consistent Sagittal 37-Limit

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volleo6144
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Re: consistent Sagittal 73-Limit

Post by volleo6144 »

I'm not exactly feeling like making a full analysis of the existing commas there (there's well over 500 commas on the list, and some of those have an N2D3P9 above 300, which suggests that commas up to the 73-limit might be worth considering), at least for now.

One interesting thing that happens with the 140th mina or 487th tina being set as the single/double-shaft boundary is that some L-dieses actually fall within the capture zone of :,::.::)||(:, which may or may not have been related to the old :)\ \!::#: problem...
I'm in college (a CS major), but apparently there's still a decent amount of time to check this out. I wonder if the main page will ever have 59edo changed to green...
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Dave Keenan
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Re: consistent Sagittal 37-Limit?

Post by Dave Keenan »

volleo6144 wrote: Fri Jul 30, 2021 9:50 am I'm not exactly feeling like making a full analysis of the existing commas there (there's well over 500 commas on the list, and some of those have an N2D3P9 above 300, which suggests that commas up to the 73-limit might be worth considering), at least for now.
Fair enough. What about checking whether the current parameter values for the LPEI badness (9.65, 1.7, 9.65, 0.8) give the maximum number of matches to the existing comma assignments when we include single-shafts past the half-apotome? I guess that suffers from the same problem, i.e. you don't think we've cast the net wide enough for candidates.
One interesting thing that happens with the 140th mina or 487th tina being set as the single/double-shaft boundary is that some L-dieses actually fall within the capture zone of :,::.::)||(:, which may or may not have been related to the old :)\ \!::#: problem...
You should find, in the latest JI notation calculator spreadsheet, that we've made an exception for the 140|141 mina boundary and its complement the 92|93 mina boundary. We've set them at the exact square-roots-of-3-commas corresponding to the size category boundaries. It was related to that old problem, and that's how we solved it.

Here's a list of all 2,3-free ratios with N2D3P9 ≤ 4981, in N2D3P9 order.
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popular23freeClassesUpToN2D3P9of4981.xlsx
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volleo6144
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Re: consistent Sagittal 37-Limit?

Post by volleo6144 »

Dave Keenan wrote: Fri Jul 30, 2021 10:28 am Fair enough. What about checking whether the current parameter values for the LPEI badness (9.65; 1.7; 9.65; 0.8) give the maximum number of matches to the existing comma assignments when we include single-shafts past the half-apotome?
I'm fairly sure there would be a better one that weights the ATE much less as the...oh, right, a 6561 is already only worth 1.25× on the N2D3P9. I also think that allowing too many decimals on the parameters is coming close to von Neumann's elephant again.

...Come to think of it, why do we even include ATE at all if AAS is basically the same thing but accounting for apotome-complements and some other things?
I guess that suffers from the same problem, i.e. you don't think we've cast the net wide enough for candidates.
By noting that 73 has a lower N2D3P9 than 5·47 and that it wouldn't actually be highlighted red under the current spreadsheet's conditional highlighting rules, I didn't actually mean to imply that 73-limit commas were worth considering—after all, then we have to completely reconsider where to stop, and our original reasoning* for stopping at 37 doesn't really work well here...

* because prime-factor Sagittal requires a mina diacritic (:`: representing 5·41n = 6560:6561 = 0.54 minas) to distinguish :`::/|: 41C from :\!: 5C; it turns out that we also need one (:,,: representing 17:43n = 1376:1377 = 2.58 minas, which is closer to :`::)!: than :,,::!:) to distinguish :,,::~|(: 43C from :~|(: 17C and that that's the last required diacritic until well beyond 61.
Last edited by volleo6144 on Mon Aug 02, 2021 5:25 am, edited 5 times in total.
I'm in college (a CS major), but apparently there's still a decent amount of time to check this out. I wonder if the main page will ever have 59edo changed to green...
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Dave Keenan
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Re: consistent Sagittal 37-Limit?

Post by Dave Keenan »

volleo6144 wrote: Sat Jul 31, 2021 12:05 am ...Come to think of it, why do we even include ATE at all if AAS is basically the same thing but accounting for apotome-complements and some other things?
AAS gives usefulness in notating EDOs. ATE gives usefulness in notating JI. And they have different expansion functions applied. AAS is only a 1.7 power while ATE is exponential.

When using a dot to mean multiplication in comma names, e.g. 5·41n, to avoid confusion with a US/British decimal point, I suggest using a middle dot, which can be typed as right-alt dot dot, if you're using my WinCompose sequences that can be downloaded from the end of this post:
viewtopic.php?p=808#p808
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