Talk:Direct approximation: Difference between revisions
Some thoughts on paraconsistent temperaments |
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: If you like, you can view the almighty master space for this idea to be the free abelian group where every single rational (possibly greater than 1/1) is treated as having its own basis vector. This group extends JI so that not only do we have the primes as basis vectors, but also have added an extra "primified" version of every rational number in this way. 2.3.5.9' is a subgroup of this, as well as anything else you could dream up, and you can always do temperament searches on the subgroups of this "beyond-JI" group. This is a group I have bumped into again and again; in addition to the above, the set of generalized patent vals on this is closely related to the zeta function, and it also may be useful with some of the subgroup temperament stuff I have been doing. I am not sure what to call this although "paraconsistent JI," "paraconsistent subgroups," etc were suggested in the past. Maybe para-JI, para-subgroup, para-interval, para-mapping, or something. [[User:Mike Battaglia|Mike Battaglia]] ([[User talk:Mike Battaglia|talk]]) 19:51, 22 December 2021 (UTC) | : If you like, you can view the almighty master space for this idea to be the free abelian group where every single rational (possibly greater than 1/1) is treated as having its own basis vector. This group extends JI so that not only do we have the primes as basis vectors, but also have added an extra "primified" version of every rational number in this way. 2.3.5.9' is a subgroup of this, as well as anything else you could dream up, and you can always do temperament searches on the subgroups of this "beyond-JI" group. This is a group I have bumped into again and again; in addition to the above, the set of generalized patent vals on this is closely related to the zeta function, and it also may be useful with some of the subgroup temperament stuff I have been doing. I am not sure what to call this although "paraconsistent JI," "paraconsistent subgroups," etc were suggested in the past. Maybe para-JI, para-subgroup, para-interval, para-mapping, or something. [[User:Mike Battaglia|Mike Battaglia]] ([[User talk:Mike Battaglia|talk]]) 19:51, 22 December 2021 (UTC) | ||
:: I hadn't heard of this 9' (9-prime) thing before. But it's really cool! And I have to say that using the ' symbol to literally prime-ify a number is a stroke of expressive genius. If there's any way you can could up a link to the old Facebook discussion that'd be fantastic. If not, no big deal, (Facebook isn't really good for that, is it), but I would just like to read more about it if I could. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 20:33, 22 December 2021 (UTC) | |||