Talk:Normal forms: Difference between revisions

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:::: That sounds good to me so far. Re: IRREF, I know it's not anywhere on the page [[generator size manipulation]], because I created that page myself only a week or two ago, and it doesn't really have anything to do with IRREF. Around the same time as I was creating that page, though, I was working on the canonical form page, and I do have a section about IRREF there: [[canonical form#IRREF]] I believe my section contains every bit of information re: IRREF and its relationship to HNF that is presently on the normal list page, and supplements it with visual diagrams that make comparison easy. So I think we could simply remove the IRREF stuff from this page. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 02:21, 29 September 2021 (UTC)

:::: Thanks for making your latest changes to the page. I'm glad to have learned about the Databox template and syntax highlighting! I've gone ahead and used it myself on other pages now.

:::: I think the technique to link out to the canonical form page works fine. Maybe I'll keep it the way it is, i.e. not work to rename it to simply "defactoring" (I did add a redirect page for that, though).

:::: Re: the beep example. I recently fixed that example myself. But I've since noticed it's not quite perfect. Normal form (and canonical form) require the pivots to be positive. And you find the pivots for comma-bases by anti-transposing them, i.e. flipping them across the anti-diagonal, between top-right and bottom-left, so that when the HNF tries to put all the zeros in the bottom-left corner, it gravitates them toward where we want them: the higher primes, and commas earlier in the list. Technically, then, the canonical commas for beep should be 25/27 and 35/36, even though with n < d those are negative in pitch and that's not the typical way we write commas. It looks less off-putting when the canonical form is presented as a matrix, i.e. {{map|{{vector|0 -3 2 0}} {{vector|2 2 -1 -1}}}}, so I suggest we write them like that. Or I'm open to other suggestions.

:::: Speaking of lists vs. matrices, I would like to rename the page from "normal lists" to "normal form". I see that this reflects my preference to think of RTT structures as matrices rather than lists of vectors or covectors. Because we are using linear algebra extensively here, I think this is the natural and appropriate way to think of them. What do you think?

:::: Re: the new "Tenney minimal" section. I think it's an interesting idea to present a comma list in a different normal form than HNF (or defactored + HNF = canonical form), namely, some definition of the simplest possible ratios. However, I have several questions.

# You state that this is already the case that temperament pages use this form. I have no reason to believe they're not. But I didn't know that was the case. How do you know this?

# Do you have a definition for this normal form somewhere? If you don't yet, I would recommend excluding it from this page until it's better developed. I can easily see how the product complexity of ratios can be easily calculated individually, but minimizing the simplicity of multiple ratios may be somewhat subtle.

# Why name it "Tenney minimal"? I do not see that this term has wide use on the wiki or Discord already. It seems like an unnecessary eponym. If it is related to the Tenney height of the ratios, wouldn't it be equivalent and simpler to just refer to their product complexity?

:::: That's all for now. Thanks for helping with this. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 18:54, 29 September 2021 (UTC)

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 :::: That sounds good to me so far. Re: IRREF, I know it's not anywhere on the page [[generator size manipulation]], because I created that page myself only a week or two ago, and it doesn't really have anything to do with IRREF. Around the same time as I was creating that page, though, I was working on the canonical form page, and I do have a section about IRREF there: [[canonical form#IRREF]] I believe my section contains every bit of information re: IRREF and its relationship to HNF that is presently on the normal list page, and supplements it with visual diagrams that make comparison easy. So I think we could simply remove the IRREF stuff from this page. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 02:21, 29 September 2021 (UTC)
+:::: Thanks for making your latest changes to the page. I'm glad to have learned about the Databox template and syntax highlighting! I've gone ahead and used it myself on other pages now.
+:::: I think the technique to link out to the canonical form page works fine. Maybe I'll keep it the way it is, i.e. not work to rename it to simply "defactoring" (I did add a redirect page for that, though).
+:::: Re: the beep example. I recently fixed that example myself. But I've since noticed it's not quite perfect. Normal form (and canonical form) require the pivots to be positive. And you find the pivots for comma-bases by anti-transposing them, i.e. flipping them across the anti-diagonal, between top-right and bottom-left, so that when the HNF tries to put all the zeros in the bottom-left corner, it gravitates them toward where we want them: the higher primes, and commas earlier in the list. Technically, then, the canonical commas for beep should be 25/27 and 35/36, even though with n < d those are negative in pitch and that's not the typical way we write commas. It looks less off-putting when the canonical form is presented as a matrix, i.e. {{map|{{vector|0 -3 2 0}} {{vector|2 2 -1 -1}}}}, so I suggest we write them like that. Or I'm open to other suggestions.
+:::: Speaking of lists vs. matrices, I would like to rename the page from "normal lists" to "normal form". I see that this reflects my preference to think of RTT structures as matrices rather than lists of vectors or covectors. Because we are using linear algebra extensively here, I think this is the natural and appropriate way to think of them. What do you think?
+:::: Re: the new "Tenney minimal" section. I think it's an interesting idea to present a comma list in a different normal form than HNF (or defactored + HNF = canonical form), namely, some definition of the simplest possible ratios. However, I have several questions.
+# You state that this is already the case that temperament pages use this form. I have no reason to believe they're not. But I didn't know that was the case. How do you know this?
+# Do you have a definition for this normal form somewhere? If you don't yet, I would recommend excluding it from this page until it's better developed. I can easily see how the product complexity of ratios can be easily calculated individually, but minimizing the simplicity of multiple ratios may be somewhat subtle.
+# Why name it "Tenney minimal"? I do not see that this term has wide use on the wiki or Discord already. It seems like an unnecessary eponym. If it is related to the Tenney height of the ratios, wouldn't it be equivalent and simpler to just refer to their product complexity?
+:::: That's all for now. Thanks for helping with this. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 18:54, 29 September 2021 (UTC)