Talk:Radical interval - Revision history

VectorGraphics: VectorGraphics moved page Talk:Fractional monzo to Talk:Radical interval: Generalize scope from "fractional monzos" to the things they represent

2025-03-05T21:55:02Z

VectorGraphics moved page Talk:Fractional monzo to Talk:Radical interval: Generalize scope from "fractional monzos" to the things they represent

← Older revision	Revision as of 21:55, 5 March 2025
(No difference)

Cmloegcmluin: reminder to admins w/ editing rights

2023-05-06T22:58:42Z

reminder to admins w/ editing rights

← Older revision		Revision as of 22:58, 6 May 2023
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	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 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)

Cmloegcmluin: /* See also link to Projection article */ new section

2022-12-11T19:17:26Z

See also link to Projection article: new section

← Older revision		Revision as of 19:17, 11 December 2022
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	:: 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)		:: 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)

Cmloegcmluin: /* Frobenius norm */

2022-11-26T19:55:36Z

Frobenius norm

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	: 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)		: 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)

FloraC: /* Frobenius norm */ re

2022-11-26T13:48:30Z

Frobenius norm: re

← Older revision		Revision as of 13:48, 26 November 2022
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	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)		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)

Cmloegcmluin: /* Frobenius norm */

2022-11-26T10:09:00Z

Frobenius norm

← Older revision		Revision as of 10:09, 26 November 2022
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	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 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)

Cmloegcmluin at 22:46, 22 July 2021

2021-07-22T22:46:37Z

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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)		::: 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)

Cmloegcmluin at 20:23, 17 April 2021

2021-04-17T20:23:04Z

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	:: Often the way with maths. Simple concepts that lead to very complicated implications when you iterate upon them. The clever stuff comes when you combine several fractional monzos to create an eigenmonzo that hits lots of near-just intervals in a small number of notes, as in miracle. Getting the numbers for all those various minmax and least squares tunings properly computed can be a real pain. --[[User:Yourmusic Productions\|Yourmusic Productions]] ([[User talk:Yourmusic Productions\|talk]]) 08:03, 17 April 2021 (UTC)		:: Often the way with maths. Simple concepts that lead to very complicated implications when you iterate upon them. The clever stuff comes when you combine several fractional monzos to create an eigenmonzo that hits lots of near-just intervals in a small number of notes, as in miracle. Getting the numbers for all those various minmax and least squares tunings properly computed can be a real pain. --[[User:Yourmusic Productions\|Yourmusic Productions]] ([[User talk:Yourmusic Productions\|talk]]) 08:03, 17 April 2021 (UTC)

			::: 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)

Yourmusic Productions: More talk.

2021-04-17T08:03:43Z

More talk.

← Older revision		Revision as of 08:03, 17 April 2021
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	: Thanks for the explanation. Well that makes sense to me, but what you've just described seems to only be a fractional monzo, the idea described in the introduction section of this page. It then goes on to define eigenmonzo as something that builds upon that concept. At least that's what it seems like to me. If fractional monzo = eigenmonzo, if it's that simple, then I think the page could be made a bit clearer. --[[User:Cmloegcmluin\|Cmloegcmluin]] ([[User talk:Cmloegcmluin\|talk]]) 22:11, 16 April 2021 (UTC)		: Thanks for the explanation. Well that makes sense to me, but what you've just described seems to only be a fractional monzo, the idea described in the introduction section of this page. It then goes on to define eigenmonzo as something that builds upon that concept. At least that's what it seems like to me. If fractional monzo = eigenmonzo, if it's that simple, then I think the page could be made a bit clearer. --[[User:Cmloegcmluin\|Cmloegcmluin]] ([[User talk:Cmloegcmluin\|talk]]) 22:11, 16 April 2021 (UTC)

			:: Often the way with maths. Simple concepts that lead to very complicated implications when you iterate upon them. The clever stuff comes when you combine several fractional monzos to create an eigenmonzo that hits lots of near-just intervals in a small number of notes, as in miracle. Getting the numbers for all those various minmax and least squares tunings properly computed can be a real pain. --[[User:Yourmusic Productions\|Yourmusic Productions]] ([[User talk:Yourmusic Productions\|talk]]) 08:03, 17 April 2021 (UTC)

Cmloegcmluin at 22:11, 16 April 2021

2021-04-16T22:11:43Z

← Older revision		Revision as of 22:11, 16 April 2021
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	The main use of these is to represent complex numbers to infinite precision in a smaller space than typing out an endless sequence of nonrepeating digits after the decimal place. A simple example would be demonstrating the difference between 1/3 comma meantone and 19edo. 1/3 comma meantone takes three generators to reach 10/3, which means the fifth's eigenmonzo is \|1/3 -1/3 1/3>. (2x5/3)^(1/3) Meanwhile 19edo's 5th has an eigenmonzo of \|11/19>, as it's a simple fraction of a power of 2. --[[User:Yourmusic Productions\|Yourmusic Productions]] ([[User talk:Yourmusic Productions\|talk]]) 19:31, 16 April 2021 (UTC)		The main use of these is to represent complex numbers to infinite precision in a smaller space than typing out an endless sequence of nonrepeating digits after the decimal place. A simple example would be demonstrating the difference between 1/3 comma meantone and 19edo. 1/3 comma meantone takes three generators to reach 10/3, which means the fifth's eigenmonzo is \|1/3 -1/3 1/3>. (2x5/3)^(1/3) Meanwhile 19edo's 5th has an eigenmonzo of \|11/19>, as it's a simple fraction of a power of 2. --[[User:Yourmusic Productions\|Yourmusic Productions]] ([[User talk:Yourmusic Productions\|talk]]) 19:31, 16 April 2021 (UTC)

			: Thanks for the explanation. Well that makes sense to me, but what you've just described seems to only be a fractional monzo, the idea described in the introduction section of this page. It then goes on to define eigenmonzo as something that builds upon that concept. At least that's what it seems like to me. If fractional monzo = eigenmonzo, if it's that simple, then I think the page could be made a bit clearer. --[[User:Cmloegcmluin\|Cmloegcmluin]] ([[User talk:Cmloegcmluin\|talk]]) 22:11, 16 April 2021 (UTC)