Talk:Consistency: Difference between revisions

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:: Sorry for the confusion: I meant this page, the main page for ''consistency'', not the main page of the entire wiki, in the manner you've described above. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 20:07, 29 July 2022 (UTC)

::: Right, that makes sense. I'll ponder over the idea I mentioned about the Conventions page, since this gave me the idea anyway. --[[User:Fredg999|Fredg999]] ([[User talk:Fredg999|talk]]) 22:16, 29 July 2022 (UTC)

== Differences and Sums ==

The main definition (with q-odd limit) only says "difference"; the definition in terms of a chord says "interval between"; I guess these make sense because some sums would stray outside the limit or the chord. But the mathematical definition is in terms of a set, and uses a sum (the first example also uses a sum, but the example is clearly valid and could be re-ordered into a difference). Is it correct to exclude sums?

PS:

* distinct vs unique: covered by cmloegcmluin above, thanks.

* closest vs nearest: no difference in meaning, I think; I chose "closest".

* best vs closest: I argue that "best" can mean different things depending on your purpose, whereas "closest" is simply factual.

--[[User:Martins|Martins]] ([[User talk:Martins|talk]]) 20:14, 1 August 2022 (UTC)

: Hi Steve! Thanks for posting here. I corrected the spelling of my username in your post, hope you don't mind (I admit it's a tough one to spell, haha). Also, FYI, people tend to sign their posts here. The way you do that is to type four tildes in a row. I usually type it with two dashes in the front because that's what I was taught by a fellow user here, like this: <nowiki>--~~~~</nowiki>. Then the wiki transforms the <nowiki>~~~~</nowiki> into your username with a link to your user page, plus a timestamp. Sorry if you knew that already and just forgot; I forget sometimes myself.

: As for your actual questions, well, I'm afraid I don't know for sure whether to exclude sums. But I would say that where you've replaced "direct approximation" with "closest approximation", I would at least preserve a link to the page for "direct approximation", since that's the name under which that concept is discussed elsewhere on the wiki at this time. I hope that makes sense, if not, just let me know. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 23:50, 31 July 2022 (UTC)

: I didn't know about the username thing (or had forgotten) so thanks. I have not replaced "direct approximation" except in my failed definition in two daughter pages. I hope someone can assist with my question. --[[User:Martins|Martins]] ([[User talk:Martins|talk]]) 20:14, 1 August 2022 (UTC)

== WP:NOUN ==

The page should be titled "Consistency" per [[Wikipedia:WP:NOUN|WP:NOUN]]. I cannot move it myself because [[Consistency]] has a non-empty edit history. The previous versions of that page are soft redirects and no significant information will be lost if the page is overwritten. If there are no objections, I would like to request that an admin moves the page. --[[User:Fredg999|Fredg999]] ([[User talk:Fredg999|talk]]) 05:20, 21 February 2023 (UTC)

== q-odd-limit harmonics? prime harmonics? ==

The current way of writing, not cover<del>ed</del> the case that direct mapping of up-to q-th harmonics is already inconsistent, e. g. Dual-fifth system.

Now I'm rewriting the article "一貫性", I think the story we approximate all q-limit interval at first, then we check consistency... --[[User:Dummy index|Dummy index]] ([[User talk:Dummy index|talk]]) 14:37, 28 April 2023 (UTC)

: If I understand correctly, your concern is that consistency is defined on edos assuming an infinitely long map (val) based specifically on all prime harmonics, therefore excluding maps with composite or fractional subgroups. It is good to keep in mind that the choice of the map affects the consistency; for example, 18edo is consistent in the 7-odd-limit, but 18b (second-best mapping for prime 3) is only consistent in the 3-odd-limit, because then 5/3 wouldn't be mapped to its direct approximation. And so we find that a dual-fifth system such as 35edo has a well-defined consistency if we assume its [[integer uniform map]] ([[patent val]]) — in this case 7-odd-limit, because 9/1 is not mapped to its direct approximation —, but if we coupled 35edo with a 2.9.5.7.11 subgroup map, we would indeed have no way to reach the interval 3/1 at all. Since the goal of consistency is to check if a given equal temperament (edo + map) can map all intervals in an odd-limit to their direct approximation, it wouldn't make sense to allow subgroups that skip over certain intervals. Therefore, a uniform map, or at least a map based on a full prime limit, should be used to evaluate an equal temperament's consistency. It would be interesting to check which equal temperaments have a higher consistency limit with a "warted" map compared to the standard one; for example, 11edo is only consistent in the 3-odd-limit, but 11b is consistent in the 7-odd-limit (but not 9-odd-limit because 9/5 is not mapped to its direct approximation). --[[User:Fredg999|Fredg999]] ([[User talk:Fredg999|talk]]) 16:20, 29 April 2023 (UTC)

:: Sorry, I don't talk about we should/shoudn't use subgroups. I talk about the Opening clause of the article. The mathematical definition section is fine <del>(but we should add the wording that determines the range of the r, odd-limit and subgroup or any other)</del>. Opening clause says... Oh, sorry I see it's no problem. 18edo in the 9-odd-limit maps 3/1 to 29 steps, 9/1 to 57 steps, therefore difference between 9/1 and 3/1 doesn't give closest approximation of 3/1.

:: Hence, I think 18b doesn't map 3/1 as closest approximation. Difference between 3/1 and 1/1 doesn't give closest approximation of 3/1. Wouldn't the premise of the discussion be different? --[[User:Dummy index|Dummy index]] ([[User talk:Dummy index|talk]]) 06:52, 30 April 2023 (UTC)

::: All edos are consistent in the 3-odd-limit since there's only 1, 3/2 and 4/3 to consider. 1 is by definition pure and closest. Take the closest 3/2 and that guarantees its octave complement 4/3 is closest too. The consistency is enabled by the patent val and not any other vals, so you're right that 18b is "inconsistent" tho consistency is defined for equal tunings rather than equal temperaments. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 08:45, 30 April 2023 (UTC)

:: I have noticed that 23edo is consistent in the no-1's 7-odd-limit ({1/1(3/3 and 5/5 and 7/7), 5/3, 3/5, 7/3, 3/7, 7/5, 5/7}). (Oh, you must have said this on 11edo.) But this is not to say that we consider 23d, it was just almost consistent and similar to 23d. <del>Direct approximation on 18edo gives 9/1 to odd-number steps, it can't be p-limit 18 nor 18b.</del> Wait, now we have to derive the mapping of up-to 7 harmonics from no-1's 7-odd-limit intervals, but can't determine uniquely... ({{val|23 36 53 64}} or {{val|23 37 54 65}} or {{val|23 38 55 66}} or ...) --[[User:Dummy index|Dummy index]] ([[User talk:Dummy index|talk]]) 13:57, 7 June 2023 (UTC)

Under consideration. By the way,

<blockquote>For instance, 12edo is consistent in the no-11's, no-13's 19-odd-limit, ...</blockquote>

Do I need the apostrophe? --[[User:Dummy index|Dummy index]] ([[User talk:Dummy index|talk]]) 15:50, 9 June 2023 (UTC)

@@ Line 49: / Line 49: @@
 :: Sorry for the confusion: I meant this page, the main page for ''consistency'', not the main page of the entire wiki, in the manner you've described above. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 20:07, 29 July 2022 (UTC)
+::: Right, that makes sense. I'll ponder over the idea I mentioned about the Conventions page, since this gave me the idea anyway. --[[User:Fredg999|Fredg999]] ([[User talk:Fredg999|talk]]) 22:16, 29 July 2022 (UTC)
+== Differences and Sums ==
+The main definition (with q-odd limit) only says "difference"; the definition in terms of a chord says "interval between"; I guess these make sense because some sums would stray outside the limit or the chord.  But the mathematical definition is in terms of a set, and uses a sum (the first example also uses a sum, but the example is clearly valid and could be re-ordered into a difference).  Is it correct to exclude sums?
+PS:
+* distinct vs unique: covered by cmloegcmluin above, thanks.
+* closest vs nearest: no difference in meaning, I think; I chose "closest".
+* best vs closest: I argue that "best" can mean different things depending on your purpose, whereas "closest" is simply factual.
+--[[User:Martins|Martins]] ([[User talk:Martins|talk]]) 20:14, 1 August 2022 (UTC)
+: Hi Steve! Thanks for posting here. I corrected the spelling of my username in your post, hope you don't mind (I admit it's a tough one to spell, haha). Also, FYI, people tend to sign their posts here. The way you do that is to type four tildes in a row. I usually type it with two dashes in the front because that's what I was taught by a fellow user here, like this: <nowiki>--~~~~</nowiki>. Then the wiki transforms the <nowiki>~~~~</nowiki> into your username with a link to your user page, plus a timestamp. Sorry if you knew that already and just forgot; I forget sometimes myself.
+: As for your actual questions, well, I'm afraid I don't know for sure whether to exclude sums. But I would say that where you've replaced "direct approximation" with "closest approximation", I would at least preserve a link to the page for "direct approximation", since that's the name under which that concept is discussed elsewhere on the wiki at this time. I hope that makes sense, if not, just let me know. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 23:50, 31 July 2022 (UTC)
+: I didn't know about the username thing (or had forgotten) so thanks.  I have not replaced "direct approximation" except in my failed definition in two daughter pages.  I hope someone can assist with my question.  --[[User:Martins|Martins]] ([[User talk:Martins|talk]]) 20:14, 1 August 2022 (UTC)
+== WP:NOUN ==
+The page should be titled "Consistency" per [[Wikipedia:WP:NOUN|WP:NOUN]]. I cannot move it myself because [[Consistency]] has a non-empty edit history. The previous versions of that page are soft redirects and no significant information will be lost if the page is overwritten. If there are no objections, I would like to request that an admin moves the page. --[[User:Fredg999|Fredg999]] ([[User talk:Fredg999|talk]]) 05:20, 21 February 2023 (UTC)
+== q-odd-limit harmonics? prime harmonics? ==
+The current way of writing, not cover<del>ed</del> the case that direct mapping of up-to q-th harmonics is already inconsistent, e. g. Dual-fifth system.
+Now I'm rewriting the article "一貫性", I think the story we approximate all q-limit interval at first, then we check consistency... --[[User:Dummy index|Dummy index]] ([[User talk:Dummy index|talk]]) 14:37, 28 April 2023 (UTC)
+: If I understand correctly, your concern is that consistency is defined on edos assuming an infinitely long map (val) based specifically on all prime harmonics, therefore excluding maps with composite or fractional subgroups. It is good to keep in mind that the choice of the map affects the consistency; for example, 18edo is consistent in the 7-odd-limit, but 18b (second-best mapping for prime 3) is only consistent in the 3-odd-limit, because then 5/3 wouldn't be mapped to its direct approximation. And so we find that a dual-fifth system such as 35edo has a well-defined consistency if we assume its [[integer uniform map]] ([[patent val]]) — in this case 7-odd-limit, because 9/1 is not mapped to its direct approximation —, but if we coupled 35edo with a 2.9.5.7.11 subgroup map, we would indeed have no way to reach the interval 3/1 at all. Since the goal of consistency is to check if a given equal temperament (edo + map) can map all intervals in an odd-limit to their direct approximation, it wouldn't make sense to allow subgroups that skip over certain intervals. Therefore, a uniform map, or at least a map based on a full prime limit, should be used to evaluate an equal temperament's consistency. It would be interesting to check which equal temperaments have a higher consistency limit with a "warted" map compared to the standard one; for example, 11edo is only consistent in the 3-odd-limit, but 11b is consistent in the 7-odd-limit (but not 9-odd-limit because 9/5 is not mapped to its direct approximation). --[[User:Fredg999|Fredg999]] ([[User talk:Fredg999|talk]]) 16:20, 29 April 2023 (UTC)
+:: Sorry, I don't talk about we should/shoudn't use subgroups. I talk about the Opening clause of the article. The mathematical definition section is fine <del>(but we should add the wording that determines the range of the r, odd-limit and subgroup or any other)</del>. Opening clause says... Oh, sorry I see it's no problem. 18edo in the 9-odd-limit maps 3/1 to 29 steps, 9/1 to 57 steps, therefore difference between 9/1 and 3/1 doesn't give closest approximation of 3/1.
+:: Hence, I think 18b doesn't map 3/1 as closest approximation. Difference between 3/1 and 1/1 doesn't give closest approximation of 3/1. Wouldn't the premise of the discussion be different? --[[User:Dummy index|Dummy index]] ([[User talk:Dummy index|talk]]) 06:52, 30 April 2023 (UTC)
+::: All edos are consistent in the 3-odd-limit since there's only 1, 3/2 and 4/3 to consider. 1 is by definition pure and closest. Take the closest 3/2 and that guarantees its octave complement 4/3 is closest too. The consistency is enabled by the patent val and not any other vals, so you're right that 18b is "inconsistent" tho consistency is defined for equal tunings rather than equal temperaments. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 08:45, 30 April 2023 (UTC)
+:: I have noticed that 23edo is consistent in the no-1's 7-odd-limit ({1/1(3/3 and 5/5 and 7/7), 5/3, 3/5, 7/3, 3/7, 7/5, 5/7}). (Oh, you must have said this on 11edo.) But this is not to say that we consider 23d, it was just almost consistent and similar to 23d. <del>Direct approximation on 18edo gives 9/1 to odd-number steps, it can't be p-limit 18 nor 18b.</del> Wait, now we have to derive the mapping of up-to 7 harmonics from no-1's 7-odd-limit intervals, but can't determine uniquely... ({{val|23 36 53 64}} or {{val|23 37 54 65}} or {{val|23 38 55 66}} or ...) --[[User:Dummy index|Dummy index]] ([[User talk:Dummy index|talk]]) 13:57, 7 June 2023 (UTC)
+Under consideration. By the way,
+<blockquote>For instance, 12edo is consistent in the no-11's, no-13's 19-odd-limit, ...</blockquote>
+Do I need the apostrophe?  --[[User:Dummy index|Dummy index]] ([[User talk:Dummy index|talk]]) 15:50, 9 June 2023 (UTC)