resulting damage elsewhere. We need to hear the music played in more than just the ubiquitous ET of today, and then, just like the theorists of old, we need to debate how the music sounds best. Regards, Ed Foote Precision Piano Works Nashville, Tn. . Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Mon, 14 Jul 1997 14:52 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA09034; Mon, 14 Jul 1997 14:52:44 +0200 Date: Mon, 14 Jul 1997 14:52:44 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA09838 Received: (qmail 25485 invoked from network); 14 Jul 1997 12:52:03 -0000 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 14 Jul 1997 12:52:03 -0000 Message-Id: <970714084913_-1694853526@emout03.mail.aol.com> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu