Xenharmonic Wiki talk:Things to do: Difference between revisions
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: I don't think it's our place as wiki editors to pass judgement on what an edo can do. Our job is just to report the facts. But any rating or metric will have some arbitrariness. We have the absolute and relative errors of each prime right there at the top of the edo's page. This lets people make their own decisions. Not to say that what you're doing isn't a worthwhile endeavor. I just don't think it belongs on the edo pages. Perhaps it could be a separate page on the xenwiki called "Godtone's analysis of EDO subgroups" or some such, that the main EDO page links to. --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 07:59, 24 January 2021 (UTC) | : I don't think it's our place as wiki editors to pass judgement on what an edo can do. Our job is just to report the facts. But any rating or metric will have some arbitrariness. We have the absolute and relative errors of each prime right there at the top of the edo's page. This lets people make their own decisions. Not to say that what you're doing isn't a worthwhile endeavor. I just don't think it belongs on the edo pages. Perhaps it could be a separate page on the xenwiki called "Godtone's analysis of EDO subgroups" or some such, that the main EDO page links to. --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 07:59, 24 January 2021 (UTC) | ||
:: The problem with just having a table of prime harmonics is that it only focuses on intervals of the form ''p''/2, and the approximations of many other intervals (which are important for subgroup temperaments) aren't immediately visible. The reason that Godtone and I originally proposed this is to reduce the bias towards edos and temperaments that approximate /2 prime harmonics well and be more fair towards subgroup temperaments such as: | :: That's a fair criticism of trying to box EDOs into subgroups, there's too much subjectivity involved. The problem with just having a table of prime harmonics is that it only focuses on intervals of the form ''p''/2, and the approximations of many other intervals (which are important for subgroup temperaments) aren't immediately visible. The reason that Godtone and I originally proposed this is to reduce the bias towards edos and temperaments that approximate /2 prime harmonics well and be more fair towards subgroup temperaments such as: | ||
::* 14edo as a 5:7:9:11 or 2.7/5.9/5.11/5 temperament | ::* 14edo as a 5:7:9:11 or 2.7/5.9/5.11/5 temperament | ||
::* 18edo as a 12:13:14:17:19:23:27 or 2.9.13/12.7/6.17/12.23/12 temperamnet | ::* 18edo as a 12:13:14:17:19:23:27 or 2.9.13/12.7/6.17/12.23/12 temperamnet | ||
::* 23edo as a 3:5:7:11 or 2.5/3.7/3.11/3 temperament | ::* 23edo as a 3:5:7:11 or 2.5/3.7/3.11/3 temperament | ||
:: So I propose that every edo page should have a subpage that catalogues the best approximations in the edo of all the intervals in the 29-odd limit. The reason I propose the 29-odd limit is that 7n-edos approximate 29/16 to within ~1c. Up to inversional equivalence and omitting 1/1 and 2/1, that's 91 intervals. If that's overkill, then the primes table at the top of every edo page should actually have all the odd harmonics from 3 to 29 and their best approximations. [[User:IlL|Inthar]] ([[User talk:IlL|talk]]) 08:34, 24 January 2021 (UTC) | :: So I propose that every edo page should have a subpage that catalogues the best approximations in the edo of all the intervals in the 29-odd limit. The reason I propose the 29-odd limit is that 7n-edos approximate 29/16 to within ~1c. Up to inversional equivalence and omitting 1/1 and 2/1, that's 91 intervals. If that's overkill, then the primes table at the top of every edo page should actually have all the odd harmonics from 3 to 29 and their best approximations. [[User:IlL|Inthar]] ([[User talk:IlL|talk]]) 08:34, 24 January 2021 (UTC) | ||