Talk:Normal forms: Difference between revisions

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::::::: Re: Tenney-minimal. My point is that some heights being simpler in formula doesn't imply they don't deserve a name – if you accept ''Wilson height'' and ''Kees height'' you may well accept ''Benedetti height'' and ''Tenney height'', even tho these are much simpler. And since ''Tenney-minimal'' derives direct from ''Tenney height'', and since it's been attested, I think it's a quite standard way to convey the idea of ratio-product simplicity. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 02:53, 30 September 2021 (UTC)

:::::::: Re: positive generator. Here's a bit more color on Dave and I's experience working on canonical form. We thought that the way it's done in Graham Breed's temperament finder was probably the most familiar and well-liked form in the community, i.e. that generators should always be positive and less than half the size of the previous generator (that's the "mingen" form that I ended up documenting somewhere on that new page I made re: generator size manipulation). But we found it problematic to extend this constraint past rank-2, and then heard from Graham that he'd never managed to find a way to do it himself either. Dave and I decided that probably preferences about generator forms would come and go over time like flavors of the month, and that if we wanted our proposal to be taken most seriously, we should laser-focus it on the main element of importance — defactoring — and leave the rest to well-established mathematical precedents like HNF that are already implemented in many code libraries. And it was right about this time I discovered the chroma-positive generator form that some folks on Discord seem to be using now, which to me was perfect evidence of changing preferences for generator form, and therefore the nail in the coffin for involving generator size considerations in the form we advocate for the express and primary purpose of uniquely identifying temperaments AKA canonicalization.

:::::::: I note that it's misleading to include the final steps in the "normal val list" and "normal interval list" in sections titled "Hermite Normal Form" because those are not part of the definition of HNF. That's part of the reason why I forgot those steps were there; the last time I read those lists, many months ago, I suppose I had written them off as tediously worded but probably ultimately accurate descriptions of how to reach HNF. But those final steps deviate them from HNF. So I think we should extract the "For any number q < 1 on this list, replace q with 1/q" and the "Find the Moore–Penrose pseudoinverse..." steps to another section, which we might call "positive comma form" and "positive generator form". This has the other benefit of allowing us to maintain the integration of canonical form into this page, as the canonical form Dave and I defined will be in a state where it extends the HNF as defined here. If you agree this is a reasonable solution, I am happy to implement it (esp. since you did the work for the previous edit).

:::::::: As a result of this change, there would now be several options for normal forms documented on this page: Hermite normal form, positive comma/generator form, Tenney-minimal form, and canonical form. At this point we may even want to tilt the other way, i.e. rather than toward a consolidated effort into a single form, a survey of all relevant forms, and therefore additionally include the chroma-positive form and mingen form, and any others you're aware of. Across the wiki many temperaments have a normal form (or "normal lists" or whatever) documented; it may be to our advantage that most of these places are given generically. Surely whatever's given in most of those places is at least one of these normal forms. I suppose over time people may revise individual pages to be more specific about which one it is, and possibly include more than one.

:::::::: Re: Tenney-minimal. I think Benedetti, Tenney, Wilson, and Kees height are all ideas that deserve names. Maybe we have a different definition of "name" here? I think "product complexity" is a name. It's not a person's name, but I prefer that it's not eponymous. Of these four heights, only Kees does not have a preexisting name in mathematics. Just now I had to look up what Wilson height was again, but if you had just used "sum of prime factors with repetition" which is often abbreviated "sopfr" I would have immediately known what you're talking about. "Tenney" is used in xen jargon as a synonym for "log", and because logarithms are so basic to xen, "Tenney" ends up in an excessive number of things' names. That it is attested in a .scl file that was uploaded to the wiki is not very persuasive to me. The old Scala file archives have tons of junk in them, as I can attest after doing an audit of them for some Sagittal-related reason recently: https://forum.sagittal.org/viewtopic.php?p=1515#p1515 I would be looking for a much stronger precedent than a single mention in a .scl file to justify "Tenney-minimal form" over "product-simplest form".

:::::::: I see that you commented out the information about IRREF. Do you mind if I simply delete it? I just noticed during a search across the wiki for misinformation re: torsion that it is one of the few places that contains it. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 17:20, 30 September 2021 (UTC)

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 ::::::: Re: Tenney-minimal. My point is that some heights being simpler in formula doesn't imply they don't deserve a name – if you accept ''Wilson height'' and ''Kees height'' you may well accept ''Benedetti height'' and ''Tenney height'', even tho these are much simpler. And since ''Tenney-minimal'' derives direct from ''Tenney height'', and since it's been attested, I think it's a quite standard way to convey the idea of ratio-product simplicity. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 02:53, 30 September 2021 (UTC)
+:::::::: Re: positive generator. Here's a bit more color on Dave and I's experience working on canonical form. We thought that the way it's done in Graham Breed's temperament finder was probably the most familiar and well-liked form in the community, i.e. that generators should always be positive and less than half the size of the previous generator (that's the "mingen" form that I ended up documenting somewhere on that new page I made re: generator size manipulation). But we found it problematic to extend this constraint past rank-2, and then heard from Graham that he'd never managed to find a way to do it himself either. Dave and I decided that probably preferences about generator forms would come and go over time like flavors of the month, and that if we wanted our proposal to be taken most seriously, we should laser-focus it on the main element of importance — defactoring — and leave the rest to well-established mathematical precedents like HNF that are already implemented in many code libraries. And it was right about this time I discovered the chroma-positive generator form that some folks on Discord seem to be using now, which to me was perfect evidence of changing preferences for generator form, and therefore the nail in the coffin for involving generator size considerations in the form we advocate for the express and primary purpose of uniquely identifying temperaments AKA canonicalization.
+:::::::: I note that it's misleading to include the final steps in the "normal val list" and "normal interval list" in sections titled "Hermite Normal Form" because those are not part of the definition of HNF. That's part of the reason why I forgot those steps were there; the last time I read those lists, many months ago, I suppose I had written them off as tediously worded but probably ultimately accurate descriptions of how to reach HNF. But those final steps deviate them from HNF. So I think we should extract the "For any number q < 1 on this list, replace q with 1/q" and the "Find the Moore–Penrose pseudoinverse..." steps to another section, which we might call "positive comma form" and "positive generator form". This has the other benefit of allowing us to maintain the integration of canonical form into this page, as the canonical form Dave and I defined will be in a state where it extends the HNF as defined here. If you agree this is a reasonable solution, I am happy to implement it (esp. since you did the work for the previous edit).
+:::::::: As a result of this change, there would now be several options for normal forms documented on this page: Hermite normal form, positive comma/generator form, Tenney-minimal form, and canonical form. At this point we may even want to tilt the other way, i.e. rather than toward a consolidated effort into a single form, a survey of all relevant forms, and therefore additionally include the chroma-positive form and mingen form, and any others you're aware of. Across the wiki many temperaments have a normal form (or "normal lists" or whatever) documented; it may be to our advantage that most of these places are given generically. Surely whatever's given in most of those places is at least one of these normal forms. I suppose over time people may revise individual pages to be more specific about which one it is, and possibly include more than one.
+:::::::: Re: Tenney-minimal. I think Benedetti, Tenney, Wilson, and Kees height are all ideas that deserve names. Maybe we have a different definition of "name" here? I think "product complexity" is a name. It's not a person's name, but I prefer that it's not eponymous. Of these four heights, only Kees does not have a preexisting name in mathematics. Just now I had to look up what Wilson height was again, but if you had just used "sum of prime factors with repetition" which is often abbreviated "sopfr" I would have immediately known what you're talking about. "Tenney" is used in xen jargon as a synonym for "log", and because logarithms are so basic to xen, "Tenney" ends up in an excessive number of things' names. That it is attested in a .scl file that was uploaded to the wiki is not very persuasive to me. The old Scala file archives have tons of junk in them, as I can attest after doing an audit of them for some Sagittal-related reason recently: https://forum.sagittal.org/viewtopic.php?p=1515#p1515 I would be looking for a much stronger precedent than a single mention in a .scl file to justify "Tenney-minimal form" over "product-simplest form".
+:::::::: I see that you commented out the information about IRREF. Do you mind if I simply delete it? I just noticed during a search across the wiki for misinformation re: torsion that it is one of the few places that contains it. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 17:20, 30 September 2021 (UTC)