Talk:Patent val: Difference between revisions

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:::::::::: 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)

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 :::::::::: 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)