Talk:Direct approximation: Difference between revisions
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: The best approximations of prime intervals specifically are what establishes the patent val for an EDO. However, the best approximations of other intervals are not necessarily identical with those approximations established by the patent val. Does that make sense? It may not be obvious that this is the case, but you can begin to see what I mean when you compare the best approximation of 49/32 in 159edo with a stack of two instances of the best approximation of 7/4 in that same EDO. Nevertheless, I can see the value in using the term "direct approximation" instead of "patent interval". --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 03:08, 22 December 2021 (UTC) | : The best approximations of prime intervals specifically are what establishes the patent val for an EDO. However, the best approximations of other intervals are not necessarily identical with those approximations established by the patent val. Does that make sense? It may not be obvious that this is the case, but you can begin to see what I mean when you compare the best approximation of 49/32 in 159edo with a stack of two instances of the best approximation of 7/4 in that same EDO. Nevertheless, I can see the value in using the term "direct approximation" instead of "patent interval". --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 03:08, 22 December 2021 (UTC) | ||
:: Yes, that does make sense to me; it's precisely the reason why I objected to the term in the first place. At least, that's what I was ''trying'' to convey. I'll say it another way now, in case it helps further: I don't think this relates to the type of ''regular'' mapping that we do in RTT; the meaning of the word ''regular'' in its name is that this theory shows how to regularize these approximations so that those sorts of inconsistencies don't happen. So I'm not sure why you then use the word "nevertheless" when you say that you can see the value in making a change; it seems like you should instead use the word "therefore". But I am ''nevertheless'' (haha, see what I did there?) glad that you can see this value, one way or another. | |||
:: If you re-read my earlier comment, you should see that I actually only suggested changing "direct mapping" to "direct approximation"; I didn't suggest that you change "patent interval" to "direct approximation", as you've said. However, now that you've said it, I ''would'' support changing "patent interval" to "direct approximation" even more than I would support changing "direct mapping" to "direct approximation". Here's why: | |||
:: So I don't suppose there's anything inconsistent with your use of the word "patent" in the xenharmonic community, but I am disappointed to see that usage propagated any further, because I think it was a bad choice in the first place. The main reason is that it may mislead people into thinking that "patent vals" are the best or only maps for their EDO. | |||
:: And as for "interval", it doesn't look like you're actually using "patent interval" to refer to the ''interval itself'', but actually a ''measurement of it''. That is, you wouldn't say "10 is the patent interval of 3/2 in 17edo", right? ''10\17edo'' would be an interval, but ''10'' is just a number of steps. And a "number of steps" are the words you use to define this thing in the first sentence. So that's a reason to choose "approximation" over "interval", because 10 ''does'' make sense to call an EDO's ''approximation''. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 13:07, 22 December 2021 (UTC) | |||