Langwidge: Difference between revisions

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In this case, the temperament's generator is a slightly flat fifth, 9 of which yield [[38/1]], meaning that when octave-reduced, this would require spelling root-3rd-P5 triad with 19:16 as C-D#-E and not as C-Eb-E, producing this peculiar violation of standard Western music theory.

Since [[355edo]] and [[722edo]] are good at supporting this kind of mapping, and they're also good at approximating [[17/16]], this makes 355 & 722 2.7.19 subgroup the most natural and simplest way to tune this temperament, producing a rank-2 temperament associated with the {{monzo|-109 0 0 0 0 0 9 17}} comma. This means that the generator fifth in question is mapped to [[6137/4096]], and nine of them make [[38/1]], meaning [[19/16]] is mapped to C-D#. The generator fifth is flat of pure [[3/2]] by [[6144/6137]].

Since [[355edo]] and [[722edo]] are good at supporting this kind of mapping, and they're also good at approximating [[17/16]], this makes 355 & 722 2.7.19 subgroup the most natural and simplest way to tune this temperament, producing a rank-2 temperament associated with the {{monzo|-109 0 0 0 0 0 9 17}} comma. This means that the generator fifth in question is mapped to [[6137/4096]], and nine of them make [[38/1]], meaning [[19/16]] is mapped to C-D#. For the purest 19th harmonic, 722edo is the best due to it being a convergent to log2(19/16). The generator fifth is flat of pure [[3/2]] by [[6144/6137]].

In the 17-limit, 17th harmonic is reached, coincidentally, 17 generators down, meaning [[17/16]] is mapped to C-Ebbb.

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 In this case, the temperament's generator is a slightly flat fifth, 9 of which yield [[38/1]], meaning that when octave-reduced, this would require spelling root-3rd-P5 triad with 19:16 as C-D#-E and not as C-Eb-E, producing this peculiar violation of standard Western music theory.
-Since [[355edo]] and [[722edo]] are good at supporting this kind of mapping, and they're also good at approximating [[17/16]], this makes 355 & 722 2.7.19 subgroup the most natural and simplest way to tune this temperament, producing a rank-2 temperament associated with the {{monzo|-109 0 0 0 0 0 9 17}} comma. This means that the generator fifth in question is mapped to [[6137/4096]], and nine of them make [[38/1]], meaning [[19/16]] is mapped to C-D#. The generator fifth is flat of pure [[3/2]] by [[6144/6137]].
+Since [[355edo]] and [[722edo]] are good at supporting this kind of mapping, and they're also good at approximating [[17/16]], this makes 355 & 722 2.7.19 subgroup the most natural and simplest way to tune this temperament, producing a rank-2 temperament associated with the {{monzo|-109 0 0 0 0 0 9 17}} comma. This means that the generator fifth in question is mapped to [[6137/4096]], and nine of them make [[38/1]], meaning [[19/16]] is mapped to C-D#. For the purest 19th harmonic, 722edo is the best due to it being a convergent to log2(19/16). The generator fifth is flat of pure [[3/2]] by [[6144/6137]].
 In the 17-limit, 17th harmonic is reached, coincidentally, 17 generators down, meaning [[17/16]] is mapped to C-Ebbb.