Xenharmonic Wiki talk:Things to do: Difference between revisions

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 : A lot of problems in this wiki can be fixed by linking improvement. The navigation will be much more friendly to novices if there are straightforward, logical links between scala files, scale structure pages, and temperaments. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 09:34, 27 January 2021 (UTC)
+:: I hadn't seen this before.
+:: I'm sure I've written this several times, but the "right" answer to this is to complete organizing things into "subgroup families," which is a nontrivial problem. Originally, the theory involved only prime limits, and after we started looking at subgroup temperaments, Gene Smith tried a variety of different naming systems for the other ones, all of which are incompatible and for which the consensus is that these are suboptimal. For instance, [[The Archipelago]] is one early naming system which was subsequently abandoned, followed by some work algorithmically naming them after [[dyadic chord|dyadic chords]] and ultimately the [[Chromatic pairs]] page. The idea on the latter page was to see subgroup temperaments as being derived from full-limit temperaments and then give it like a weird, variant/misspelled name. But, it is clearly not great for us to have a thousand different versions of "Porcupine" named "Porkypine" or whatever, or "Mohaha" and "Mohoho" as subgroup versions of Mohajira.
+:: The correct answer would be to generalize the way "families" are laid out, so that instead of 2.3.5.7 temperaments being "extensions" of 2.3.5 temperaments, we have 2.3.5.7 temperaments "extending" both 2.3.5, 2.3.7, 2.5.7, or even 2.3.7/5, etc. Then we can look for just the "best" "root" temperaments which start a tree of extensions and focus on those. These would become the "main" temperaments of the theory, and everything else would be different extensions. For instance, "meantone" is a "main" temperament, and we know there are many meantone extensions ("meantone", "meanpop", "flattone", "meanenneadecal", etc), but these are all grouped in the "meantone" family. Similarly, the 2.3.11 243/242 temperament (called "neutral") is a *VERY* important subgroup temperament of which mohajira, suhajira, migration, "mohoho" and "mohaha" and *all* of these related temperaments are extensions of.
+:: This is a very interesting and nontrivial problem. Not every "good" comma leads to a "good" rank-2 temperament, for instance. 36/35 is simpler than 49/48, for instance, but 49/48 is "better" for rank-2 temperaments because it is supported on a simple rank-3 subgroup (2.3.7) whereas 36/35 doesn't have any good rank-3 subgroup that it is part of. Similarly, 225/224 is not as "good" as 1029/1024 for the same reason.
+:: There is quite a bit of partially developed theory on this and a few missing puzzle pieces. I don't know how mathematical you Discord folks are, but perhaps someone sees something that I'm missing on how to put it all together. But it would be *great* to get this done, as we could then just "close the book" on this subgroup temperament problem and then move onto whatever the next part of the theory is.
+:: Lastly, the consensus we came to on Facebook was, rather than just arbitrarily organizing them into families, we ought to be somewhat methodical in figuring out which ones really matter, by ranking them the same way we do temperaments and etc. So I hope that any proposed reorganizational scheme will either be compatible with this structure, or leave us adequate room to do this properly later. [[User:Mike Battaglia|Mike Battaglia]] ([[User talk:Mike Battaglia|talk]]) 02:41, 13 April 2021 (UTC)
 === New format for temperament entries ===