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)

@@ 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)