Talk:Normal forms: Difference between revisions

Line 74:

::::: Re: Tenney minimal. 1. By examining some comma lists. For septimal meantone, the normal form would be {81/80, 59049/57344}. Yet the comma list shown in the temp page is {81/80, 126/125}. 2. I've worked out a lot of comma bases and haven't encountered a single example where the definition shown in this page leads to ambiguous results. Now I definitely can't assert there's no exceptions, I'm afraid it'd better be there since all the comma bases shown in the temp pages need an explanation. 3. It's attested in the ''Genesisplus'' page. We can call it ''ratio-product simplest form'', but that's longer and still needs explanation. You know, you can also remove ''Benedetti height'' in favor of ''ratio-product'', and remove ''Tenney height'' in favor of ''logarithm of ratio-product''. I just don't think that's how human language works. Benedetti height is one of many types of heights. In the topic of heights, each type is equally distinct despite one of them being simpler in formula, so each type equally deserves a name. From there is derived ''Tenney-minimal'' as one of many possible minimal forms. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 23:55, 29 September 2021 (UTC)

:::::: Re: flipping the sign of a row for a positive generator or comma. I hadn't thought about that last step given there in a while. You're right; the normal form as defined here ensures positive generators. So it would be consistent with that for the commas to also be flipped to be positive using a similar process. That said, as discussed on the canonical form page, Dave and I iterated on and ultimately decided to explicitly reject any stipulations of that sort from our definition. So in that case, canonical form is ''not'' necessarily equivalent to normal form in all defactored cases. This a perfect example of why it was a good decision for us not to conflate the two or override one with the other! Certainly some people may prefer to normalize to positive commas and generators, while Dave and I prefer the simplicity and purity of our canonicalization method. For instance, I have no intention or desire to complicate the functions I implemented in my RTT library for Wolfram Language by incorporating this sort of comma or generator positivity. So, this leads me to think that we should keep the two pages more separate than we originally planned.

:::::: Re: rename and standardization. Good point. Okay. The paint's still wet. Let's give it some time. Because even this seemingly innocuous issue that cropped up for beep is throwing me for a loop, so I am no position to propose such widespread changes yet. Never mind.

:::::: Re: Tenney minimal. Yes, I am aware that "Benedetti height" is xen jargon for "product complexity" and "Tenney height" is xen jargon for "log product complexity". In fact I recently added notes about that to their wiki pages here. I prefer descriptive names over eponymous ones, and established ones over new coinages, whenever possible. I agree that there are many distinct types of height that deserve names and that some are simpler than others, but I'm not sure what your point by that is. Anyway, because "simple" and "complex" are antonyms, we might be able to get away with "product-simplest form" then. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 01:07, 30 September 2021 (UTC)

@@ Line 74: / Line 74: @@
 ::::: Re: Tenney minimal. 1. By examining some comma lists. For septimal meantone, the normal form would be {81/80, 59049/57344}. Yet the comma list shown in the temp page is {81/80, 126/125}. 2. I've worked out a lot of comma bases and haven't encountered a single example where the definition shown in this page leads to ambiguous results. Now I definitely can't assert there's no exceptions, I'm afraid it'd better be there since all the comma bases shown in the temp pages need an explanation. 3. It's attested in the ''Genesisplus'' page. We can call it ''ratio-product simplest form'', but that's longer and still needs explanation. You know, you can also remove ''Benedetti height'' in favor of ''ratio-product'', and remove ''Tenney height'' in favor of ''logarithm of ratio-product''. I just don't think that's how human language works. Benedetti height is one of many types of heights. In the topic of heights, each type is equally distinct despite one of them being simpler in formula, so each type equally deserves a name. From there is derived ''Tenney-minimal'' as one of many possible minimal forms. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 23:55, 29 September 2021 (UTC)
+:::::: Re: flipping the sign of a row for a positive generator or comma. I hadn't thought about that last step given there in a while. You're right; the normal form as defined here ensures positive generators. So it would be consistent with that for the commas to also be flipped to be positive using a similar process. That said, as discussed on the canonical form page, Dave and I iterated on and ultimately decided to explicitly reject any stipulations of that sort from our definition. So in that case, canonical form is ''not'' necessarily equivalent to normal form in all defactored cases. This a perfect example of why it was a good decision for us not to conflate the two or override one with the other! Certainly some people may prefer to normalize to positive commas and generators, while Dave and I prefer the simplicity and purity of our canonicalization method. For instance, I have no intention or desire to complicate the functions I implemented in my RTT library for Wolfram Language by incorporating this sort of comma or generator positivity. So, this leads me to think that we should keep the two pages more separate than we originally planned.
+:::::: Re: rename and standardization. Good point. Okay. The paint's still wet. Let's give it some time. Because even this seemingly innocuous issue that cropped up for beep is throwing me for a loop, so I am no position to propose such widespread changes yet. Never mind.
+:::::: Re: Tenney minimal. Yes, I am aware that "Benedetti height" is xen jargon for "product complexity" and "Tenney height" is xen jargon for "log product complexity". In fact I recently added notes about that to their wiki pages here. I prefer descriptive names over eponymous ones, and established ones over new coinages, whenever possible. I agree that there are many distinct types of height that deserve names and that some are simpler than others, but I'm not sure what your point by that is. Anyway, because "simple" and "complex" are antonyms, we might be able to get away with "product-simplest form" then. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 01:07, 30 September 2021 (UTC)