Talk:Direct approximation: Difference between revisions
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:: 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) | :: 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) | ||
::: The thing is that when you temper out multiple commas, you also temper out not only multiples of each comma, but also the sums and differences of those commas. The sums and multiples of those tempered out commas can get pretty big, and thus, the inconsistences I'm talking about are guaranteed to happen at some point no matter what you do. To me, the term "regular" in "regular temperament" is more about regularizing the approximations of prime intervals and building a consistent mapping of various other intervals based on that regularization, however, I'm under no illusion that this process always results in the best approximation of all intervals within any given EDO. Therefore, there is a valid reason for me to have used the term "nevertheless" rather than the term "therefore" in my original reply. | ::: The thing is that when you temper out multiple commas, you also temper out not only multiples of each comma, but also the sums and differences of those commas. The sums and multiples of those tempered out commas can get pretty big, and thus, the inconsistences I'm talking about with respect to JI are guaranteed to happen at some point no matter what you do. To me, the term "regular" in "regular temperament" is more about regularizing the approximations of prime intervals and building a consistent mapping of various other intervals based on that regularization, however, I'm under no illusion that this process always results in the best approximation of all intervals within any given EDO. Therefore, there is a valid reason for me to have used the term "nevertheless" rather than the term "therefore" in my original reply. | ||
::: At any rate, it seems that we are mostly on the same page regarding the need to change "patent interval" and "direct mapping" to "direct approximation". However, as for the term "patent", we need some way of designating the maps which utilize the best approximations of all prime intervals. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 14:33, 22 December 2021 (UTC) | ::: At any rate, it seems that we are mostly on the same page regarding the need to change "patent interval" and "direct mapping" to "direct approximation". However, as for the term "patent", we need some way of designating the maps which utilize the best approximations of all prime intervals. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 14:33, 22 December 2021 (UTC) | ||