Xenharmonic Wiki:Things to do: Difference between revisions

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== 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~~. 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:~~

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.

* 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

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 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.

* 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.

This can be discussed in [[Xenharmonic Wiki talk: Things to do#Reduce over-2 and prime-limit bias]].

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 == 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. 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:
+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.
-* 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
+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 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.
-* 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.
 This can be discussed in [[Xenharmonic Wiki talk: Things to do#Reduce over-2 and prime-limit bias]].