Thanks, ric, for taking the time to read and respond! Good info on the historical "purpose".... hope you have some sucess, report back as you find out more. I'm afraid my journey has been less theoretical and more applied tuning. I started to use graphing to get a "drift" of what was going on with the temperaments, then looked for patterns. The basic bell shape curve in the circle of fifths order for the well temperaments, for example. What drove me to look into other intervals were the "surprises"... Take the Moore, with it's flat-top graph, instead of a bell shape. Even though all of the remote keys are equally wide (in cents) of pure, the Ab triad sounds the roughest. <ric wrote> > Armed with spreadsheets, graphs, available pianos I would like to see the historical evidence that historical theorists were aware of and cultivating this m3-M3 aspect. And how do you define this? I'll post two temperaments below, that I'd like to get feedback from >those of you willing/able to give them a test. These are modern rather than historical? ---rm.... <end> As far as I know, the look at the m3/M3 ratio is a new phenomenon. It involves predicting the beat rates in a temperament for various intervals. Then dividing the beat rate of the minor third by the beat rate of the major third. So in the CEG triad, divide EG by CE. And Yes, the temperaments I posted are all creations of living people. Ron Koval _________________________________________________________________ STOP MORE SPAM with the new MSN 8 and get 2 months FREE* http://join.msn.com/?page=features/junkmail
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