Xenharmonic Wiki:Things to do: Difference between revisions

* I pick the variance over the standard deviation because squaring the error leads to a "least-squares" optimisation, which is then much more "compatible" with the tuning optimisations represented by the Riemann Zeta function.

* 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.