Talk:Direct approximation
Applicability
I wished to express that the concept of "patent interval" is not only useful for just intervals which can be represented by rational numbers, but any given real value treated as an interval an be approximated this way. The overall intention of the article was to link "patent fifth" to something more practical than the more abstract patent val. But maybe this wasn't such a great idea... --Xenwolf (talk) 09:11, 18 January 2021 (UTC)
- I would say the page is still useful.
- (And you can in principle make a patent val for any set of intervals, say {3/2, 236 cents, φ}, not necessarily just intervals like {2/1, 3/1, 5/1}. Just remember what interval corresponds to which entry. The notation used on the wiki is p-limit-centric though; we could talk about extending the notation for JI subgroups.) Inthar (talk) 10:00, 18 January 2021 (UTC)
Plea for direct mapping
The patent val notation (like val notation in general) contains approximations of prime intervals. That these can be combined additively will be understood by readers who are familiar with primes and fractions. But the implicit consistency of this method can lead to confusion (and also the impression of inconsistency), see for example the divergence between direct and consistent mappings of 7/5 in 23edo:
7/5 == 11,16…\23 ~ 11\23
vs.
(7/4)/(5/4) ~ (19\23)-(7\23) == 12\23
Personally, I'm not really convinced by the concept of consistency which builds on the concept of odd limit. Since consistent mapping is so present in the wiki, would it be too confusing if the term "patent interval" implied direct mapping? --Xenwolf (talk) 11:57, 18 January 2021 (UTC)
- I certainly don't mind the idea of "direct mapping", I mean my concept from earlier- which I have since renamed "telicity"- hinges on "direct" and "consistent" mappings of intervals in a given prime chain being identical up until the prime chain itself connects with an interval of a lower p-limit prime chain on account of the chain not exceeding 50% relative error. --Aura (talk) 14:41, 18 January 2021 (UTC)