Talk:Consistency: Difference between revisions

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::: 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}). But this is not to say that we consider 23d, it was just almost consistent ~~like a~~ 23d. Direct approximation on 18edo gives 9/1 to odd-number steps, it can't be p-limit 18 nor 18b.

:: 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)

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 ::: 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}). But this is not to say that we consider 23d, it was just almost consistent like a 23d. Direct approximation on 18edo gives 9/1 to odd-number steps, it can't be p-limit 18 nor 18b.
+:: 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)