Mintaka: Difference between revisions
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There are two reasonable ways to incorporate prime 19 into the subgroup. For tunings of the generator ''flatter'' than 9\22edt, it is the most accurate to find [[19/9]] at (9/7)^3, 9 generators up, tempering out the comma [[6561/6517]]; for tunings ''sharper'' than 9\22edt, the step 81/77 approaches or exceeds 20/19 in quality, and therefore can be identified with 20/19 by tempering out S20 = [[400/399]], equating 19/9 to 1540/729 = (77/81)(20/9), 13 generators down. The two representations meet at 22edt. | There are two reasonable ways to incorporate prime 19 into the subgroup. For tunings of the generator ''flatter'' than 9\22edt, it is the most accurate to find [[19/9]] at (9/7)^3, 9 generators up, tempering out the comma [[6561/6517]]; for tunings ''sharper'' than 9\22edt, the step 81/77 approaches or exceeds 20/19 in quality, and therefore can be identified with 20/19 by tempering out S20 = [[400/399]], equating 19/9 to 1540/729 = (77/81)(20/9), 13 generators down. The two representations meet at 22edt. | ||
If we combine all of the above, we find the complete 3.4.5.7.11.19.23 temperament with commas [[133/132]] | If we combine all of the above, we find the complete 3.4.5.7.11.19.23 temperament with commas [[100/99]], [[133/132]], 253/252, 484/483, and 540/539. | ||
== Interval chains == | == Interval chains == | ||