Mintaka: Difference between revisions

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=== 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 {{nowrap|S22<sup>2</sup> {{**}} S23}}, one can reliably choose to temper both {{nowrap|S22 {{=}} [[484/483]]}} and {{nowrap|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 {{nowrap|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 {{nowrap|S22<sup>2</sup> {{times}} S23}}, one can reliably choose to temper both {{nowrap|S22 {{=}} [[484/483]]}} and {{nowrap|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 {{nowrap|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 ===

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 === 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 {{nowrap|S22<sup>2</sup> {{**}} S23}}, one can reliably choose to temper both {{nowrap|S22 {{=}} [[484/483]]}} and {{nowrap|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 {{nowrap|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 {{nowrap|S22<sup>2</sup> {{times}} S23}}, one can reliably choose to temper both {{nowrap|S22 {{=}} [[484/483]]}} and {{nowrap|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 {{nowrap|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 ===