In a message dated 4/17/00 8:20:00 AM Central Daylight Time, remoody@midstatesd.net (Richard Moody) writes: << If we want a pure 3rd from C we simply tune E beatless to C. If however we want a beatless 3rd from C by tuning a series of four 5ths, we must diminish (temper) each of the FOUR 5ths to arrive at a pure 3rd.. This diminished amount is 1/4 of the syntonic comma and thus the name Quarter Comma Meantone. The old theorists proposed temperaments from cycles of fifths and since the syntonic comma was used to get the thirds, most of meantones were expressed as some fraction of that comma. The practice of tuning them was something else. It is rather impossible to tune four narrow fifths and come to a good pure 3rd. So you cheat and tune the pure third first. >> Thank you, this is the best explanation I have ever heard. It also tells me how, if instead of pure 3rds, you allow 3rds which are open, you get differing fractions of the comma from 1/5, 1/6, 1/7, all the way to 1/11, the equivilent oe ET where the last 5th ends up beling tempered 2 cents narrow just like all the others. There would also be other possibilities, other fractions of the comma. Bill Bremmer RPT Madison, Wisconsin
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