Talk:Optimal ET sequence

Is "Val list" the best name for this thing?

I note that this isn't really a list of maps ("vals"), like ⟨12 19 28], but actually a list of ETs given in wart notation. So I could see this being called an "ET list", with the other distinguishing facts left opaque (those being that they are [a] only ETs whose maps are uniform maps ("GPVs") and [b] where each subsequent map improves upon TE error). Unless some people don't consider e.g. 17p to be a different ET from 17c, but only different maps for the same ET, but then that's getting pretty philosophical I think. Or the title could attempt to convey both those facts, such as "Error-decreasing GPV sequence" (though of course I would prefer my own term "uniform map", I understand I should defer to the convention here.) --Cmloegcmluin (talk) 17:47, 18 November 2021 (UTC)

You're right. Val list isn't the best name for this thing. Imo list should be avoided and sequence is a good substitute. ET sequence is a name I reckon very proper. I'm afraid further constraints like error-decreasing or GPV are less essential, but are somewhat heuristic choices that help to shape a neat sequence. The error-decreasing constraint is good at limiting the length of the sequence. It's possible to make another sequence that's quite similar but different – the MOS numbers for the optimal tuning. The GPV constraint is handy in that it makes the sequence terminate. FloraC (talk) 19:14, 18 November 2021 (UTC)

Oh, interesting — I didn't know the GPV constraint made the sequence terminate. Reviewing your code, it looks more like one of a couple arbitrary thresholds/ranges are ending the search; even `find_next_gpv` doesn't seem to have an exit condition related to having found the final GPV. But perhaps I'm misinterpreting one or many things here :) When you have a minute, would you be able to explain how/why this is or what you meant? And also, does the article need a correction with regards to that fact, then? I wrote, "No standard beginning or ending cutoff to the list has been specified", but if the GPV constraint forces termination, then I'd think that'd constitute such a "standard ending" to the list.

After I understand this particular detail, I'll make a brief post on the Facebook Xenwiki Work Group and the Discord wiki channel to see if anyone has any dispute with renaming this "ET sequence", which I agree should suit this feature well (and better than "val list"). --Cmloegcmluin (talk) 19:36, 23 November 2021 (UTC)

The sequence "terminates" as no more GPVs turn up after a sufficiently large index. Any temperament has a fixed error, whereas the sequence of all GPV's errors converges to zero, so all GPVs has less error than the temperament past a certain point. Obviously my code doesn't know it, and you must set the range yourself. FloraC (talk) 21:28, 23 November 2021 (UTC)

I expect that most readers who see "optimal GPV sequence" in temperament catalogs, if they can figure it out at all, will assume that "GPV" must mean "supporting ET" (i.e. "ET that supports this temperament"), which of course it does not. So I think these should be called "optimal supporting-ET sequence" or if that's considered too long then "optimal ET sequence" since why would it be listed against the temperament if it didn't support it. Is there such a thing as an ET that doesn't have a uniform map/GPV? If so, the uniform map/GPV requirement can simply be made part of the optimality requirement. Dave Keenan (talk) 02:13, 4 May 2023 (UTC)