Xenharmonic Wiki talk:Things to do: Difference between revisions
→Set a semi-objective standard for classifying edos as subgroup temperaments: More moved to here |
→Set a semi-objective standard for classifying edos as subgroup temperaments: Reply to Godtone's proposal |
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* We can take an alternative strategy to tuning a subgroup less focused on the regular temperament theory interpretation and more focused on what consonant chords and intervals are approximated that you want to use. In such a case, you pick ''any'' subset of X corresponding to ''any'' subset of L, which is to say that the r-dimensional vectors ''are not'' required (or even recommended) to be linearly independent. Then the subset of L represents a generalisation of [[odd limit]]s, where odd limits are specific to where your subset of L is only odd harmonics due to the discarding of 2's in the prime factorisations due to being specific to ED2s. This interpretation/use fits very nicely with the notion of [[Consistent#Consistency_to_distance_d|consistency to distance d]], with the standard deviation being an "expected overall consistency" which is less discrete/rigid. The only potential problem with this is it seems like a very large number of possibilities can result with different subsets being preferable for subjective reasons. | * We can take an alternative strategy to tuning a subgroup less focused on the regular temperament theory interpretation and more focused on what consonant chords and intervals are approximated that you want to use. In such a case, you pick ''any'' subset of X corresponding to ''any'' subset of L, which is to say that the r-dimensional vectors ''are not'' required (or even recommended) to be linearly independent. Then the subset of L represents a generalisation of [[odd limit]]s, where odd limits are specific to where your subset of L is only odd harmonics due to the discarding of 2's in the prime factorisations due to being specific to ED2s. This interpretation/use fits very nicely with the notion of [[Consistent#Consistency_to_distance_d|consistency to distance d]], with the standard deviation being an "expected overall consistency" which is less discrete/rigid. The only potential problem with this is it seems like a very large number of possibilities can result with different subsets being preferable for subjective reasons. | ||
--[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 04:01, 22 January 2021 (UTC) | --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 04:01, 22 January 2021 (UTC) | ||
: @Godtone your proposal looks like a measure of absolute error very similar to [[TE error]] (weighted RMS error of primes). I suggest you check that if you have not. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 11:54, 22 January 2021 (UTC) | |||