Mintaka: Difference between revisions

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=== Add 4 and 5 ===

For tunings of the generator that possess a sharp 9/7 (sharper than 1/3 comma), it is reasonable to combine this temperament with [[BPS]] (as well as [[Deneb]] in the 3.5.11 subgroup), and additionally temper out [[245/243]], thereby equating [[5/3]] to 81/49 at 6 generators up. This is ''~~mintra~~'' temperament, which splits the BPS generator in three. In this range, the "canonical" extension to primes 13 and 19 makes sense, though it is worth noting that the Minalzidar extension corresponds directly to the 3.5.7.13.19 extension of BPS. With the inclusion of 20 in the subgroup above, [[4/3]] would therefore also appear, at the position of (20/9)/(5/3), 14 generators down.

For tunings of the generator that possess a sharp 9/7 (sharper than 1/3 comma), it is reasonable to combine this temperament with [[BPS]] (as well as [[Deneb]] in the 3.5.11 subgroup), and additionally temper out [[245/243]], thereby equating [[5/3]] to 81/49 at 6 generators up. This is ''Mintra'' temperament, which splits the BPS generator in three. In this range, the "canonical" extension to primes 13 and 19 makes sense, though it is worth noting that the Minalzidar extension corresponds directly to the 3.5.7.13.19 extension of BPS. With the inclusion of 20 in the subgroup above, [[4/3]] would therefore also appear, at the position of (20/9)/(5/3), 14 generators down.

If we combine all of the above, using the sharper representation of 5, 13, and 19, we find the complete 3.4.5.7.11.13.19.23 temperament with commas [[100/99]], [[133/132]], 247/245, 253/252, 484/483, and 540/539.

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 === Add 4 and 5 ===
-For tunings of the generator that possess a sharp 9/7 (sharper than 1/3 comma), it is reasonable to combine this temperament with [[BPS]] (as well as [[Deneb]] in the 3.5.11 subgroup), and additionally temper out [[245/243]], thereby equating [[5/3]] to 81/49 at 6 generators up. This is ''mintra'' temperament, which splits the BPS generator in three. In this range, the "canonical" extension to primes 13 and 19 makes sense, though it is worth noting that the Minalzidar extension corresponds directly to the 3.5.7.13.19 extension of BPS. With the inclusion of 20 in the subgroup above, [[4/3]] would therefore also appear, at the position of (20/9)/(5/3), 14 generators down.
+For tunings of the generator that possess a sharp 9/7 (sharper than 1/3 comma), it is reasonable to combine this temperament with [[BPS]] (as well as [[Deneb]] in the 3.5.11 subgroup), and additionally temper out [[245/243]], thereby equating [[5/3]] to 81/49 at 6 generators up. This is ''Mintra'' temperament, which splits the BPS generator in three. In this range, the "canonical" extension to primes 13 and 19 makes sense, though it is worth noting that the Minalzidar extension corresponds directly to the 3.5.7.13.19 extension of BPS. With the inclusion of 20 in the subgroup above, [[4/3]] would therefore also appear, at the position of (20/9)/(5/3), 14 generators down.
 If we combine all of the above, using the sharper representation of 5, 13, and 19, we find the complete 3.4.5.7.11.13.19.23 temperament with commas [[100/99]], [[133/132]], 247/245, 253/252, 484/483, and 540/539.