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== Temperaments ==

[[Tempering out]] this comma means the fourth is divided into an equal stepped tetrachord, the step of which is a ''trienfourth'' (from 1/3 of a fourth) or ''submajor second'' and because it is an [[ultraparticular]] it makes 12/11 and 10/9 equidistant from 11/10.

[[Tempering out]] this comma means the fourth is divided into an equal stepped tetrachord, the step of which is a ''trienfourth'' (from 1/3 of a fourth) or ''submajor second'' and because it is an [[ultraparticular]] it makes [[12/11]] and [[10/9]] equidistant from 11/10.

On the low-accuracy end, this may be reminiscent of how the [[250/243|porcupine comma]] splits 4/3 into three [[10/9]]'s instead ~~and it is for these reasons that~~ 2.3.5.11 [[Porcupine family #2.3.5.11 subgroup (porkypine)|porcupine]] equates 11/10 ~~with the [[superparticular]]s adjacent to it of~~ 12/11 ~~and 10/9, tempering out S10 and S11 as the porcupine comma is S10<sup>2</sup> × S11~~ so ~~through the extension to~~ the 11~~-limit we make~~ [[porcupine]] as efficient and elegant as it can reasonably be.

On the low-accuracy end, this may be reminiscent of how the [[250/243|porcupine comma]] splits 4/3 into three 10/9's instead. In fact, 2.3.5.11 [[Porcupine family #2.3.5.11 subgroup (porkypine)|porcupine]] equates 10/9 with 11/10 and 12/11 so that the equally-split fourth represents 9:10:11:12, making [[porcupine]] as efficient and elegant as it can reasonably be. (As a [[rank-3]] detemperament of porcupine, one way to extend it to include prime 7 is by tempering [[385/384]], which [[Porcupine family #Septimal porcupine|septimal porcupine]] also tempers.)

Tempering it out along with the [[schisma]] results in the rank-2 [[tertiaschis]] temperament. Tempering it out with the trimitone comma S9/S10 = [[8019/8000]] (so that three [[10/9]]'s are also an [[11/8]]) implies also tempering out the [[semiparticular]] [[243/242]] = ([[3/2]])/([[11/9]])<sup>2</sup> = S9/S11 leading to [[Gravity family #Larry|larry]] in the [[gravity family]]. Tempering it out with both the [[schisma]] and [[trimitone comma]] gives a description of [[65edo]] in the no-7's [[11-limit]], making it an excellent way to extend schismic to include prime 11.

@@ Line 10: / Line 10: @@
 == Temperaments ==
-[[Tempering out]] this comma means the fourth is divided into an equal stepped tetrachord, the step of which is a ''trienfourth'' (from 1/3 of a fourth) or ''submajor second'' and because it is an [[ultraparticular]] it makes 12/11 and 10/9 equidistant from 11/10.
+[[Tempering out]] this comma means the fourth is divided into an equal stepped tetrachord, the step of which is a ''trienfourth'' (from 1/3 of a fourth) or ''submajor second'' and because it is an [[ultraparticular]] it makes [[12/11]] and [[10/9]] equidistant from 11/10.
-On the low-accuracy end, this may be reminiscent of how the [[250/243|porcupine comma]] splits 4/3 into three [[10/9]]'s instead and it is for these reasons that 2.3.5.11 [[Porcupine family #2.3.5.11 subgroup (porkypine)|porcupine]] equates 11/10 with the [[superparticular]]s adjacent to it of 12/11 and 10/9, tempering out S10 and S11 as the porcupine comma is S10<sup>2</sup> × S11 so through the extension to the 11-limit we make [[porcupine]] as efficient and elegant as it can reasonably be.
+On the low-accuracy end, this may be reminiscent of how the [[250/243|porcupine comma]] splits 4/3 into three 10/9's instead. In fact, 2.3.5.11 [[Porcupine family #2.3.5.11 subgroup (porkypine)|porcupine]] equates 10/9 with 11/10 and 12/11 so that the equally-split fourth represents 9:10:11:12, making [[porcupine]] as efficient and elegant as it can reasonably be. (As a [[rank-3]] detemperament of porcupine, one way to extend it to include prime 7 is by tempering [[385/384]], which [[Porcupine family #Septimal porcupine|septimal porcupine]] also tempers.)
 Tempering it out along with the [[schisma]] results in the rank-2 [[tertiaschis]] temperament. Tempering it out with the trimitone comma S9/S10 = [[8019/8000]] (so that three [[10/9]]'s are also an [[11/8]]) implies also tempering out the [[semiparticular]] [[243/242]] = ([[3/2]])/([[11/9]])<sup>2</sup> = S9/S11 leading to [[Gravity family #Larry|larry]] in the [[gravity family]]. Tempering it out with both the [[schisma]] and [[trimitone comma]] gives a description of [[65edo]] in the no-7's [[11-limit]], making it an excellent way to extend schismic to include prime 11.