Talk:Direct approximation: Difference between revisions
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: Thanks. I really was wondering about that, but if that's the case, then "patent interval" really is not a dispensable term because it allows you to distinguish the tempered version of interval like 49/32 obtained by ''direct mapping'' from the tempered version obtained from stacking two tempered 7/4 intervals and octave-reducing. The question is how to distinguish these two tempered versions. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 08:31, 19 January 2021 (UTC) | : Thanks. I really was wondering about that, but if that's the case, then "patent interval" really is not a dispensable term because it allows you to distinguish the tempered version of interval like 49/32 obtained by ''direct mapping'' from the tempered version obtained from stacking two tempered 7/4 intervals and octave-reducing. The question is how to distinguish these two tempered versions. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 08:31, 19 January 2021 (UTC) | ||
== Not about mapping? == | |||
I'm unclear on what the concept of "best approximation" has to do with prime mappings or vals at all, patent, best, or otherwise. It's inconsistent with ''any'' val if it is the case that best_approximation(5/4, 17edo) + best_approximation(6/5, 17edo) ≠ best_approximation(3/2, 17edo). Each individual result is the best approximation of a given interval in a given EDO, but it is not the same thing as a val-mapped interval in a given EDO, such as a patent-val-mapped interval or a best-val-mapped interval. | |||
The sentence: 'Just as the patent val itself can be referred to as the "nearest edomapping", so a patent interval can be referred to as a "direct mapping"' seems to be making a category mistake based on the "ing"-ending words being usable as both a name for a process and the end-result of that process. To make it clear, when one is referring the end result, one can instead use the ending "-ed interval". e.g. "patent-val-mapped interval", as I've done above. | |||
I believe what the author may be trying to do in this sentence is to contrast the patent-val-mapped interval with the "directly-mapped interval". But this might suggest the existence of a "direct val". So I suggest referring to it as the "direct approximation", since this implies that it does not go via the intermediary of any prime mapping or val. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 22:35, 28 June 2021 (UTC) | |||