Xenharmonic Wiki talk:Things to do: Difference between revisions
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== Reduce over-2 and prime-limit bias == | == Reduce over-2 and prime-limit bias == | ||
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 and cannot always be obtained from the approximations for primes. The reason that Godtone and I originally proposed this is not to go full primodal, but 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) | ||