Squares: Difference between revisions

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However, since the fifth in skwares is tuned flat, it is very natural to combine the temperament with [[meantone]] to create full [[11-limit]] '''squares''', which additionally can be restricted to the [[7-limit]] as the temperament with comma basis [[81/80]] and [[2401/2400]]. The 11-limit temperament is considered below.

There is also a natural extension adding prime 23~~, done~~ by equating the generator to [[23/18]], and so finding 23 itself seven generators down, tempering out [[161/160]].

There is also a natural extension adding prime 23 by equating the generator to [[23/18]], and so finding 23 itself seven generators down, tempering out [[161/160]].

As for prime 13, the way to map it is less clear. The canonical squares mapping tempers out [[144/143]] in order to equate the tridecimal neutral sixth, [[13/8]], with 18/11, finding 13 two generators up, while '''agora''' tempers out [[105/104]] to equate [[8/7]] with [[15/13]], finding the 13th harmonic 29 generators down. These two mappings are enharmonically equivalent in [[31edo]]. Finally, '''squad''' tempers out [[351/343]] (which is the same as 3.7.11.13 [[Mintaka#Extensions of Mintaka|Minalzidar]]'s tempering of that prime) so that 13 is equated with (7/3)<sup>3</sup>, and found 15 generators down.

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 However, since the fifth in skwares is tuned flat, it is very natural to combine the temperament with [[meantone]] to create full [[11-limit]] '''squares''', which additionally can be restricted to the [[7-limit]] as the temperament with comma basis [[81/80]] and [[2401/2400]]. The 11-limit temperament is considered below.
-There is also a natural extension adding prime 23, done by equating the generator to [[23/18]], and so finding 23 itself seven generators down, tempering out [[161/160]].
+There is also a natural extension adding prime 23 by equating the generator to [[23/18]], and so finding 23 itself seven generators down, tempering out [[161/160]].
 As for prime 13, the way to map it is less clear. The canonical squares mapping tempers out [[144/143]] in order to equate the tridecimal neutral sixth, [[13/8]], with 18/11, finding 13 two generators up, while '''agora''' tempers out [[105/104]] to equate [[8/7]] with [[15/13]], finding the 13th harmonic 29 generators down. These two mappings are enharmonically equivalent in [[31edo]]. Finally, '''squad''' tempers out [[351/343]] (which is the same as 3.7.11.13 [[Mintaka#Extensions of Mintaka|Minalzidar]]'s tempering of that prime) so that 13 is equated with (7/3)<sup>3</sup>, and found 15 generators down.