Talk:Direct approximation - Revision history

Godtone: /* Rounding function symbol */

2024-05-27T09:40:49Z

Rounding function symbol

← Older revision		Revision as of 09:40, 27 May 2024
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)		::: 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? ==		== Standardize "direct mapping" to "direct approximation" across wiki? ==

Godtone: /* Standardize "direct mapping" to "direct approximation" across wiki? */

2024-05-27T09:33:49Z

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

← Older revision		Revision as of 09:33, 27 May 2024
Line 173:		Line 173:

	::: 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)		::: 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)

FloraC: /* Standardize "direct mapping" to "direct approximation" across wiki? */ re

2024-05-26T08:12:21Z

Standardize "direct mapping" to "direct approximation" across wiki?: re

← Older revision		Revision as of 08:12, 26 May 2024
Line 163:		Line 163:

	:: 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:		:: 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"]]		::* [[The Riemann zeta function and tuning#Interpretation of results: "cosine relative error"]]
	::: * [[TOP tuning#TOP with "inconsistent" rational tuning extensions]]		::* [[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:		:: 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=4th-octave_temperaments&type=revision&diff=145002&oldid=138306
	::: * https://en.xen.wiki/index.php?title=1984edo&type=revision&diff=145003&oldid=144911		::* 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)		:: --[[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)

Cmloegcmluin: /* Standardize "direct mapping" to "direct approximation" across wiki? */

2024-05-25T01:52:06Z

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

← Older revision		Revision as of 01:52, 25 May 2024
Line 159:		Line 159:

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

FloraC: /* Standardize "direct mapping" to "direct approximation" across wiki? */ re

2024-05-24T07:56:01Z

Standardize "direct mapping" to "direct approximation" across wiki?: re

← Older revision		Revision as of 07:56, 24 May 2024
Line 157:		Line 157:

	I noticed Flora correcting one copy of "direct mapping" to "direct approximation" today, and it piqued my curiosity, so I searched the wiki for occurrences of "direct mapping". There's a bunch! I suggest, per the reasons covered in discussion topics on this page which led to the reworking of this page from "direct mapping" to "direct approximation", that we should change these all to "direct appoximation". --[[User:Cmloegcmluin\|Cmloegcmluin]] ([[User talk:Cmloegcmluin\|talk]]) 16:51, 23 May 2024 (UTC)		I noticed Flora correcting one copy of "direct mapping" to "direct approximation" today, and it piqued my curiosity, so I searched the wiki for occurrences of "direct mapping". There's a bunch! I suggest, per the reasons covered in discussion topics on this page which led to the reworking of this page from "direct mapping" to "direct approximation", that we should change these all to "direct appoximation". --[[User:Cmloegcmluin\|Cmloegcmluin]] ([[User talk:Cmloegcmluin\|talk]]) 16:51, 23 May 2024 (UTC)

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

Cmloegcmluin: /* Standardize "direct mapping" to "direct approximation" across wiki? */ new section

2024-05-23T16:51:33Z

Standardize "direct mapping" to "direct approximation" across wiki?: new section

← Older revision		Revision as of 16:51, 23 May 2024
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)		::: 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)

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

			I noticed Flora correcting one copy of "direct mapping" to "direct approximation" today, and it piqued my curiosity, so I searched the wiki for occurrences of "direct mapping". There's a bunch! I suggest, per the reasons covered in discussion topics on this page which led to the reworking of this page from "direct mapping" to "direct approximation", that we should change these all to "direct appoximation". --[[User:Cmloegcmluin\|Cmloegcmluin]] ([[User talk:Cmloegcmluin\|talk]]) 16:51, 23 May 2024 (UTC)

FloraC: /* Rounding function symbol */ re

2022-02-24T22:13:02Z

Rounding function symbol: re

← Older revision		Revision as of 22:13, 24 February 2022
Line 151:		Line 151:

	:: Feel free to change it if you think it's best. My reasoning for using was this: because "round" was spelled out in the preceding text, the context was sufficient to make <math>⌈·⌋</math> acceptable despite not being well-established. And I like <math>⌈·⌋</math> because it's concise, and also because it's logical w/r/t to the well-established ceil <math>⌈·⌉</math> and floor <math>⌊·⌋</math> notations. I knew it was used at least sometimes but couldn't remember specifically where I'd seen <math>⌈·⌋</math> before, but a web search confirmed that it's at least not entirely unheard of. --[[User:Cmloegcmluin\|Cmloegcmluin]] ([[User talk:Cmloegcmluin\|talk]]) 21:22, 24 February 2022 (UTC)		:: Feel free to change it if you think it's best. My reasoning for using was this: because "round" was spelled out in the preceding text, the context was sufficient to make <math>⌈·⌋</math> acceptable despite not being well-established. And I like <math>⌈·⌋</math> because it's concise, and also because it's logical w/r/t to the well-established ceil <math>⌈·⌉</math> and floor <math>⌊·⌋</math> notations. I knew it was used at least sometimes but couldn't remember specifically where I'd seen <math>⌈·⌋</math> before, but a web search confirmed that it's at least not entirely unheard of. --[[User:Cmloegcmluin\|Cmloegcmluin]] ([[User talk:Cmloegcmluin\|talk]]) 21:22, 24 February 2022 (UTC)

			::: 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)

Cmloegcmluin: /* Rounding function symbol */

2022-02-24T21:22:52Z

Rounding function symbol

← Older revision		Revision as of 21:22, 24 February 2022
Line 149:		Line 149:

	: I've definitely seen this before. See: https://mathworld.wolfram.com/NearestIntegerFunction.html Hoewever I think <math>\text{round}(x)</math> is much clearer. -- [[User:Sintel\|Sintel]] ([[User talk:Sintel\|talk]]) 12:12, 24 February 2022 (UTC)		: I've definitely seen this before. See: https://mathworld.wolfram.com/NearestIntegerFunction.html Hoewever I think <math>\text{round}(x)</math> is much clearer. -- [[User:Sintel\|Sintel]] ([[User talk:Sintel\|talk]]) 12:12, 24 February 2022 (UTC)

			:: Feel free to change it if you think it's best. My reasoning for using was this: because "round" was spelled out in the preceding text, the context was sufficient to make <math>⌈·⌋</math> acceptable despite not being well-established. And I like <math>⌈·⌋</math> because it's concise, and also because it's logical w/r/t to the well-established ceil <math>⌈·⌉</math> and floor <math>⌊·⌋</math> notations. I knew it was used at least sometimes but couldn't remember specifically where I'd seen <math>⌈·⌋</math> before, but a web search confirmed that it's at least not entirely unheard of. --[[User:Cmloegcmluin\|Cmloegcmluin]] ([[User talk:Cmloegcmluin\|talk]]) 21:22, 24 February 2022 (UTC)

Sintel at 12:12, 24 February 2022

2022-02-24T12:12:26Z

← Older revision		Revision as of 12:12, 24 February 2022
Line 147:		Line 147:

	I never heard of "⌈⌋". No occurrence in [[Wikipedia: Rounding]] either. Is it attested anywhere? I reckon round () isn't too verbose? [[User:FloraC\|FloraC]] ([[User talk:FloraC\|talk]]) 09:56, 24 February 2022 (UTC)		I never heard of "⌈⌋". No occurrence in [[Wikipedia: Rounding]] either. Is it attested anywhere? I reckon round () isn't too verbose? [[User:FloraC\|FloraC]] ([[User talk:FloraC\|talk]]) 09:56, 24 February 2022 (UTC)

			: I've definitely seen this before. See: https://mathworld.wolfram.com/NearestIntegerFunction.html Hoewever I think <math>\text{round}(x)</math> is much clearer. -- [[User:Sintel\|Sintel]] ([[User talk:Sintel\|talk]]) 12:12, 24 February 2022 (UTC)

FloraC: /* Rounding function symbol */ new section

2022-02-24T09:56:09Z

Rounding function symbol: new section

← Older revision		Revision as of 09:56, 24 February 2022
Line 143:		Line 143:

	::::: Oh! My bad. Yes, I see what you're saying now. Sorry I didn't read carefully enough the first time. Of course, you would need to contrast a direct fifth with a patent fifth. That makes sense and is totally fine with me. As you may know I prefer "simple map" to "patent val" and so would prefer "simple fifth" to "patent fifth", but I won't begrudge you for using "patent", as it's patently ;) well-established. --[[User:Cmloegcmluin\|Cmloegcmluin]] ([[User talk:Cmloegcmluin\|talk]]) 03:51, 24 February 2022 (UTC)		::::: Oh! My bad. Yes, I see what you're saying now. Sorry I didn't read carefully enough the first time. Of course, you would need to contrast a direct fifth with a patent fifth. That makes sense and is totally fine with me. As you may know I prefer "simple map" to "patent val" and so would prefer "simple fifth" to "patent fifth", but I won't begrudge you for using "patent", as it's patently ;) well-established. --[[User:Cmloegcmluin\|Cmloegcmluin]] ([[User talk:Cmloegcmluin\|talk]]) 03:51, 24 February 2022 (UTC)

			== Rounding function symbol ==

			I never heard of "⌈⌋". No occurrence in [[Wikipedia: Rounding]] either. Is it attested anywhere? I reckon round () isn't too verbose? [[User:FloraC\|FloraC]] ([[User talk:FloraC\|talk]]) 09:56, 24 February 2022 (UTC)