source file: m1362.txt Date: Sun, 22 Mar 1998 20:26:24 -0800 (PST) Subject: Meantone and Well-Temperaments From: John Chalmers A couple of comments re Meantone and "Well-Temperament": Because the chromatic and diatonic semitones are of different sizes, different meantone keys should sound subtlely different even if their principal triads are tuned the same when one plays all 12 tones. This should be true to a greater or lesser extent for all varieties of meantone short of 12-tet itself. Perhaps these melodic differences were part of the alleged "affections." The late Peter Yates, building on the work of Wesley Kuhnle, described well-temperaments as irregular systems. According to his rather vague descriptions, one started with 1/4-comma meantone and adjusted the fifths until one could play in all keys. Thus one would obtain a type of circulating temperament with a variety of 5th and thirds. J.M. Barbour took this idea to its rational conclusion with his "Tuning by Regularly Varied Fifths," where one started by tuning the fifth D-A to about 697 cents and increased the size as one went around the circle in both directions with the widest fifth, Ab-Eb having 703 cents. The thirds ranged from 392 cents to 408. Barbour posited a linear increment of 0.16666.. cents, but one could experiment with other increments, wider ranges, non-linear steps, etc. My recollection is that when this topic came up on the list a couple of years ago, the consensus of people who had tried it was that it is too subtle an effect to be worth the trouble of tuning it accurately and that meantone or one of the less extreme historical temperaments is adequate for performing Baroque music. I might add that Augusto Novaro claimed the several of his mildly stretched and shrunk 12-tone tempered octave tunings were were perceptibly different and worth trying. --John