Talk:Patent val: Difference between revisions

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:::::::: I understand what I'm tryna argue is counterintuitive. Maybe I failed to make the context clear. It's this: ''val'' can't be replaced entirely by ''map''. You can replace this word in the phrase ''patent val'', but beyond this phrase, it can't be replaced by all occurrences. It turns up in all the temp pages, for example, where simply replacing the lines of ''vals'' to ''maps'' isn't appropriate. It has to do with the concern that ''val'' isn't totally synonymous with ''map''. ''Val'' or ''edomapping'' (I reckon these two are synonymous) emphasises itself being an individual row of the map. Therefore, ''val'' remains a word that's likely to be encountered by those who work with RTT even if it's removed from the phrase ''patent val''. That's why we hope to keep people familiar with both terms by using the term of lower use rate more, which can be explained through Shannon entropy. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 01:26, 29 September 2021 (UTC)

::::::::: If we can't agree on a replacement for "val", there seems little point in pursuing the other proposed terminology changes. So, Kite and/or Flora, please explain why you claim that "edomapping" is a suitable replacement for "val" when, as Douglas mentioned, vals need not be related to EDOs at all, e.g. they may be ED3 maps, or as the [[Val]] article says, "It's very common for vals to refer to EDOs specifically, although they also show us how to relate larger chains of generators to JI as well (such as a stack of meantone fifths)". i.e. a val can be a single row of a mapping for a temperament of rank greater than 1, and therefore not directly related to an ED of any kind. In short: "non-edo val" makes perfect sense while "non-edo edomapping" does not.

::::::::: And in case that isn't enough, the [[Mapping]] article makes it clear that a "mapping" is a ''list'' of vals, which can be viewed as a matrix. Of course some mappings contain only one val, and so a val could be considered to be a rank-1 mapping. But it would be somewhat circular to define a mapping as a list of rank-1 mappings, as seems to be implied by your clam that "edomapping" is synonymous with "val".

::::::::: And please explain what prevents us from defining "map" in RTT as synonymous with "val", given that the [[Val]] article begins, "A val is a linear map representing ...". I see that [[Map]] currently redirects to [[Mapping]], but I see no reason why it must do so. Why not use the shorter term "map" for the lower-level objects of which mappings are composed? And aren't we more likely to succeed in replacing "val" in people's existing usage, if the replacement has only one syllable, like the original? And "bimap", "trimap", "multimap" work so much better than "biedomapping", "triedomapping", "multiedomapping", as replacements for "bival", "trival" and "multival" in the exterior algebra formulation. --[[User:Dave Keenan|Dave Keenan]] ([[User talk:Dave Keenan|talk]]) 04:40, 5 October 2021 (UTC)

:::::::::: Aren't ''mapping'' and ''map'' just the same word in different inflections? I don't see how anyone would use them for different entities instead of interchangeably. It only makes things confusing. Also switching to ''mapping'' from ''map'' is a relatively recent change I believe.

:::::::::: ''Edomapping'' is synonymous with ''val'' because it's meant to be so. The circular definition problem is independent of names. If you define a val as a single row of the mapping and the mapping as a list of vals, it's circular definition whatever you call it. That said, I agree that it's less appropriate for non-edo vals and that's why I'd stick to ''val''.

:::::::::: Finally, if you're planning to replace every occurrence of ''val'': how about the "vals" in each temp page? [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 08:44, 5 October 2021 (UTC)

::::::::: It is true that, in mathematics generally, ''mapping'' and ''map'', when used as nouns, are synonyms, and both are synonymous with ''function''. But there is very little difference between an individual row of a mapping, and a mapping with only one row. So if we were to agree that, in RTT, only an individual row should be called a ''map'', and someone new to the field assumes that a map is the same as a mapping, then there are almost no consequences of that temporary confusion, if it can even be called confusion. For 12edo, its 5-limit ''map'' is ⟨12 19 28], and its 5-limit ''mapping'' is [⟨12 19 28]⟩. The mnemonic is simple: The shorter term applies to the smaller object. The difference rarely matters to anyone, but when it does, at least we would have descriptive terms rather than the confusing and unnecessary jargon of "val", which acts as a barrier to understanding.

::::::::: You may be aware that I am one of the founders of regular temperament theory along with Paul Erlich, Graham Breed, Gene Smith and others, since 1998. In online discussions of regular temperaments, and in our writings, all four of us have referred to any array of numbers whose units are "generators per prime", as a mapping, ever since we first referred to them as anything at all, which seems to have been in early 2001. Only rarely has this been shortened to "map" — typically only as a heading in tables of temperament data generated by Gene Smith. But even Gene is on record as defining a "prime mapping" as a "list of vals", here: http://www.tonalsoft.com/enc/p/prime-mapping.aspx

::::::::: I didn't rely on my memory for the above, but spent several hours going through the results of the following tuning archive searches:

::::::::: site:yahootuninggroupsultimatebackup.github.io "mapping"

::::::::: site:yahootuninggroupsultimatebackup.github.io "map"

::::::::: Of course most of the temperament data in the Xen Wiki was generated by Gene, so it is not surprising if it contained "map" as an abbreviation of "mapping". So I assume, when you say that switching to ''mapping'' from ''map'' is a relatively recent change, you are referring to someone having expanded these occurrences of "map" to "mapping". That would be a good thing. It would make them consistent with the output from Graham Breed's temperament finder, and it would open the way to defining "map" as synonymous with "val".

::::::::: In the Xen Wiki and Graham Breed's temperament finder and the tuning archives, [there is a case in which*] the term "map" (and not "mapping") already consistently refers to an individual row of the form ⟨...]. This is in the case of a "tuning map", which maps from generators to cents. This is a map in "tuning space". By analogy, a val is therefore a map in "temperament space", and so it would be perfectly consistent with existing terminology, to refer to a val as a "temperament map" as opposed to a temperament mapping. We are merely proposing that an unqualified "map" should be assumed to be a temperament map, i.e. a val, not a tuning map. Or at least that when it is clear from the context that it is a temperament map, the qualifier "temperament" can be dropped. [*clarification added 30 Dec 2021] --[[User:Dave Keenan|Dave Keenan]] ([[User talk:Dave Keenan|talk]]) 16:29, 6 October 2021 (UTC)

:::::::::: I guess I agree that ''map'' is a possible replacement for ''val'', but my point has always been practical. What's the plan? How do you make all the RTT users forget about ''val''? How about all these pages? The letter ''V'' in the formulae? [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 00:24, 7 October 2021 (UTC)

:::::::::: And with so many legacies, I must oppose this change since I oppose forced language reforms. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 00:38, 7 October 2021 (UTC)

::::::::: Thanks FloraC.

::::::::: It is arguable that the introduction of ''val'' was a forced language reform since, before that, and after, tuning list contributors were happy to use descriptive terms like "ET mapping" and "mapping row". So arguably, ''if'' we replaced ''val'' we would merely be ''undoing'' a forced language reform.

::::::::: However I don't actually want to replace any existing occurrences of ''val''. I only want to ensure that the way is open for Douglas to use ''map'' as a synonym for it, in his excellent pedagogical articles. And for others to use ''map'' in that way, if they choose, going forward.

::::::::: The first thing to do in that regard would be to redirect "Map" to the "Val" page instead of the "Mapping" page, and to mention ''map'' as a synonym near the start of the "Val" page.

::::::::: The only other thing would be to check all existing (whole-word) occurrences of "map" in the wiki (outside of Douglas' articles), and if they refer to a matrix, as opposed to a row vector ⟨...], expand them to "mapping". --[[User:Dave Keenan|Dave Keenan]] ([[User talk:Dave Keenan|talk]]) 09:41, 8 October 2021 (UTC)

:::::::::: However val was introduced in the first place, it's the status quo and what's undoing of language reform is simultaneously another layer of language reform. Anyway, you've clearly presented the feasible first steps to switch to ''map'' and I'll follow, although I'd like to make ''map'' a disambiguation page to catch all the usage. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 11:26, 8 October 2021 (UTC)

::::::::: I dislike val strongly because the dictionary says it's an abbreviation for value. Which is not only vague, but also misleading because there are multiple values in a single val. I don't see why val can't be replaced with something better. I still like edomapping. I think it's the opposite of jargon, because it's very self-explanatory. For the ED3 case, I propose edt-mapping or ed3-mapping. For the general case of rank-1 mappings that aren't edos, I propose edonoi-mapping. In other words, you just specify what the mapping is used for in the name. For the even more general case of the combination of edomappings and edonoi-mappings, I propose rank-1 mapping. For everything outside of that, I propose mapping-row. I'm OK with mapping being shortened to map in any or all of these cases. I'm also OK with hyphenating, e.g. edo-map or edo-mapping. --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 06:29, 9 October 2021 (UTC)

::::::::::That's a good solution. Thanks FloraC.

::::::::::Kite, I find all those terms you suggest above to be acceptable (except I don't know what "edonoi" means). I have used many of them myself in the past. But none of them is a potential replacement for "val" since vals include both "rank-1 mappings" and "mapping rows". Douglas and I have chosen to use "map" for this purpose in our pedagogical materials, thereby giving it a more specific meaning than "mapping" within the domain of tuning theory. --[[User:Dave Keenan|Dave Keenan]] ([[User talk:Dave Keenan|talk]]) 06:45, 10 October 2021 (UTC)

::::::::::: EDONOI means equal division of a non-octave interval. It's a fairly widespread term. "none of them is a potential replacement for val" I'm proposing edonoi-mapping, mapping-row etc. as replacements for specific use cases of val, and the term map or mapping as the general replacement for val. So I think we agree that val can be completely replaced by map/mapping. --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 21:09, 16 October 2021 (UTC)

== proposal to rename "generalize patent val" to "uniform map" ==

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::::::::: I do like "scaled", thank you I will use it! I'm good with "nearest scaled edomappings". The phrase is admittedly a bit intimidating, but I could see it working. The newcomer should first learn about edomappings, then nearest edomappings, then scaled edomappings, then nearest scaled edomappings. We could call them NSEs or something, unless we call them proper/uniform. --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 00:47, 30 September 2021 (UTC)

:::::::::: I'm glad we're on the same page now re: GPVs. I agree "proper" is a reasonable choice. I probably like it better than "generalized". But I still prefer "uniform". Of course, the fact that I need to provide extra explanation for "uniform" to you doesn't bode well for my case :) But let me give it a shot, leaning on the dictionary definition you provided. Please glance back up at my charts I pasted above. Again, the perfectly straight vertical lines I draw through the chart represent uniform maps. I suppose you could think of these lines, as you follow them vertically through the chart, as "choosing" the mapping for each prime. The fact that I require the line to be perfectly straight up-and-down is what makes it work. So if I had not uniformly scaled the lines per each of the primes, the line wouldn't be perfectly straight, and I wouldn't have a uniform map. That's the uniform part: uniform per prime, no variations in scale between them, identical and consistent scaling per prime. Does that work? As I explain it, I'm realizing that "straight map" might work just as well or better. What are your thoughts on that?

:::::::::: I'm glad you like "scaled". But I still prefer uniform map. I don't know what you mean by a "scaled edomapping" (one that's not a "nearest scaled edomapping"... what is scaled ''of'', then?). In my opinion a newcomer would first learn about maps, then uniform maps, then integer uniform maps. That's the order I present the ideas in my RTT How-To at present. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 01:36, 30 September 2021 (UTC)

::::::::::: A scaled edomapping is a mapping for a scaled edo, e.g. 16.9-edo. There are many possible edomappings for 16.9. One of them is the nearest scaled edomapping. The definition of proper/uniform edomapping is that it is also a nearest scaled edomapping for some scaling.

::::::::::: Oh I just had a horrible thought. When calculating tuning errors for unscaled edos, there's never an exact tie, because that would imply a JI comma of exactly 0 cents, which contradicts the unique factorization theorem. Because there's never an exact tie, there is only 1 nearest edomapping. BUT if we allow non-integral edos, ties are possible, and there can be two nearest edomappings!! For example there exists a number N near 12 such that 11/8 falls exactly midway between 5\N and 6\N. 11/8 = 5.5\N, and 551.3¢/1200¢ = 5.5 / N, and N = 5.5 * (1200 / 551.3) = about 11.97. This corresponds to the vertical line passing through the boundary between prime 11's 41 block and 42 block. --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 07:35, 2 October 2021 (UTC)

== alternative proposal: add new page for uniform map ==

I am wondering how people here would feel about me adding a new page for "uniform map". Through discussion on this Talk page here, I have realized that my concerns about the current page go beyond merely terminological. My terminological concerns can be addressed by adding some parenthetical statements here and there. But my main concern is on a conceptual level, and I don't think it could be properly addressed without turning the page completely inside-out, which I don't think is reasonable.

The main problem is that I think the two topics are presented inside-out from the way that would be best. To be clear, I think it would be more logical to first present the version of this concept which uses real numbers as the basic kind ("uniform map"), and then introduce the integers-only version as a specific kind of that ("integer uniform map"). The current page does it the other way around, presenting the integer version as the basic kind ("patent val"), and then the reals version as a generalized kind of it ("generalized patent val").

I think both ways of presenting the concept are reasonable. And I think one could even make the case that these opposite perspectives on the concept are actually tantamount to two different conceptualizations of the shared mathematical reality — two conceptualizations which are each justified in having their own respective page to be documented on. I do think there are many people who would significantly benefit from my conceptualization, who are currently missing out on it.

So what would people think if I added a parallel page? This proposal assumes that the two pages should be firmly linked to each other, and be very clear and up-front about their synonymies. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 01:42, 4 October 2021 (UTC)

: Okay, I've gone ahead and done this now: [[uniform map]]. Comments and criticism welcome, of course. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 00:23, 12 December 2021 (UTC)

== Thoughts on changing "patent val," and other terminology changes in general ==

I just want to chime in that I also strongly disagree with changing "patent val" to "uniform map." If Doug + Dave want to do that for their pages then that's alright, but to the extent this is really a recommendation to make a general change to the Wiki then I strongly disagree with it. My thoughts pretty are much on the same page as FloraC on the matter, who has probably articulated it better than I could.

In general, if you have some proposal to change core RTT terminology, please also bring it to the attention of the [https://www.facebook.com/groups/xenwiki/permalink Facebook Xenwiki] group. [[User:Mike Battaglia|Mike Battaglia]] ([[User talk:Mike Battaglia|talk]]) 21:49, 16 November 2021 (UTC)

: Yes, strong agree on bringing proposals to the attention of that Facebook group. I would go even further and say that it's also important to run stuff like this by the very active XA Discord server's channel for the wiki. I was certainly planning on doing both of those before I would make any actual changes like this. I merely ''began'' here on the wiki discussion pages themselves, which seemed like a good place to test the waters before wasting wider audiences' time. And as you can see there hasn't been a lot of activity over the past month as we've been focusing on other things.

: Looking back on it, I can see that the original language with which I posted stuff here (which was pasted in September, but originally composed back in May!) was from a time when I felt a lot more bold about reforming this stuff. So yeah, I certainly don't think anymore that I could manage to demote "patent val" to a secondary term for this concept. I would be happy enough to be able to include links from this page to our work that say "Dave Keenan and Douglas Blumeyer use the term 'uniform map' for this," or whatever. Maybe one day it will earn the right to be listed with the main words, such as how Kite's "nearest edomapping" gets to be listed. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 22:11, 16 November 2021 (UTC)

:: That sounds good - it would really be nice if we could get a "Douglas + Dave Theory" main page of some kind so we could see this all organized at some point. (And I thought you went by Doug or is it always Douglas?) [[User:Mike Battaglia|Mike Battaglia]] ([[User talk:Mike Battaglia|talk]]) 23:00, 16 November 2021 (UTC)

::: I'm trying to go with "Douglas". Thanks for asking. Dave writes little on the wiki himself. Here's my work: https://en.xen.wiki/w/Douglas_Blumeyer#Some_of_his_work_here_on_the_wiki --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 23:38, 16 November 2021 (UTC)

=== Concern about the confusingness of nearest edomapping ===

It strikes me that the "nearest edomapping" would be the [[direct approximation]], so that the name is exactly a wrong self-description. Contrast with something like "nearest edomapping val" where the presence of the word "val" makes the meaning clearer. I really do not think it is a good idea to have this as a synonym for "patent val"; I don't think I've ever even seen it used. If it stays on the page at all, the name needs to be changed to something less confusing. --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 21:56, 31 January 2025 (UTC)

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 :::::::: I understand what I'm tryna argue is counterintuitive. Maybe I failed to make the context clear. It's this: ''val'' can't be replaced entirely by ''map''. You can replace this word in the phrase ''patent val'', but beyond this phrase, it can't be replaced by all occurrences. It turns up in all the temp pages, for example, where simply replacing the lines of ''vals'' to ''maps'' isn't appropriate. It has to do with the concern that ''val'' isn't totally synonymous with ''map''. ''Val'' or ''edomapping'' (I reckon these two are synonymous) emphasises itself being an individual row of the map. Therefore, ''val'' remains a word that's likely to be encountered by those who work with RTT even if it's removed from the phrase ''patent val''. That's why we hope to keep people familiar with both terms by using the term of lower use rate more, which can be explained through Shannon entropy. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 01:26, 29 September 2021 (UTC)
+::::::::: If we can't agree on a replacement for "val", there seems little point in pursuing the other proposed terminology changes. So, Kite and/or Flora, please explain why you claim that "edomapping" is a suitable replacement for "val" when, as Douglas mentioned, vals need not be related to EDOs at all, e.g. they may be ED3 maps, or as the [[Val]] article says, "It's very common for vals to refer to EDOs specifically, although they also show us how to relate larger chains of generators to JI as well (such as a stack of meantone fifths)". i.e. a val can be a single row of a mapping for a temperament of rank greater than 1, and therefore not directly related to an ED of any kind. In short: "non-edo val" makes perfect sense while "non-edo edomapping" does not.
+::::::::: And in case that isn't enough, the [[Mapping]] article makes it clear that a "mapping" is a ''list'' of vals, which can be viewed as a matrix. Of course some mappings contain only one val, and so a val could be considered to be a rank-1 mapping. But it would be somewhat circular to define a mapping as a list of rank-1 mappings, as seems to be implied by your clam that "edomapping" is synonymous with "val".
+::::::::: And please explain what prevents us from defining "map" in RTT as synonymous with "val", given that the [[Val]] article begins, "A val is a linear map representing ...". I see that [[Map]] currently redirects to [[Mapping]], but I see no reason why it must do so. Why not use the shorter term "map" for the lower-level objects of which mappings are composed? And aren't we more likely to succeed in replacing "val" in people's existing usage, if the replacement has only one syllable, like the original? And "bimap", "trimap", "multimap" work so much better than "biedomapping", "triedomapping", "multiedomapping", as replacements for "bival", "trival" and "multival" in the exterior algebra formulation. --[[User:Dave Keenan|Dave Keenan]] ([[User talk:Dave Keenan|talk]]) 04:40, 5 October 2021 (UTC)
+:::::::::: Aren't ''mapping'' and ''map'' just the same word in different inflections? I don't see how anyone would use them for different entities instead of interchangeably. It only makes things confusing. Also switching to ''mapping'' from ''map'' is a relatively recent change I believe.
+:::::::::: ''Edomapping'' is synonymous with ''val'' because it's meant to be so. The circular definition problem is independent of names. If you define a val as a single row of the mapping and the mapping as a list of vals, it's circular definition whatever you call it. That said, I agree that it's less appropriate for non-edo vals and that's why I'd stick to ''val''.
+:::::::::: Finally, if you're planning to replace every occurrence of ''val'': how about the "vals" in each temp page? [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 08:44, 5 October 2021 (UTC)
+::::::::: It is true that, in mathematics generally, ''mapping'' and ''map'', when used as nouns, are synonyms, and both are synonymous with ''function''. But there is very little difference between an individual row of a mapping, and a mapping with only one row. So if we were to agree that, in RTT, only an individual row should be called a ''map'', and someone new to the field assumes that a map is the same as a mapping, then there are almost no consequences of that temporary confusion, if it can even be called confusion. For 12edo, its 5-limit ''map'' is ⟨12 19 28], and its 5-limit ''mapping'' is [⟨12 19 28]⟩. The mnemonic is simple: The shorter term applies to the smaller object. The difference rarely matters to anyone, but when it does, at least we would have descriptive terms rather than the confusing and unnecessary jargon of "val", which acts as a barrier to understanding.
+::::::::: You may be aware that I am one of the founders of regular temperament theory along with Paul Erlich, Graham Breed, Gene Smith and others, since 1998. In online discussions of regular temperaments, and in our writings, all four of us have referred to any array of numbers whose units are "generators per prime", as a mapping, ever since we first referred to them as anything at all, which seems to have been in early 2001. Only rarely has this been shortened to "map" — typically only as a heading in tables of temperament data generated by Gene Smith. But even Gene is on record as defining a "prime mapping" as a "list of vals", here: http://www.tonalsoft.com/enc/p/prime-mapping.aspx
+::::::::: I didn't rely on my memory for the above, but spent several hours going through the results of the following tuning archive searches:
+::::::::: site:yahootuninggroupsultimatebackup.github.io "mapping"
+::::::::: site:yahootuninggroupsultimatebackup.github.io "map"
+::::::::: Of course most of the temperament data in the Xen Wiki was generated by Gene, so it is not surprising if it contained "map" as an abbreviation of "mapping". So I assume, when you say that switching to ''mapping'' from ''map'' is a relatively recent change, you are referring to someone having expanded these occurrences of "map" to "mapping". That would be a good thing. It would make them consistent with the output from Graham Breed's temperament finder, and it would open the way to defining "map" as synonymous with "val".
+::::::::: In the Xen Wiki and Graham Breed's temperament finder and the tuning archives, [there is a case in which*] the term "map" (and not "mapping") already consistently refers to an individual row of the form ⟨...]. This is in the case of a "tuning map", which maps from generators to cents. This is a map in "tuning space". By analogy, a val is therefore a map in "temperament space", and so it would be perfectly consistent with existing terminology, to refer to a val as a "temperament map" as opposed to a temperament mapping. We are merely proposing that an unqualified "map" should be assumed to be a temperament map, i.e. a val, not a tuning map. Or at least that when it is clear from the context that it is a temperament map, the qualifier "temperament" can be dropped. [*clarification added 30 Dec 2021] --[[User:Dave Keenan|Dave Keenan]] ([[User talk:Dave Keenan|talk]]) 16:29, 6 October 2021 (UTC)
+:::::::::: I guess I agree that ''map'' is a possible replacement for ''val'', but my point has always been practical. What's the plan? How do you make all the RTT users forget about ''val''? How about all these pages? The letter ''V'' in the formulae? [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 00:24, 7 October 2021 (UTC)
+:::::::::: And with so many legacies, I must oppose this change since I oppose forced language reforms. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 00:38, 7 October 2021 (UTC)
+::::::::: Thanks FloraC.
+::::::::: It is arguable that the introduction of ''val'' was a forced language reform since, before that, and after, tuning list contributors were happy to use descriptive terms like "ET mapping" and "mapping row". So arguably, ''if'' we replaced ''val'' we would merely be ''undoing'' a forced language reform.
+::::::::: However I don't actually want to replace any existing occurrences of ''val''. I only want to ensure that the way is open for Douglas to use ''map'' as a synonym for it, in his excellent pedagogical articles. And for others to use ''map'' in that way, if they choose, going forward.
+::::::::: The first thing to do in that regard would be to redirect "Map" to the "Val" page instead of the "Mapping" page, and to mention ''map'' as a synonym near the start of the "Val" page.
+::::::::: The only other thing would be to check all existing (whole-word) occurrences of "map" in the wiki (outside of Douglas' articles), and if they refer to a matrix, as opposed to a row vector ⟨...], expand them to "mapping". --[[User:Dave Keenan|Dave Keenan]] ([[User talk:Dave Keenan|talk]]) 09:41, 8 October 2021 (UTC)
+:::::::::: However val was introduced in the first place, it's the status quo and what's undoing of language reform is simultaneously another layer of language reform. Anyway, you've clearly presented the feasible first steps to switch to ''map'' and I'll follow, although I'd like to make ''map'' a disambiguation page to catch all the usage. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 11:26, 8 October 2021 (UTC)
+::::::::: I dislike val strongly because the dictionary says it's an abbreviation for value. Which is not only vague, but also misleading because there are multiple values in a single val. I don't see why val can't be replaced with something better. I still like edomapping. I think it's the opposite of jargon, because it's very self-explanatory. For the ED3 case, I propose edt-mapping or ed3-mapping. For the general case of rank-1 mappings that aren't edos, I propose edonoi-mapping. In other words, you just specify what the mapping is used for in the name. For the even more general case of the combination of edomappings and edonoi-mappings, I propose rank-1 mapping. For everything outside of that, I propose mapping-row. I'm OK with mapping being shortened to map in any or all of these cases. I'm also OK with hyphenating, e.g. edo-map or edo-mapping. --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 06:29, 9 October 2021 (UTC)
+::::::::::That's a good solution. Thanks FloraC.
+::::::::::Kite, I find all those terms you suggest above to be acceptable (except I don't know what "edonoi" means). I have used many of them myself in the past. But none of them is a potential replacement for "val" since vals include both "rank-1 mappings" and "mapping rows". Douglas and I have chosen to use "map" for this purpose in our pedagogical materials, thereby giving it a more specific meaning than "mapping" within the domain of tuning theory. --[[User:Dave Keenan|Dave Keenan]] ([[User talk:Dave Keenan|talk]]) 06:45, 10 October 2021 (UTC)
+::::::::::: EDONOI means equal division of a non-octave interval. It's a fairly widespread term. "none of them is a potential replacement for val" I'm proposing edonoi-mapping, mapping-row etc. as replacements for specific use cases of val, and the term map or mapping as the general replacement for val. So I think we agree that val can be completely replaced by map/mapping. --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 21:09, 16 October 2021 (UTC)
 == proposal to rename "generalize patent val" to "uniform map" ==
@@ Line 157: / Line 208: @@
 ::::::::: I do like "scaled", thank you I will use it! I'm good with "nearest scaled edomappings". The phrase is admittedly a bit intimidating, but I could see it working. The newcomer should first learn about edomappings, then nearest edomappings, then scaled edomappings, then nearest scaled edomappings. We could call them NSEs or something, unless we call them proper/uniform. --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 00:47, 30 September 2021 (UTC)
+:::::::::: I'm glad we're on the same page now re: GPVs. I agree "proper" is a reasonable choice. I probably like it better than "generalized". But I still prefer "uniform". Of course, the fact that I need to provide extra explanation for "uniform" to you doesn't bode well for my case :) But let me give it a shot, leaning on the dictionary definition you provided. Please glance back up at my charts I pasted above. Again, the perfectly straight vertical lines I draw through the chart represent uniform maps. I suppose you could think of these lines, as you follow them vertically through the chart, as "choosing" the mapping for each prime. The fact that I require the line to be perfectly straight up-and-down is what makes it work. So if I had not uniformly scaled the lines per each of the primes, the line wouldn't be perfectly straight, and I wouldn't have a uniform map. That's the uniform part: uniform per prime, no variations in scale between them, identical and consistent scaling per prime. Does that work? As I explain it, I'm realizing that "straight map" might work just as well or better. What are your thoughts on that?
+:::::::::: I'm glad you like "scaled". But I still prefer uniform map. I don't know what you mean by a "scaled edomapping" (one that's not a "nearest scaled edomapping"... what is scaled ''of'', then?). In my opinion a newcomer would first learn about maps, then uniform maps, then integer uniform maps. That's the order I present the ideas in my RTT How-To at present. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 01:36, 30 September 2021 (UTC)
+::::::::::: A scaled edomapping is a mapping for a scaled edo, e.g. 16.9-edo. There are many possible edomappings for 16.9. One of them is the nearest scaled edomapping. The definition of proper/uniform edomapping is that it is also a nearest scaled edomapping for some scaling.
+::::::::::: Oh I just had a horrible thought. When calculating tuning errors for unscaled edos, there's never an exact tie, because that would imply a JI comma of exactly 0 cents, which contradicts the unique factorization theorem. Because there's never an exact tie, there is only 1 nearest edomapping. BUT if we allow non-integral edos, ties are possible, and there can be two nearest edomappings!! For example there exists a number N near 12 such that 11/8 falls exactly midway between 5\N and 6\N. 11/8 = 5.5\N, and 551.3¢/1200¢ = 5.5 / N, and N = 5.5 * (1200 / 551.3) = about 11.97. This corresponds to the vertical line passing through the boundary between prime 11's 41 block and 42 block. --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 07:35, 2 October 2021 (UTC)
+== alternative proposal: add new page for uniform map ==
+I am wondering how people here would feel about me adding a new page for "uniform map". Through discussion on this Talk page here, I have realized that my concerns about the current page go beyond merely terminological. My terminological concerns can be addressed by adding some parenthetical statements here and there. But my main concern is on a conceptual level, and I don't think it could be properly addressed without turning the page completely inside-out, which I don't think is reasonable.
+The main problem is that I think the two topics are presented inside-out from the way that would be best. To be clear, I think it would be more logical to first present the version of this concept which uses real numbers as the basic kind ("uniform map"), and then introduce the integers-only version as a specific kind of that ("integer uniform map"). The current page does it the other way around, presenting the integer version as the basic kind ("patent val"), and then the reals version as a generalized kind of it ("generalized patent val").
+I think both ways of presenting the concept are reasonable. And I think one could even make the case that these opposite perspectives on the concept are actually tantamount to two different conceptualizations of the shared mathematical reality — two conceptualizations which are each justified in having their own respective page to be documented on. I do think there are many people who would significantly benefit from my conceptualization, who are currently missing out on it.
+So what would people think if I added a parallel page? This proposal assumes that the two pages should be firmly linked to each other, and be very clear and up-front about their synonymies. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 01:42, 4 October 2021 (UTC)
+: Okay, I've gone ahead and done this now: [[uniform map]]. Comments and criticism welcome, of course. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 00:23, 12 December 2021 (UTC)
+== Thoughts on changing "patent val," and other terminology changes in general ==
+I just want to chime in that I also strongly disagree with changing "patent val" to "uniform map." If Doug + Dave want to do that for their pages then that's alright, but to the extent this is really a recommendation to make a general change to the Wiki then I strongly disagree with it. My thoughts pretty are much on the same page as FloraC on the matter, who has probably articulated it better than I could.
+In general, if you have some proposal to change core RTT terminology, please also bring it to the attention of the [https://www.facebook.com/groups/xenwiki/permalink Facebook Xenwiki] group. [[User:Mike Battaglia|Mike Battaglia]] ([[User talk:Mike Battaglia|talk]]) 21:49, 16 November 2021 (UTC)
+: Yes, strong agree on bringing proposals to the attention of that Facebook group. I would go even further and say that it's also important to run stuff like this by the very active XA Discord server's channel for the wiki. I was certainly planning on doing both of those before I would make any actual changes like this. I merely ''began'' here on the wiki discussion pages themselves, which seemed like a good place to test the waters before wasting wider audiences' time. And as you can see there hasn't been a lot of activity over the past month as we've been focusing on other things.
+: Looking back on it, I can see that the original language with which I posted stuff here (which was pasted in September, but originally composed back in May!) was from a time when I felt a lot more bold about reforming this stuff. So yeah, I certainly don't think anymore that I could manage to demote "patent val" to a secondary term for this concept. I would be happy enough to be able to include links from this page to our work that say "Dave Keenan and Douglas Blumeyer use the term 'uniform map' for this," or whatever. Maybe one day it will earn the right to be listed with the main words, such as how Kite's "nearest edomapping" gets to be listed. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 22:11, 16 November 2021 (UTC)
+:: That sounds good - it would really be nice if we could get a "Douglas + Dave Theory" main page of some kind so we could see this all organized at some point. (And I thought you went by Doug or is it always Douglas?) [[User:Mike Battaglia|Mike Battaglia]] ([[User talk:Mike Battaglia|talk]]) 23:00, 16 November 2021 (UTC)
+::: I'm trying to go with "Douglas". Thanks for asking. Dave writes little on the wiki himself. Here's my work: https://en.xen.wiki/w/Douglas_Blumeyer#Some_of_his_work_here_on_the_wiki --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 23:38, 16 November 2021 (UTC)
+=== Concern about the confusingness of nearest edomapping ===
+It strikes me that the "nearest edomapping" would be the [[direct approximation]], so that the name is exactly a wrong self-description. Contrast with something like "nearest edomapping val" where the presence of the word "val" makes the meaning clearer. I really do not think it is a good idea to have this as a synonym for "patent val"; I don't think I've ever even seen it used. If it stays on the page at all, the name needs to be changed to something less confusing. --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 21:56, 31 January 2025 (UTC)