80edo: Difference between revisions

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Though a strange tuning* in lower prime limits, 80edo offers a very unique composite structure that can aid with familiarization/conceptualization by way of its subset edos of (2, 4, 5,) 8, 10, 16 and 20. Initially this doesn't seem very useful unless one is interested in learning those edos, but 80edo supports a plethora of multiperiod temperaments with accurate JI interval interpretations based on these edos; to see a fairly comprehensive list of these temperaments and of their most accurate JI interpretations w.r.t. (integer multiples of) their period, see [[#Consistent circles|the section on consistent circles]]. These represent a large number of practically completely unexplored and novel high-limit temperaments with varying musical potential.

<nowiki>*</nowiki> The strangeness of its tuning can largely be explained by the addition of vals [[80edo]] = [[53edo]] + [[27edo]], where [[27edo]] exaggerates the idiosyncratic mapping of the 2.3.5.7.13 subgroup, as while 53edo tempers {[[625/624|S25]], [[676/675|S26]], [[729/728|S27]]} (supporting [[catakleismic]]), 27edo tempers {[[325/324|S25*S26]], [[351/350|S26*S27]]} [[Square superparticular|implying]] {[[4375/4374|S25/S27]], [[169/168|S13]]} but maps S25~S27 positively and S26 negatively. This is not insignificant, because this plays a special role (as we'll see in the next section on subsets).

<nowiki>*</nowiki> The strangeness of its tuning can largely be explained by the addition of vals [[80edo]] = [[53edo]] + [[27edo]], where [[27edo]] exaggerates the idiosyncratic mapping of the 2.3.5.7.13 subgroup, as while 53edo tempers {[[625/624|S25]], [[676/675|S26]], [[729/728|S27]]} (supporting [[catakleismic]]) and {[[1728/1715|S6/S7]], [[5120/5103|S8/S9]]} (supporting [[buzzard]]), 27edo tempers {[[1728/1715|S6/S7]], [[64/63|S8]], [[325/324|S25*S26]], [[351/350|S26*S27]]} [[Square superparticular|implying]] {[[4375/4374|S25/S27]], [[169/168|S13]]} but maps S25~S27 positively and S26 negatively, which 80et thus inherits though with less damage. This is not insignificant, because this plays a special role (as we'll see in the next section on subsets).

==== Based on subsets ====

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 Though a strange tuning* in lower prime limits, 80edo offers a very unique composite structure that can aid with familiarization/conceptualization by way of its subset edos of (2, 4, 5,) 8, 10, 16 and 20. Initially this doesn't seem very useful unless one is interested in learning those edos, but 80edo supports a plethora of multiperiod temperaments with accurate JI interval interpretations based on these edos; to see a fairly comprehensive list of these temperaments and of their most accurate JI interpretations w.r.t. (integer multiples of) their period, see [[#Consistent circles|the section on consistent circles]]. These represent a large number of practically completely unexplored and novel high-limit temperaments with varying musical potential.
-<nowiki>*</nowiki> The strangeness of its tuning can largely be explained by the addition of vals [[80edo]] = [[53edo]] + [[27edo]], where [[27edo]] exaggerates the idiosyncratic mapping of the 2.3.5.7.13 subgroup, as while 53edo tempers {[[625/624|S25]], [[676/675|S26]], [[729/728|S27]]} (supporting [[catakleismic]]), 27edo tempers {[[325/324|S25*S26]], [[351/350|S26*S27]]} [[Square superparticular|implying]] {[[4375/4374|S25/S27]], [[169/168|S13]]} but maps S25~S27 positively and S26 negatively. This is not insignificant, because this plays a special role (as we'll see in the next section on subsets).
+<nowiki>*</nowiki> The strangeness of its tuning can largely be explained by the addition of vals [[80edo]] = [[53edo]] + [[27edo]], where [[27edo]] exaggerates the idiosyncratic mapping of the 2.3.5.7.13 subgroup, as while 53edo tempers {[[625/624|S25]], [[676/675|S26]], [[729/728|S27]]} (supporting [[catakleismic]]) and {[[1728/1715|S6/S7]], [[5120/5103|S8/S9]]} (supporting [[buzzard]]), 27edo tempers {[[1728/1715|S6/S7]], [[64/63|S8]], [[325/324|S25*S26]], [[351/350|S26*S27]]} [[Square superparticular|implying]] {[[4375/4374|S25/S27]], [[169/168|S13]]} but maps S25~S27 positively and S26 negatively, which 80et thus inherits though with less damage. This is not insignificant, because this plays a special role (as we'll see in the next section on subsets).
 ==== Based on subsets ====