Talk:Patent val: Difference between revisions

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::::::::::: 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)

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 ::::::::::: 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)