On Jan 15, 2009, at 7:20 PM, A440A at aol.com wrote: > There are many instructions that, if followed, created an > orderly, > (not necessarily perfect), increase in the size of the thirds. The > Prinz, > Jean Jousse, Rousseau, several Kirnbergers, as well as Stanhope's > improvement on > the Kirnberger, (Pg. 285 in "Tuning"). This version of Stanhope's > temperament > has two pure M3, 6 M3's at 20 cents, and steps of 6 and 13 cents for > the D > and A thirds, and 7 and 14 cents for the F-A and Bb-D respectively. > This is one > of the rougher temperaments, but still follows the general order > that almost > all others have written. Perhaps I overstated my case. What I intended was to make the point that there are many temperament designs/recipes from this period that were presented with no instructions for arriving at them, and others that are difficult to achieve with accuracy. Just as one may be skeptical about whether ET was achieved (wherever you want to draw the threshold) during the 19th century, and base that skepticism on lack of adequate instructions and method, so you may be skeptical about the majority of well temperament schemes that are extant. When it come to actual tuning instructions, the predominant ones in practical handbooks are along the lines I quoted earlier: 5ths as narrow and the ear can bear, thirds as wide as the ear can bear. These methods derive directly in historical progress from 1/4 comma mean tone, where the thirds would have been just. In the historical progression, we go to 1/6 comma mean tone and the like in an effort to make the wolf less prominent and the fifths less objectionable, at the expense of the thirds (but improving the diminished 4ths). Eventually, sometimes with a "modification" or two, we arrive at a circulating temperament. It seems to me that this is likely the predominant mode among "practical musicians." While the writings of the theorists are interesting, and are indicative of the musical taste and ideas of the time (at least among the intellectuals, not necessarily among practical musicians), they can't be taken at face value as being "the way people tuned." We need to look further, at how they were presented, whether or not there was a practical means of arriving at them, whether it was accessible to someone of normal intelligence and skill. Unless we know the actual source of each tuning scheme, and the history of that source, we can't judge how likely it would be that practical musicians would make use of it, or how likely it would be that their rendering would be accurate. If Jorgensen's book is our main source, we should carefully read the text, where he usually sets out the source in some detail. And we should read it skeptically and not merely accept Jorgensen's interpretation. IOW, we need to deal with WTs as Jorgensen dealt with the question of ET in the 19th century, skeptically, not just following the recipes blindly as it is so easy to do with ETDs. At least if our aim is historical authenticity. (Valotti and Young are relatively easy to achieve, but their history argues against them). Regards, Fred Sturm University of New Mexico fssturm at unm.edu
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