140th mina

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Re: 140th mina

Post by ᴄᴍʟᴏᴇɢᴄᴍʟᴜɪɴ »

Whoa. So right after I posted that, I noticed that the the 92nd mina has the primary comma 13/19S. So I began questioning my suggestion of the 19/13M as the primary comma for the 93rd mina, since those two commas seemed so similar, and possibly the same.

My immediate assumption was that I had made an error in the configuration of my script and it had returned me a comma that was too big (meaning that its apotome complement would be too small, crossing over from the 93rd mina into the 92nd mina's territory). But I hadn't.

My next assumption was that I had made an error earlier when I claimed that moving the boundary between the 92nd and 93rd mina downwards we wouldn't cross over the primary comma of the 92nd mina. But I hadn't done that either.

I finally realized that my 13/19L has a rather large count of 2's and 3's in its monzo. Enough that it contains an entire ditonic comma within it. That's | -19 12 >, or 23.460¢. So actually it's the same comma as the 13:19S, just shifted up 23.460¢ from 44.970¢ to 68.430¢. Probably I should revise my script to not suggest commas which contain a ditonic comma in them.

Although it may not be obvious where to cut myself off. Clearly the 29/55L and 253/13L I submitted should have much simpler small diesis versions that would be preferable if they were to be included at all. But what about the 1/875L? That only has a monzo of | 13 -2 -3 -1 >, but I see that it too already exists as a comma, the 875C at 21.902¢ (in this case it's a ditonic comma off from the 875M).

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Re: 140th mina

Post by ᴄᴍʟᴏᴇɢᴄᴍʟᴜɪɴ »

So: I think with the 1/875L and 13/19L out of the running due to already being covered by ditonic-comma-off commas, 25/77L is the clear winner.

It should be reiterated that by sum-of-elements, both the :``::)|\ \: and the :,,::)/ /|: will be exact using this comma and its apotome complement.

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Re: 140th mina

Post by ᴄᴍʟᴏᴇɢᴄᴍʟᴜɪɴ »

So: I think with the 1/875L and 13/19L out of the running due to already being covered by ditonic-comma-off commas, 25/77L is the clear winner.
I have just reviewed the Sagittal commas and find many pairs of commas apart by a ditonic comma (the 1C). In fact, I'm a bit embarrassed to say that with 61 of the 148 commas related by the 1C (that number 61 is odd because I'm counting the 1C but not the 1n AKA 1/1), ~41% of them are related by it!

19/5C 19/5n
11/13C 11/13k
5/7C 5/7k
7/11C 7/11k
17/5S 17/5C
11/23S 11/23C
245S 245C
23S 23C
17/7S 17/7C
91/5S 91/5C
1/25S 1/25C
25/13M 25/13C
13M 13C
1/35M 1/35C
65M 65C
1/7M 1/7C
625M 625C
85/11M 85/11C
55M 55C
11/91M 11/91C
31L 31S
49L 49S
1/11L 1/11S
23/5L 23/5S
11/17L 11/17S
5/11L 5/11S
1/125L 1/125S
35L 35S
175L 175S
5/13L 5/13S

So, I retract this as a reason to dismiss a comma.

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Re: 140th mina

Post by ᴄᴍʟᴏᴇɢᴄᴍʟᴜɪɴ »

Also, if anyone is curious, the reason the 19/13M and 13/19S were so close is that they were separated by a 361/169n, a remarkably small schismina:

comma		cents	monzo				ratio
19/13M		45.255	[  9 -6  0 0 0 -1 0  1 ⟩	9728/9477
13/19S		44.970	[ -1  1  0 0 0  1 0 -1 ⟩	39/38
361/169n	0.28570	[ 10 -7  0 0 0 -2 0  2 ⟩	369664/369603

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Re: 140th mina

Post by Dave Keenan »

I note that Pythagorean comma and 3C are alternative names for ditonic comma and 1C.

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Re: 140th mina

Post by ᴄᴍʟᴏᴇɢᴄᴍʟᴜɪɴ »

140th Mina.pdf
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140th Mina.png
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An illustration to help us make a decision. Anything in red is proposed to go away; anything in blue is proposed to replace it.

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Re: 140th mina

Post by ᴄᴍʟᴏᴇɢᴄᴍʟᴜɪɴ »

cmloegcmluin wrote: Sun May 17, 2020 11:50 amIt should be reiterated that by sum-of-elements, both the :``::)|\ \: and the :,,::)/ /|: will be exact using this comma and its apotome complement.
What I would have said then if I understood what I do now about the difference between sum-of-elements (SoE) and sum-of-core-and-accents (SoCA) (learn more here: viewtopic.php?p=1417#p1417), I would have said that it is under the SoCA method of element arithmetic that these symbols exactly represent their commas. By SoE, as you can see in the diagram in my previous post, they are not exact.

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Re: 140th mina

Post by Dave Keenan »

This is wonderful. Thanks for doing this. It really shows what's going on. And I love the "here be dragons".

Could you please add marks where the half-minas really are, before they are rounded to half-tinas, and a mark for 488.5 tinas. And could you please also show the effect it has on the 3 lower levels, the Herculean, Promethean and Athenian, below it.

I don't need you to expand the width anywhere. The lower level symbols don't need to be shown in their correct location. I just want to see what symbols and commas are on either side of the two new boundaries, and what their deltas are.

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Re: 140th mina

Post by Dave Keenan »

Cute though the dragon is, there really are more symbols there. In the Evo (mixed) notation they will be a combination of a conventional sharp with an accented downward single-shaft Sagittal. In the Revo (pure) notation they will be accented upward double-shaft symbols.

It would be good to show one of those (evo or revo) for the 140th and 141st minas, and to show that the 140th mina was previously a no-mans-land, which resulted in a bug in the JI calculator spreadsheet, which is precisely why we are proposing this change.

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Re: 140th mina

Post by ᴄᴍʟᴏᴇɢᴄᴍʟᴜɪɴ »

Dave Keenan wrote: Tue May 19, 2020 12:23 pm I love the "here be dragons".
Cute though the dragon is, there really are more symbols there. In the Evo (mixed) notation they will be a combination of a conventional sharp with an accented downward single-shaft Sagittal. In the Revo (pure) notation they will be accented double-shaft symbols.

It would be good to show one of those for the 140th and 141st minas, and to show that the 140th mina was previously a no-mans-land, which resulted in a bug in the JI calculator spreadsheet, and is precisely why we are proposing this change.
I first wrote "edge of the world", but then realized that's beyond the four-shaft symbols, not the single-shaft symbols. But the dragon just looked so majestic hanging out there, though, I had to keep it; I justified its presence as representing not the edge of the entire map, but merely the place where single-shafts dare not go.

You are correct though, that a more pragmatic use of that real estate would be something that explained the purpose of the proposal. And the proposal, fundamentally, involves the relationship between single-shaft symbols emanating toward each other from neighboring apotomes.

I think Evo (mixed) will make for a better illustration. It will show how by mirror-imaging the upper bound of the 140th mina and the lower bound of the 93rd mina, locking one to the L|SS bound and one to the M|S bound, these two bounds will perfectly coincide.

Perhaps in the final version I can keep the dragon, but make him red, representing the elimination of the "no man's land"/"here be dragons" gap we are proposing eliminating between
  • the capture zone of the symbol for the largest L away from the base nominal and
  • the capture zone of the symbol for largest S coming back toward the base nominal away from the apotome.
Update: so here's the next version of the helpful illustration (sadly sans dragon):
140th Mina v2.png
(81.1 KiB) Downloaded 344 times
I feel like this chart has gotten complex enough that it warrants some explanation.

Issue origin recap

So we identified the issue of the missing coverage of single-shaft symbols up through the L-size (large diesis) category limit through a bug in the Sagittal Standard JI Notation Calculator Spreadsheet, where it would suggest
:)\ \!::#: to you instead of :)|\ \: . The problem being that :)\ \!: represents a M-sized (medium diesis) comma, and any single-shaft symbol bigger than S-sized (small diesis) is not meant to be applied counteracting against a sharp or flat in Evo (mixed) flavor Sagittal, since that pitch should instead be able to be notated by a single single-shaft symbol of up to L-size.

I note that this would only ever happen in that most special of precision levels, the High precision level. This is due to how :)/ /|: encroaches a little bit into the territory of :/ /|: at that precision level before :/ /|: reclaims it (in the form of :'::/ /|: ) in the Very High and Extreme precision levels. You can see this clearly either in the JI Precision Level chart or in the latest diagram for this 140th mina issue (in the top right). So the lack of coverage up quite up through the L-size limit was not causing any obvious issues at the other precision levels, since in those levels, the exposed area was falling back to a :/ /|: - based symbol. So in a sense, the wonkiness of the High precision level saved our butts here. Thanks, Promethean. You get a gold star. :star:

Note that the :`::'::/ /|: getting assigned to the 93rd mina in the first place, as opposed to :,,::)/ /|: , therefore contributed to the obfuscation of this issue. Clearly this mina occupies pitch space above the S|M size category boundary and there should have been a core change from the 92nd to the 93rd mina.

Boundaries of lower precision levels

...could you please also show the effect it has on the 3 lower levels, the Herculean, Promethean and Athenian, below it.

I don't need you to expand the width anywhere. The lower level symbols don't need to be shown in their correct location. I just want to see what symbol and commas are on either side of the two new boundaries, and what their deltas are.
@Dave Keenan was good to call for showing the lower precision levels on this chart, since this raises some interesting issues.

We definitely at least have to move the boundary at the Very High precision level to avoid a DAFLL exception. No DAFLL exceptions occur from Olympian down to Herculean, and we don't want to be the first and only one.

The DAFLL exception from Herculean to Promethean is less important to fix, since there are a bunch of those... but I still think it would be good to fix, unless there are some other considerations I'm not aware of. As you can see, it doesn't cause any primary commas to go out of bounds, or SoE or SoCA or SoLFS exceptions.

And after some consideration, I think we should actually move the boundary at every precision level to lock onto the S|M + L|SS bound. I think this should be one of those handful of bounds that cuts straight through all four precision levels. The other two don't actually have anything to do with the comma size category boundaries (the first one is at 13.420¢ between :)|(: and :~|(: and the second one is at 18.760¢ between :~|(: and :/|: while the comma size category boundaries are at 1.808, 4.500, 11.730, 33.382, 45.112, 56.842, and 68.573 cents). Nonetheless, I think this is an important enough one of these boundaries, given its more intimate connection to the anatomy of the apotome, that it deserves to have this much influence over the capture zone boundaries.

Other side notes
Could you please add marks where the half-minas really are, before they are rounded to half-tinas, and a mark for 488.5 tinas.
I wasn't sure what Dave was interested in with respect to adding markers for the actual half-mina boundaries, but something interesting has come of it already: I note that shifting the boundary in the Extreme Precision level results in the size of the capture zone for :,,::)/ /|: coming incredibly close to the size of a 233-EDA mina, just ~0.0000589 cents off! it's just offset by about 0.02 cents.

And I want to take this moment to say to Dave that... yeah, I know we've said in the past that sometimes it's a fun challenge to avoid resorting to diagrams, to attempt to explain everything in words ... but in this case the diagram doesn't cheapen the experience, I feel. Hopefully you agree.

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