Talk:Wilson norm: Difference between revisions
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I'm just posting here as a reminder to admins about these two requests, in case they all missed them the first time. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 22:58, 6 May 2023 (UTC) | I'm just posting here as a reminder to admins about these two requests, in case they all missed them the first time. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 22:58, 6 May 2023 (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/log<sub>2</sub>(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 {{nowrap|(increase in Wilson norm)/(increase in Tenney norm)}} and {{nowrap|(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.--[[User:Overthink|Overthink]] ([[User talk:Overthink|talk]]) 06:10, 1 November 2025 (UTC) | |||
Revision as of 06:10, 1 November 2025
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)
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)
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)