On Mar 8, 2009, at 3:22 PM, Dan Reed wrote: > Three contiguous Mj3rd can be used to balance the octave..is there a > better way aurally to set two precise markers inside the octave? I was fascinated to discover recently that this method goes all the way back to Rome in the 1640s, as the procedure used by Atanasio Kircher to produce ET (there was a small group of ET advocates in Rome at that time). This is attested by Galeazzo Sabbatini in a manuscript from around 1650, examined by Patricio Barbieri and reported in an article published in 1986. Sabbatini himself used a method involving three M3s (dividing each into its "component" four 5ths), but in order to create 1/4 comma mean tone. His M3s were GB, EbG, and EG# (which obviously don't, together, form an octave). He commented on the similarity of his method to that of Kircher in producing ET, saying that Kircher divided the octave into three equal M3s in his method (then proceeding to divide each M3 into its "component" four 5ths). It's amazing how little has changed, and how many things are constantly rediscovered. The method was again "discovered," this time in Germany, around 1750 by Marpurg and Sorge. And by Montal in the 1830s. And popularized by John Travis in the mid 20th century. And I agree, it is a good one. Regards, Fred Sturm University of New Mexico fssturm at unm.edu
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