Talk:Constrained tuning

KE is not CTWE

According to Mike (here: https://www.facebook.com/groups/xenharmonicmath/posts/2549402798533260/?comment_id=2561594020647471&reply_comment_id=2566545800152293), Kees tuning was defined as destretched Tenney-Weil (destretched-octave minimax-lils-S), so I have to assume that Kees-Euclidean would be destretched Tenney-Weil-Euclidean (destretched-octave minimax-E-lils-S), not constrained Tenney-Weil-Euclidean (held-octave minimax-E-lils-S).

I also have evidence that this is so, because after followed his advice, I was finally able to get my code to agree with historically posted Kees and Kees-Euclidean tuning results (here: https://www.facebook.com/groups/xenharmonicmath/posts/2363908480416027/?comment_id=2363994823740726 and here: https://www.facebook.com/groups/xenharmonicmath/posts/2086012064872338)

I think we (addressing Flora here) briefly covered this on Discord somewhat recently, but maybe you haven't had time to update the article since.

Yes, I certainly agree that it's unfortunate and confusing that Kees tuning does not correspond to minimizing the tuning with damage weight based on Kees semiheight (and KE on KE seminorm), but that's just apparently how it is.

This might require some updates here as well: Weil_norm,_Tenney-Weil_norm,_and_TWp_interval_and_tuning_space#Kees-Euclidean_seminorm

If you wanted to lobby to revise the definition, I wouldn't be opposed. But since I prefer Dave and I's systematic descriptive naming for tuning schemes, I don't really have a horse in the race.

--Cmloegcmluin (talk) 19:17, 6 February 2023 (UTC)

I do prefer CTWE to KE as its name, so I'll simply remove KE from this article. But I don't see why Mike has kept that part in Weil norm, Tenney-Weil norm, and TWp interval and tuning space #Kees-Euclidean seminorm, if the same term is historically associated with something else. FloraC (talk) 11:44, 7 February 2023 (UTC)

Oh, my. Yes, I can see that he himself added that information: https://en.xen.wiki/index.php?title=Weil_norm%2C_Tenney-Weil_norm%2C_and_TWp_interval_and_tuning_space&type=revision&diff=91295&oldid=91294 Well, that's even more confusing, then! Maybe he wasn't thinking about the inconsistency in naming between tuning and norm when he wrote that, and assumed that logically they would match. The tests in my code confirm that the historical KE results which he posted equal the destretched-octave version of this tuning, not the held-octave.

However, I see that he used the pseudoinverse to find his results, which I'd suppose would correspond with the held-octave (constrained) version, not the destretched. So... perhaps in the special case of Euclideanized tunings, the destretched and held versions work out the same?

Unfortunately I don't have time to look into this further. If you find anything out, please let me know, as I may need to amend D&D's guide accordingly. Thanks for letting me know about this complication. --Cmloegcmluin (talk) 16:23, 7 February 2023 (UTC)

OK, I see there's some confusion about what the term KE actually means: if it's constrained-octave or destretched-octave.

I'm not quite sure myself, actually. There seems to be a long history of these terms being used in conflicting ways, and going back through some of my notes I see that I've used both at one point (probably because someone else I was talking to at the time insisted it be one way or the other).

I do agree KE would make the most sense as constrained octave. In the recent discussions we've been having, I've been referring to the constrained octave version. I'd like to see if both/either of these results are similar to POTE. Mike Battaglia (talk) 02:39, 19 March 2024 (UTC)

CTWE, CWE, KE, etc

The way the term "TWE" is being used on this page is not correct. I'm not sure where the confusion is from, but the Tenney-Weil norm is a general norm with two free parameters p and k that interpolate between Wp and Tp. For p=2, then there's one free parameter k, and if k=0 it's TE and if k=1 it's WE. The thing called KE would be the "CWE" tuning, not in general the "CTWE" tuning. It'd be a special case of CTWE with k=1, but of course you don't want to say CTWE = CWE by default. Mike Battaglia (talk)

I did set the default CTWE to k = 1 in my code cuz in the case of other norms, like the equilateral one where each prime is weighted the same, it's useful to introduce a 30-degree skew like Weil and that needs a term. Calling it "equilateral-Weil-Euclidean" is a possibility and if so, the Tenney-weighted counterpart is automatically "Tenney-Weil". Otherwise I'd always have to say "equilateral-Weil[1]-Euclidean" with the number in the brackets specifying that k = 1. So what do you think? FloraC (talk) 03:27, 19 March 2024 (UTC)