Talk:Direct approximation: Difference between revisions

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::: Not gonna lie, I prefer spelling out all of them – floor, ceil, and round. Maybe it's cuz I do codes more than math. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 22:13, 24 February 2022 (UTC)

:::: FWIW I like \lfloor \rfloor and \lceil \rceil for floor and ceil in maths; my only slight issue with them is that they seem to imply rectangular brackets are "round()" which doesn't feel right because there is no obvious choice for which way to round half-integers. Therefore I often lean to \operatorname{floor}() and \operatorname{ceil}() for this reason. --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 09:40, 27 May 2024 (UTC)

== Standardize "direct mapping" to "direct approximation" across wiki? ==

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: Good idea. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 07:56, 24 May 2024 (UTC)

:: I saw you did most of the work already. Thanks. I did what I think to be the remainder just now.

:: It was interesting to find a separate case on the wiki where "direct mapping" and "consistent mapping" were used as terminology, in the context of some theory about tunings of temperaments (where mapping ''does'' apply). I found it on two wiki pages. Here those two pages are, if you're curious:

::* [[The Riemann zeta function and tuning#Interpretation of results: "cosine relative error"]]

::* [[TOP tuning#TOP with "inconsistent" rational tuning extensions]]

:: I was also interested to find a couple places where the author was using the term "consistent mapping" along with "direct mapping". I changed "direct mapping" to "direct approximation", but I hesitated to change "consistent mapping" to "consistent approximation". Unlike "direct approximation", the name "consistent approximation" is not self-explanatory; in fact, I would say it's a bit confusing. From what I could understand, what was meant by "consistent mapping" (and what would be meant by "consistent approximation") was this: the sum of the direct approximations of an interval's constituent odd harmonics (such as would be used in a check for [[consistency]] of an EDO). If you like, you may feel free to push for this terminology, but if so, I think it should be bolded and defined on the consistency page. I'm not so sure about it myself; it seems a bit strained. For now, I simply unpacked the meaning in both places:

::* https://en.xen.wiki/index.php?title=4th-octave_temperaments&type=revision&diff=145002&oldid=138306

::* https://en.xen.wiki/index.php?title=1984edo&type=revision&diff=145003&oldid=144911

:: --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 01:52, 25 May 2024 (UTC)

::: I agree ''conistent mapping'' isn't quite self-explanatory. I know it means the same as ''mapping with a val'', ''val mapping'', ''RTT mapping'' or whatever that describes the opposite of direct approximation. Personally I find ''val mapping'' clear enough, but if you don't like ''val'', and replace it with ''map'', you get ''map mapping'' which is absurd. So idk. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 08:12, 26 May 2024 (UTC)

:::: FWIW I prefer "a/b is mapped to [x, y, ...]" where a/b is the interval and [x, y, ...] are the coordinates in the tempered space of the temperament. In other words, "mapped" already by default implicates a regularity to me if you don't specify that it's a "direct mapping". For example [[32/27]] is mapped to 285{{cent}} in [[80edo|80et]]. --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 09:33, 27 May 2024 (UTC)

@@ Line 153: / Line 153: @@
 ::: Not gonna lie, I prefer spelling out all of them – floor, ceil, and round. Maybe it's cuz I do codes more than math. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 22:13, 24 February 2022 (UTC)
+:::: FWIW I like \lfloor \rfloor and \lceil \rceil for floor and ceil in maths; my only slight issue with them is that they seem to imply rectangular brackets are "round()" which doesn't feel right because there is no obvious choice for which way to round half-integers. Therefore I often lean to \operatorname{floor}() and \operatorname{ceil}() for this reason. --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 09:40, 27 May 2024 (UTC)
 == Standardize "direct mapping" to "direct approximation" across wiki? ==
@@ Line 159: / Line 161: @@
 : Good idea. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 07:56, 24 May 2024 (UTC)
+:: I saw you did most of the work already. Thanks. I did what I think to be the remainder just now.
+:: It was interesting to find a separate case on the wiki where "direct mapping" and "consistent mapping" were used as terminology, in the context of some theory about tunings of temperaments (where mapping ''does'' apply). I found it on two wiki pages. Here those two pages are, if you're curious:
+::* [[The Riemann zeta function and tuning#Interpretation of results: "cosine relative error"]]
+::* [[TOP tuning#TOP with "inconsistent" rational tuning extensions]]
+:: I was also interested to find a couple places where the author was using the term "consistent mapping" along with "direct mapping". I changed "direct mapping" to "direct approximation", but I hesitated to change "consistent mapping" to "consistent approximation". Unlike "direct approximation", the name "consistent approximation" is not self-explanatory; in fact, I would say it's a bit confusing. From what I could understand, what was meant by "consistent mapping" (and what would be meant by "consistent approximation") was this: the sum of the direct approximations of an interval's constituent odd harmonics (such as would be used in a check for [[consistency]] of an EDO). If you like, you may feel free to push for this terminology, but if so, I think it should be bolded and defined on the consistency page. I'm not so sure about it myself; it seems a bit strained. For now, I simply unpacked the meaning in both places:
+::* https://en.xen.wiki/index.php?title=4th-octave_temperaments&type=revision&diff=145002&oldid=138306
+::* https://en.xen.wiki/index.php?title=1984edo&type=revision&diff=145003&oldid=144911
+:: --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 01:52, 25 May 2024 (UTC)
+::: I agree ''conistent mapping'' isn't quite self-explanatory. I know it means the same as ''mapping with a val'', ''val mapping'', ''RTT mapping'' or whatever that describes the opposite of direct approximation. Personally I find ''val mapping'' clear enough, but if you don't like ''val'', and replace it with ''map'', you get ''map mapping'' which is absurd. So idk. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 08:12, 26 May 2024 (UTC)
+:::: FWIW I prefer "a/b is mapped to [x, y, ...]" where a/b is the interval and [x, y, ...] are the coordinates in the tempered space of the temperament. In other words, "mapped" already by default implicates a regularity to me if you don't specify that it's a "direct mapping". For example [[32/27]] is mapped to 285{{cent}} in [[80edo|80et]]. --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 09:33, 27 May 2024 (UTC)