Talk:Radical interval: Difference between revisions

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::: Hm. Okay. Well I'm still confused about anything beyond "fractional monzo" then and I reiterate my original ask which was for a specific example or two. Thanks for trying to explain! --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 20:23, 17 April 2021 (UTC)

== Frobenius norm ==

The article says, "Perhaps the easiest norm to work with is the Frobenius norm, which simply treats a matrix like a vector and takes the square root of the sum of squares of the coefficients of the matrix. The associated tuning is the Frobenius tuning, which is the same as the unweighted RMS tuning which can be found using the pseudoinverse. If r is the rank of the temperament, the Frobenius norm of the Frobenius tuning is sqrt(r)..."

I am testing my understanding of this concept on 5-limit meantone, with mapping [⟨1 1 0] ⟨0 1 4]⟩. According to the first sentence of this, I understand that the Frobenius tuning would be √(1² + 1² + 0² + 0² + 1² + 4²) = √(1 + 1 + 1 + 16) = √19. However, according to the last sentence of this, I understand that the Frobenius tuning would be √2, which is a different result. Which is correct? I think the paragraph could be revised to make the answer clearer. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 22:46, 22 July 2021 (UTC)

I'm still seeking clarity on this issue, if anyone can provide it. Thank you! --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 10:09, 26 November 2022 (UTC)

: The Frobenius norm is said with respect to the projection map, not the temperament map. The projection map of meantone in the Frobenius tuning is [{{val| 17/33 16/33 -4/33 }}, {{val| 16/33 17/33 4/33 }}, {{val| -4/33 4/33 32/33 }}], whose norm is indeed sqrt (2). [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 13:48, 26 November 2022 (UTC)

:: Oh, wow! That's great: <math>\sqrt{\strut (\frac{17}{33})^2 + (\frac{16}{33})^2 + (\frac{-4}{33})^2 + (\frac{16}{33})^2 + (\frac{17}{33})^2 + (\frac{4}{33})^2 + (\frac{-4}{33})^2 + (\frac{4}{33})^2 + (\frac{32}{33})^2} = \sqrt{2}</math>. Thank you so much for clearing that up. Now I finally understand and accept the name "Frobenius". Maybe the article doesn't need any revision — maybe its target audience is better equipped to discern this — but FWIW this was not clear to me without your help. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 19:55, 26 November 2022 (UTC)

== See also link to Projection article ==

I recently got a dedicated article going for the projection matrix object in RTT: [[Projection]] Previously, this article on fractional monzos was the only resource available for this topic. The two topics are closely related, of course, and I think the pages should link to each other. I already had the Projection article link back here in its See also section, but I can't edit this page because it has been locked and I'm not a wiki admin. Could someone please add a See also section to this article and use it to link to the new article on projections? Thank you. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 19:17, 11 December 2022 (UTC)

I'm just posting here as a reminder to admins about this request, in case they all missed it the first time. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 22:58, 6 May 2023 (UTC)

@@ Line 8: / Line 8: @@
 ::: Hm. Okay. Well I'm still confused about anything beyond "fractional monzo" then and I reiterate my original ask which was for a specific example or two. Thanks for trying to explain! --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 20:23, 17 April 2021 (UTC)
+== Frobenius norm ==
+The article says, "Perhaps the easiest norm to work with is the Frobenius norm, which simply treats a matrix like a vector and takes the square root of the sum of squares of the coefficients of the matrix. The associated tuning is the Frobenius tuning, which is the same as the unweighted RMS tuning which can be found using the pseudoinverse. If r is the rank of the temperament, the Frobenius norm of the Frobenius tuning is sqrt(r)..."
+I am testing my understanding of this concept on 5-limit meantone, with mapping [⟨1 1 0] ⟨0 1 4]⟩. According to the first sentence of this, I understand that the Frobenius tuning would be √(1² + 1² + 0² + 0² + 1² + 4²) = √(1 + 1 + 1 + 16) = √19. However, according to the last sentence of this, I understand that the Frobenius tuning would be √2, which is a different result. Which is correct? I think the paragraph could be revised to make the answer clearer. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 22:46, 22 July 2021 (UTC)
+I'm still seeking clarity on this issue, if anyone can provide it. Thank you! --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 10:09, 26 November 2022 (UTC)
+: The Frobenius norm is said with respect to the projection map, not the temperament map. The projection map of meantone in the Frobenius tuning is [{{val| 17/33 16/33 -4/33 }}, {{val| 16/33 17/33 4/33 }}, {{val| -4/33 4/33 32/33 }}], whose norm is indeed sqrt (2). [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 13:48, 26 November 2022 (UTC)
+:: Oh, wow! That's great: <math>\sqrt{\strut (\frac{17}{33})^2 + (\frac{16}{33})^2 + (\frac{-4}{33})^2 + (\frac{16}{33})^2 + (\frac{17}{33})^2 + (\frac{4}{33})^2 + (\frac{-4}{33})^2 + (\frac{4}{33})^2 + (\frac{32}{33})^2} = \sqrt{2}</math>. Thank you so much for clearing that up. Now I finally understand and accept the name "Frobenius". Maybe the article doesn't need any revision — maybe its target audience is better equipped to discern this — but FWIW this was not clear to me without your help. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 19:55, 26 November 2022 (UTC)
+== See also link to Projection article ==
+I recently got a dedicated article going for the projection matrix object in RTT: [[Projection]] Previously, this article on fractional monzos was the only resource available for this topic. The two topics are closely related, of course, and I think the pages should link to each other. I already had the Projection article link back here in its See also section, but I can't edit this page because it has been locked and I'm not a wiki admin. Could someone please add a See also section to this article and use it to link to the new article on projections? Thank you. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 19:17, 11 December 2022 (UTC)
+I'm just posting here as a reminder to admins about this request, in case they all missed it the first time. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 22:58, 6 May 2023 (UTC)