Mintaka: Difference between revisions
added CEE tuning |
added extension to 19 |
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=== Add 23/4 & 20 === | === Add 23/4 & 20 === | ||
Off the bat, given that 1331/1323 is a [[Square superparticular#Sk2_.2A_S.28k_.2B_1.29_and_S.28k_-_1.29_.2A_Sk2_.28lopsided_commas.29|lopsided comma]] with S-expression S22<sup>2</sup> * S23, one can reliably choose to temper both S22 = [[484/483]] and S23 = [[529/528]] in the 3.7.11.23/4 subgroup, which equates the 11/7 generator to [[36/23]], and the interval [[11/9]] to [[28/23]]. Furthermore, the tiny comma S161 = [[25921/25920]] can be tempered to add harmonic 20 to the subgroup, finding it 8 generators down. More neatly, this can be expressed as the temperament that tempers out the commas [[253/252]], 484/483, and [[540/539]] in the 3.7.11.20.23/4 subgroup. | Off the bat, given that 1331/1323 is a [[Square superparticular#Sk2_.2A_S.28k_.2B_1.29_and_S.28k_-_1.29_.2A_Sk2_.28lopsided_commas.29|lopsided comma]] with S-expression S22<sup>2</sup> * S23, one can reliably choose to temper both S22 = [[484/483]] and S23 = [[529/528]] in the 3.7.11.23/4 subgroup, which equates the 11/7 generator to [[36/23]], and the interval [[11/9]] to [[28/23]]. Furthermore, the tiny comma S161 = [[25921/25920]] can be tempered to add harmonic 20 to the subgroup, finding it 8 generators down. More neatly, this can be expressed as the temperament that tempers out the commas [[253/252]], 484/483, and [[540/539]] in the 3.7.11.20.23/4 subgroup. | ||
=== Add 19 === | |||
Noting that the interval [[21/19]] is fairly close to the square of [[81/77]], in tunings near 2/5-comma it is reasonable to temper out [[41553/41503]] or equivalently [[16929/16807]] to place 21/19 ten generators up, and the 19th harmonic itself 13 generators down. | |||
=== Add 13 === | === Add 13 === | ||