Talk:Wilson norm

Extract fact from main Height article to here

Presently the information about the historical origin of this terminology is only found on the page for Height in general:

This is called "Wilson's Complexity" in [[John Chalmers]]'s "Division of the Tetrachord."<ref>See http://lumma.org/tuning/chalmers/DivisionsOfTheTetrachord.pdf, page 55</ref>

I think that information is not relevant there, but should be included here instead. But I cannot edit this page as it has been locked to admins only. (Edit: I forgot to sign this the first time around, in April 2022) --Cmloegcmluin (talk) 19:22, 11 December 2022 (UTC)

Resolved. —FloraC (talk) 11:59, 1 November 2025 (UTC)

errors in "L1 Norm on Monzos" formula

It looks like we're missing a multiplication 2 in there and have an extra multiplication by 3. (Edit: I forgot to sign this the first time around, in April 2022) --Cmloegcmluin (talk) 19:22, 11 December 2022 (UTC)

I'm just posting here as a reminder to admins about these two requests, in case they all missed them the first time. --Cmloegcmluin (talk) 22:58, 6 May 2023 (UTC)

Resolved. —FloraC (talk) 11:59, 1 November 2025 (UTC)

This metric is flawed

While the overall idea of prioritizing lower limits makes sense, there's a bit of a flaw. For example, 2048/1 has a Wilson norm of 22, while 2187/1 has a Wilson norm of 21. If primes are weighted by 1/log₂(p), then this views factors of 3 as less complex than factors of 2, and prime 5 is barely more complex than 2. I propose a modified version, where if a/b is a ratio, each prime factor q of ab increases the norm of a/b by q-1, rather than q. This brings much more weight to prime 2, and lower limits in general. Here is a list of (increase in Wilson norm)/(increase in Tenney norm) and (increase in Wilson norm)/(increase in my norm) per factor of each prime in ab for a ratio a/b.

2: Wilson/Tenney: 2.000; Mine/Tenney: 1.000

3: W/T: 1.893; M/T: 1.262

5: W/T: 2.153; M/T: 1.723

7: W/T: 2.493; M/T: 2.137

11: W/T: 3.180; M/T: 2.891

13: W/T: 3.513; M/T: 3.243

17: W/T: 4.159; M/T: 3.914

19: W/T: 4.473; M/T: 4.237

As you can see, the wilson norm sees prime 13 as over half as important as 2, while mine sees 13 as less than a third as important as 2. My norm sees prime 3 as somewhat less important than 2, and prime 5 is seen as considerably more complex.--Overthink (talk) 06:10, 1 November 2025 (UTC)

You're correct that Wilson weights prime 3 less than Tenney relative to prime 2. Whether it's a flaw is debatable.

I have a section to add to this article where I'll address the extrapolation on Tenney and Wilson and note that fact along the way.

—FloraC (talk) 09:21, 1 November 2025 (UTC)

Now that I think of it, maybe it isn't so much of a flaw. Greater weight on prime 2 means encouraging voicings that contain less factors of 2 for chords. In any case, it's only a 5% difference or so, and at least prime 5 is weighted more than prime 3. Also, the 13-limit is a relatively low limit, and 1.75x as much weight as prime 2 relative to tenney makes more sense than 3.24x. --Overthink (talk) 07:12, 27 December 2025 (UTC)