Xenharmonic Wiki: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 best approximations of primes. | 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 directly obtained from the best approximations of primes. | ||
So we 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 for choosing 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. | So we 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 for choosing 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. | ||
This can be discussed in [[Xenharmonic Wiki talk: Things to do#Reduce over-2 and prime-limit bias]]. | This can be discussed in [[Xenharmonic Wiki talk: Things to do#Reduce over-2 and prime-limit bias]]. | ||