Mintaka: Difference between revisions

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=== Add 13 ===

There are two reasonable ways to incorporate prime 13 into the subgroup. For tunings of the generator ''sharper'' than 9\22edt, the step 81/77 approaches or exceeds 260/243 in quality, and therefore can be identified with 260/243 by tempering out [[20020/19683]], equating 27/13 to (77/81)(20/9), 13 generators down (or alternatively, if one refuses to admit the even number 20 into the subgroup, by tempering out [[218491/216513]]); this is the extension listed as "tridecimal Mintaka". The alternative extension to include prime 13, known as ''Minalzidar'', works better for tunings ''flatter'' than 9\22edt, where it is the most accurate to find [[13/9]] at 3(9/7)<sup>-3</sup>, 9 generators up, tempering out the comma [[351/343]]. The two representations meet at 22edt.

There are two reasonable ways to incorporate prime 13 into the subgroup. For tunings of the generator ''sharper'' than 9\22edt, the step 81/77 approaches or exceeds 260/243 in quality, and therefore can be identified with 260/243 by tempering out [[20020/19683]], equating 27/13 to (77/81)(20/9), 13 generators down (or alternatively, if one refuses to admit the even number 20 into the subgroup, by tempering out [[218491/216513]]); this is the extension listed as "tridecimal Mintaka". The alternative extension to include prime 13, known as ''Minalzidar'', works better for tunings ''flatter'' than 9\22edt, where it is the most accurate to find [[13/9]] at 3(9/7)<sup>-3</sup>, 9 generators down, tempering out the comma [[351/343]]. The two representations meet at 22edt.

=== Add 5 ===

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 === Add 13 ===
-There are two reasonable ways to incorporate prime 13 into the subgroup. For tunings of the generator ''sharper'' than 9\22edt, the step 81/77 approaches or exceeds 260/243 in quality, and therefore can be identified with 260/243 by tempering out [[20020/19683]], equating 27/13 to (77/81)(20/9), 13 generators down (or alternatively, if one refuses to admit the even number 20 into the subgroup, by tempering out [[218491/216513]]); this is the extension listed as "tridecimal Mintaka". The alternative extension to include prime 13, known as ''Minalzidar'', works better for tunings ''flatter'' than 9\22edt, where it is the most accurate to find [[13/9]] at 3(9/7)<sup>-3</sup>, 9 generators up, tempering out the comma [[351/343]]. The two representations meet at 22edt.
+There are two reasonable ways to incorporate prime 13 into the subgroup. For tunings of the generator ''sharper'' than 9\22edt, the step 81/77 approaches or exceeds 260/243 in quality, and therefore can be identified with 260/243 by tempering out [[20020/19683]], equating 27/13 to (77/81)(20/9), 13 generators down (or alternatively, if one refuses to admit the even number 20 into the subgroup, by tempering out [[218491/216513]]); this is the extension listed as "tridecimal Mintaka". The alternative extension to include prime 13, known as ''Minalzidar'', works better for tunings ''flatter'' than 9\22edt, where it is the most accurate to find [[13/9]] at 3(9/7)<sup>-3</sup>, 9 generators down, tempering out the comma [[351/343]]. The two representations meet at 22edt.
 === Add 5 ===