4000/3993: Difference between revisions

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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.

Another strategy is to take advantage of the size of S11 so as to equate it with [[144/143]] = ([[16/13]])/([[11/9]]) = S12, for those seeking to keep the undecimal and tridecimal neutral thirds distinct, thus tempering out the marveltwin comma, [[325/324]] = S10/S12, a comma with various advantages. Observing that 4000/3993 = (540/539)/(9801/9800) ~~then~~ shows a natural path, if one is willing to split the octave in half, leading to [[hades]], which extends naturally to the 17-limit by tempering out [[289/288]] = ([[17/12]])/([[24/17]]).

Another strategy is to take advantage of the size of S11 so as to equate it with [[144/143]] = ([[16/13]])/([[11/9]]) = S12, for those seeking to keep the undecimal and tridecimal neutral thirds distinct, thus tempering out the marveltwin comma, [[325/324]] = S10/S12, a comma with various advantages.

Observing that 4000/3993 = (540/539)/(9801/9800) also shows a natural path, if one is willing to split the octave in half, leading to [[hades]], which extends naturally to the 17-limit by tempering out [[289/288]] = ([[17/12]])/([[24/17]]).

There is a massive wealth of possible high-accuracy temperaments that temper out this comma, including [[311edo]].

@@ Line 16: / Line 16: @@
 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.
-Another strategy is to take advantage of the size of S11 so as to equate it with [[144/143]] = ([[16/13]])/([[11/9]]) = S12, for those seeking to keep the undecimal and tridecimal neutral thirds distinct, thus tempering out the marveltwin comma, [[325/324]] = S10/S12, a comma with various advantages. Observing that 4000/3993 = (540/539)/(9801/9800) then shows a natural path, if one is willing to split the octave in half, leading to [[hades]], which extends naturally to the 17-limit by tempering out [[289/288]] = ([[17/12]])/([[24/17]]).
+Another strategy is to take advantage of the size of S11 so as to equate it with [[144/143]] = ([[16/13]])/([[11/9]]) = S12, for those seeking to keep the undecimal and tridecimal neutral thirds distinct, thus tempering out the marveltwin comma, [[325/324]] = S10/S12, a comma with various advantages.
+Observing that 4000/3993 = (540/539)/(9801/9800) also shows a natural path, if one is willing to split the octave in half, leading to [[hades]], which extends naturally to the 17-limit by tempering out [[289/288]] = ([[17/12]])/([[24/17]]).
 There is a massive wealth of possible high-accuracy temperaments that temper out this comma, including [[311edo]].