Talk:Constrained tuning: Difference between revisions

(4 intermediate revisions by 2 users not shown)

Line 17:

: 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. [[User:FloraC|FloraC]] ([[User talk: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.

:: Oh, my. Yes, I can see that he himself added that information: https://en.xen.wiki/index.php?title=Weil_norm%2C_Tenney%E2%80%93Weil_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?

Line 41:

::: Isn't the "Hahn norm" a modification on Hahn distance and is dependent on a chosen maximum odd limit? For example in the 7-odd-limit 2, 3, 5, and 7 are weighted equal whereas in the 9-odd-limit 2, 9, 5, and 7 are weighted equal. At least that's what you documented in the ''Hahn distance'' article. But there's a norm where all primes are weighted equal regardless of the odd limit and is fit for those who require higher accuracy in higher primes.

::: And what I noted isn't limited to one type of weight. There's also the skewed variant of Wilson-Euclidean. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 06:26, 19 March 2024 (UTC)

:::: I don't remember anymore; I thought Gene told me at one point on IRC that the unweighted Weil norm was the Hahn norm. Looking at it now, it seems the Hahn distance is only a seminorm and it equals the unweighted version of Kees expressibility up to the 7-limit and then something else thereafter. So I'm not sure. But Tenney-Weil already means something, and Weil is "Tenney-weighted by default." So I would call your norm something else. Paul Erlich may have some ideas about if anyone's used it before. If nobody's claimed it then I say go with the Canou norm. [[User:Mike Battaglia|Mike Battaglia]] ([[User talk:Mike Battaglia|talk]]) 08:44, 19 March 2024 (UTC)

::::: Then I'm simply gonna call the skew by 30 degrees (''k'' = 1) "skewed" in the next iteration, okay? So there's skewed-equilateral-Euclidean (SEE), skewed-Wilson/Benedetti-Euclidean (SBE). Weil-Euclidean is skewed-Tenney-Euclidean which probably isn't needed as an alias. Hahn is also skewed already so the unskewed variant I laid out in my essay needs a distinct name. I might happily claim that one instead. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 09:14, 19 March 2024 (UTC)

:::::: OK, so you want some kind of general name for adding the extra coordinate in, times some scaling factor, and then taking the norm? Similarly to going from Tenney to Weil. Is that the idea? I guess you could call that "skewed." I don't want to go change all references from Weil to skewed-Tenney or whatever throughout the Wiki, but I agree it would be good to have a systematic name.

:::::: I'm not sure what unskewed Hahn would mean - wouldn't the unskewed version just be the regular L1 norm? This is sometimes called the "nopf" or "number of prime factors." Gene called the L2 version of this the Frobenius tuning, which I really think is a silly name.

:::::: There is an important difference between the Wilson and Benedetti tunings - they happen to be the same for full-limits, but I don't think they will in general for arbitrary subgroups. The Wilson tuning basically weights intervals using the sum-of-prime-factors, whereas the BE tuning uses the exponential of the Tenney norm. They happen to be the same on prime-limits because the convex hull of all intervals, divided by the exponential of their norm, is also the Wilson unit sphere, so both optimizations give the same thing.

:::::: The "exp-Weil" tuning, or whatever you want to call it, which weights intervals by max(n,d) instead of log(max(n,d)), is probably really important. I haven't thought through what the convex hull is yet. I'm not really sure if it's just the skewed Wilson norm. This would be good to figure out. [[User:Mike Battaglia|Mike Battaglia]] ([[User talk:Mike Battaglia|talk]]) 09:50, 19 March 2024 (UTC)

::::::: Well it's not as systematic as in D&D's guide, but I'm not super fond of their terminology since it something completely new. I'm just trying to add the missing pieces with minimal changes to existing materials.

::::::: Since Hahn is a norm with a parameter for the maximum relevant odd limit, it's not the same as the equilateral/nonweighted norm whenever the odd limit > 7, and so is the unskewed variant. I'm adding support for them in my code.

::::::: Interesting that Wilson and Benedetti aren't the same in subgroup tunings. I never thought about that before. It appears to me that Wilson is the most straightforward choice, so I'm not sure why you'd insist on using Benedetti. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 08:27, 20 March 2024 (UTC)

@@ Line 17: / Line 17: @@
 : 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. [[User:FloraC|FloraC]] ([[User talk: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.
+:: Oh, my. Yes, I can see that he himself added that information: https://en.xen.wiki/index.php?title=Weil_norm%2C_Tenney%E2%80%93Weil_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?
@@ Line 41: / Line 41: @@
 ::: Isn't the "Hahn norm" a modification on Hahn distance and is dependent on a chosen maximum odd limit? For example in the 7-odd-limit 2, 3, 5, and 7 are weighted equal whereas in the 9-odd-limit 2, 9, 5, and 7 are weighted equal. At least that's what you documented in the ''Hahn distance'' article. But there's a norm where all primes are weighted equal regardless of the odd limit and is fit for those who require higher accuracy in higher primes.
 ::: And what I noted isn't limited to one type of weight. There's also the skewed variant of Wilson-Euclidean. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 06:26, 19 March 2024 (UTC)
+:::: I don't remember anymore; I thought Gene told me at one point on IRC that the unweighted Weil norm was the Hahn norm. Looking at it now, it seems the Hahn distance is only a seminorm and it equals the unweighted version of Kees expressibility up to the 7-limit and then something else thereafter. So I'm not sure. But Tenney-Weil already means something, and Weil is "Tenney-weighted by default." So I would call your norm something else. Paul Erlich may have some ideas about if anyone's used it before. If nobody's claimed it then I say go with the Canou norm. [[User:Mike Battaglia|Mike Battaglia]] ([[User talk:Mike Battaglia|talk]]) 08:44, 19 March 2024 (UTC)
+::::: Then I'm simply gonna call the skew by 30 degrees (''k'' = 1) "skewed" in the next iteration, okay? So there's skewed-equilateral-Euclidean (SEE), skewed-Wilson/Benedetti-Euclidean (SBE). Weil-Euclidean is skewed-Tenney-Euclidean which probably isn't needed as an alias. Hahn is also skewed already so the unskewed variant I laid out in my essay needs a distinct name. I might happily claim that one instead. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 09:14, 19 March 2024 (UTC)
+:::::: OK, so you want some kind of general name for adding the extra coordinate in, times some scaling factor, and then taking the norm? Similarly to going from Tenney to Weil. Is that the idea? I guess you could call that "skewed." I don't want to go change all references from Weil to skewed-Tenney or whatever throughout the Wiki, but I agree it would be good to have a systematic name.
+:::::: I'm not sure what unskewed Hahn would mean - wouldn't the unskewed version just be the regular L1 norm? This is sometimes called the "nopf" or "number of prime factors." Gene called the L2 version of this the Frobenius tuning, which I really think is a silly name.
+:::::: There is an important difference between the Wilson and Benedetti tunings - they happen to be the same for full-limits, but I don't think they will in general for arbitrary subgroups. The Wilson tuning basically weights intervals using the sum-of-prime-factors, whereas the BE tuning uses the exponential of the Tenney norm. They happen to be the same on prime-limits because the convex hull of all intervals, divided by the exponential of their norm, is also the Wilson unit sphere, so both optimizations give the same thing.
+:::::: The "exp-Weil" tuning, or whatever you want to call it, which weights intervals by max(n,d) instead of log(max(n,d)), is probably really important. I haven't thought through what the convex hull is yet. I'm not really sure if it's just the skewed Wilson norm. This would be good to figure out. [[User:Mike Battaglia|Mike Battaglia]] ([[User talk:Mike Battaglia|talk]]) 09:50, 19 March 2024 (UTC)
+::::::: Well it's not as systematic as in D&D's guide, but I'm not super fond of their terminology since it something completely new. I'm just trying to add the missing pieces with minimal changes to existing materials.
+::::::: Since Hahn is a norm with a parameter for the maximum relevant odd limit, it's not the same as the equilateral/nonweighted norm whenever the odd limit > 7, and so is the unskewed variant. I'm adding support for them in my code.
+::::::: Interesting that Wilson and Benedetti aren't the same in subgroup tunings. I never thought about that before. It appears to me that Wilson is the most straightforward choice, so I'm not sure why you'd insist on using Benedetti. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 08:27, 20 March 2024 (UTC)