## Magrathean diacritics

cmloegcmluin
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### Re: Magrathean diacritics

Dave Keenan wrote: Wed Nov 04, 2020 10:19 am
... when I just literally transcribe your formula it works (which is how I've been doing it in the occam semitinas script too). And you'll be happy to know that adding that mina error actually improves the situation from a metric score of 21 down to only 18
123 total - 18 non-matches = 105 matches. I only got 102 matches, so what's going on here?
To be clear: without the mina error included, I get the same result as you: 102 matches.

You asked me to see what I get when I when I add the mina error. When I add mina error, I get 105 matches.

I didn't realize that you'd already implemented mina error on your end. It sounds like you have implemented mina error on your end, and with it included, you get 102 matches. So you're surprised why I got 105.

I was excited to show that mina error actually improved the match count, suggesting that we had managed to find something that you and George had probably taken into consideration when choosing commas for the Extreme notation. But it sounds like I should have been not excited, but rather disappointed, that I didn't exactly get the same 102 match count that you did.

Please correct me if any of this is wrong.

And let me know if you want me to re-run my check with mina error included, and this time log out more information like which commas are and aren't matching, and how far off their scores are, etc.
As nice as that would be, I know it's not what George would want, although he'd thank you for the sentiment. And I don't think there's any evidence that George knew about 7/425n, and so he might have had a different opinion if he had known about it.
Fair enough. Let's not spend too long devising an objective tiebreaker then.
Are you saying you ignored my definition of "list-B" here: viewtopic.php?f=10&t=430&p=2619&hilit=list+B#p2619
which involves "the existing commas", and instead substituted the lowest-badness comma in the same semitina zone as each existing Ultra comma?

I don't see any justification for doing that?

I have had similar thoughts. But these involve, in some sense, using the Ultra commas we should have had. But that would mean substituting the lowest-badness comma in the same mina zone as each existing Ultra comma, not the same semitina zone.
I did not ignore your instructions. I ran my scripts that produced the recently shared results following those instructions. It is merely the case that as an afterthought I wondered aloud whether maybe we should have done it this way.

Based on your response, you definitely understand what I was getting at; in fact, you've understood it well enough to suggest that if we did do this, it would be the best (I treat "best" as synonymous with "lowest-badness" / "least bad") comma per mina zone, a suggestion that I agree is correct where I wasn't quite right yet.

And you've had similar thoughts. But you still don't see the justification. That's fine. I didn't mention it because I had any good reason to believe it was a more correct approach. I just wasn't sure whether the possibility had even occurred to you yet, or if it had, you'd dismissed it for some reason and I'd be interested in that reason.

Dave Keenan
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### Re: Magrathean diacritics

I think I've figured out at least part of the cause of the discrepancies in our match versus non-match counts.

I've been counting 1u, If I omit that, the total number of extreme commas in the half-apotome is 122. And I've been keeping 19/4375s and 14641k (the two with very high values of N2D3P9 that we plan to replace with their lowest badness counterparts 1/575s and 143/5k).

When I replace those two commas and ignore 1u, I get 103 matches and 19 non-matches, which add to 122.

But I'm still getting one more non-match than you are.

Dave Keenan
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### Re: Magrathean diacritics

OK. So you are including 1u. I'll go back to including it too. But I'll continue to replace 19/4375s with 1/575s and 14641k with 143/5k.

I found the problem. I had
)/| _19_5_C:
as a non-match, apparently because I managed to delete 19/5C from the list of candidates for that symbol, when manually editing its list of candidates down from its introduction-level zone to its extreme zone.

I now have 105 matches and 18 non-matches, same as you. Phew! Sorry about that.

While I was at it, I checked to see if any of the 18 non-matches involved symbols with no mina accents. There was one:
~~| _11_49_C:
which LPEI badness (and several other complexity and badness metrics) say should be 25/11C. I suspect it was only the Scala archive stats that favoured 49/11 over 25/11.

So it would be good to make that one substitution to list-B, to see if by some miracle it breaks the tie.

cmloegcmluin
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### Re: Magrathean diacritics

Good detective work. I do include the 1u, but I am excluding 19/4375s and 14641k. So I don't actually have 105 matches. I have 103 matches and 18 non-matches, for a total of 121 commas. Because my code goes by non-matches, if you have the wrong assumption about the comma count being 123, which I did, you report the wrong match count

Matches:
_1_u
_1_455_n
_65_77_n
_19_5_n
_5_s
_1_91_s
_19_s
_49_55_s
_385_k
_11_13_k
_5_7_k
_5_343_k
_1_85_k
_25_7_k
_343_k
_1_17_k
_7_11_k
_275_k
_35_11_k
_1_143_C
_17_5_C
_7_125_C
_245_C
_17_C
_143_7_C
_7_25_C
_1225_C
_23_C
_1_169_C
_91_5_C
_1_25_C
_1_19_C
_91_C
_1_5_C
_875_C
_25_13_C
_19_25_C
_3_C
_77_5_C
_125_13_C
_19_5_C
_13_C
_1_35_C
_77_C
_11_65_C
_65_C
_1_7_C
_625_C
_11_13_C
_325_C
_5_7_C
_3125_C
_85_11_C
_19_7_C
_7_55_C
_55_C
_11_91_C
_7_11_C
_17_25_S
_25_49_S
_31_S
_49_S
_17_5_S
_1_11_S
_245_S
_23_5_S
_7_13_S
_11_17_S
_5_11_S
_23_S
_91_25_S
_1_125_S
_35_S
_17_7_S
_91_5_S
_1_25_S
_175_S
_5_13_S
_49_17_S
_13_19_S
_77_25_M
_25_13_M
_13_5_M
_1_175_M
_11_325_M
_13_M
_1_35_M
_125_M
_11_19_M
_1_7_M
_625_M
_11_5_M
_17_11_M
_5_23_M
_7_275_M
_11_M
_85_11_M
_65_7_M
_1_49_M
_1_31_M
_55_M
_11_91_M
_5_49_M

Non-matches:
_31_11_k
_1_1225_k
_49_13_k
_1_8575_k
_11_23_C
_11_49_C
_11_31_C
_17_7_C
_1_253_C
_4375_C
_125_23_C
_13_17_S
_7_247_S
_11_23_S
_1_1001_S
_37_M
_65_M
_595_M

cmloegcmluin
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### Re: Magrathean diacritics

I didn't notice you'd posted yet when I just posted.
Dave Keenan wrote: Wed Nov 04, 2020 11:41 am OK. So you are including 1u. I'll go back to including it too. But I'll continue to replace 19/4375s with 1/575s and 14641k with 143/5k.
Cool. Well, I don't literally include 1/575s and 143/5k yet, but that's irrelevant for these purposes, because since those are the best commas, they wouldn't be non-matches, and my code counts non-matches. So our results essentially check out. Good.
I found the problem. I had
)/| _19_5_C:
as a non-match, apparently because I managed to delete 19/5C from the list of candidates for that symbol, when manually editing its list of candidates down from its introduction-level zone to its extreme zone.
Oof! I'd be peeved if I were you!
I now have 105 matches and 18 non-matches, same as you. Phew! Sorry about that.
No big deal.
While I was at it, I checked to see if any of the 18 non-matches involved symbols with no mina accents. There was one:
~~| _11_49_C:
which LPEI badness (and several other complexity and badness metrics) say should be 25/11C. I suspect it was only the Scala archive stats that favoured 49/11 over 25/11.

So it would be good to make that one substitution to list-B, to see if by some miracle it breaks the tie.
Yeah! I was wondering about that (when I wrote "Or does it not matter because almost certainly all 18 of those are in the Extreme level?") Thanks for actually checking for us. Alright, I'll give it a shot, and get right back to you.

cmloegcmluin
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### Re: Magrathean diacritics

CANDIDATES FOR TINA 7
7/425n		13
143/1715n	11


Edit: And no other surprised for the other tinas or the semitina. They stay the same. I gotta go make dinner now. bbiab.

Dave Keenan
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### Re: Magrathean diacritics

I can only think that George must have interceded on our behalf, with the gods of Mount Olympus, to deliver such a miracle. Thanks George! And thank you, Douglas, for crunching the numbers. Woot!

And yes, my non-matches are exactly the same as yours.

The following (post-mortem of a miscommunication) fades into insignificance, but since I'd already written it:
cmloegcmluin wrote: Wed Nov 04, 2020 10:41 am
Are you saying you ignored my definition of "list-B" here: viewtopic.php?f=10&t=430&p=2619&hilit=list+B#p2619
which involves "the existing commas", and instead substituted the lowest-badness comma in the same semitina zone as each existing Ultra comma?

I don't see any justification for doing that?

I have had similar thoughts. But these involve, in some sense, using the Ultra commas we should have had. But that would mean substituting the lowest-badness comma in the same mina zone as each existing Ultra comma, not the same semitina zone.
I did not ignore your instructions. I ran my scripts that produced the recently shared results following those instructions. It is merely the case that as an afterthought I wondered aloud whether maybe we should have done it this way.
Good to know. Thanks. So then I misunderstood your second sentence here:
cmloegcmluin wrote: Wed Nov 04, 2020 4:55 am For our list of 809 best commas per tina zone... we know that there are 21 (well now 18) of those which are not matches for the commas that are actually in Sagittal. When finding the metacommas, I've been doing it against these 18 theoretically best commas, even though those aren't the actual ones the minas would be applying to.
Although I understood the first sentence was about list-A (thanks to the "809"), in the second sentence the words "against" and "[commas] the minas would be applying to" suggested the second sentence was about list-B. We start with Ultra symbols and apply mina (and in future tina) accents to them, so I took the "[commas] the minas would be applying to" to be the list-B commas, since these were (at least originally) the existing Ultra commas.

I now assume both sentences were about list-A, the lowest-badness comma for every semitina zone. 809 of them. And you were wondering whether, for the 123 semitina zones of list-A that encompass the existing Extreme commas we should replace the lowest-badness Insane comma with the existing Extreme comma.

And you thought that would only involve changing 18 of them, because the other 105 would match. That's probably true, but it's not necessarily the case. 105 of them match the lowest badness comma in their mina zone, but that's not necessarily the lowest badness comma in their semitina zone, unless their semitina zone is wholly contained within their mina zone. But that doesn't matter. If we were doing this, we'd just replace all 123.

I still haven't figured out if I think this is a good idea or not.
Based on your response, you definitely understand what I was getting at; in fact, you've understood it well enough to suggest that if we did do this, it would be the best (I treat "best" as synonymous with "lowest-badness" / "least bad") comma per mina zone, a suggestion that I agree is correct where I wasn't quite right yet.
Apparently I didn't understand it, and I'm surprised you think I did. I was talking about modifying list-B to use best instead of existing, while you were talking about modifying list-A to use existing instead of best. Is that correct?
And you've had similar thoughts. But you still don't see the justification. That's fine. I didn't mention it because I had any good reason to believe it was a more correct approach. I just wasn't sure whether the possibility had even occurred to you yet, or if it had, you'd dismissed it for some reason and I'd be interested in that reason.
They weren't similar thoughts. The possibility hadn't occurred to me. I haven't yet rejected it. [Edit: I have now. Lets leave list-A as best Insane commas, and now we have list-B as best Ultra commas (which only differs from existing Ultra commas in one place, and may become actual Ultra commas in future). Such mathematical purity. ]

cmloegcmluin
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### Re: Magrathean diacritics

I'll respond in detail later. Just wanted to say woo-hoo!! I guess even if the election results are not good tonight in my country, at least I've got this to be happy about.

Dave Keenan
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### Re: Magrathean diacritics

Dave Keenan wrote: Wed Nov 04, 2020 11:41 am I suspect it was only the Scala archive stats that favoured {49/11}2,3 over {25/11}2,3.
I just checked this, and found I was wrong. As we can see here
https://en.xen.wiki/w/N2D3P9#Table_of_T ... _by_N2D3P9 (see N2D3P9 ranks 27 and 53),
the Scala stats rank them in the same order that N2D3P9 ranks them, although the Scala stats do rank them closer together (ranks 47 and 54).

They have the same ATE (2) and they only differ in size by about 1 tina. But 11/49C has a much lower apotome slope than 25/11C (0.9 vs 3.1), so it may have been the lower slope that caused {49/11}2,3 to win when using the closer Scala ranks or the closer SoPFRs (21 vs 25) as the unpopularity metric. We discussed them here:
viewtopic.php?p=2261#p2261

So, in theory 11/49C is better for notating EDOs, but the only EDO I can find being used for is 198-edo. It's used for 3 degrees. But I just checked and 25/11C is also 3 degrees of 198-edo. So that's no barrier to redefining as 25/11C. Such a redefinition would involve an update to the SMuFL notation, but it needn't delay the current update re Magrathean.

Even if say we searched George/Dave email and found some really good reason to keep as 11/49C, there are other reasons given, earlier in this thread, to break the tie for 7 tinas in favour of 7/425n.

So we go with the list given here:
viewtopic.php?p=2633#p2633

I will draft an email to Daniel Spreadbury and send it to you for comment/completion.

Dave Keenan
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### Re: Magrathean diacritics

I searched George/Dave email re 11:49C versus 11:25C.

See the cyan hilited text in these emails:

From May 2005:
viewtopic.php?p=1569#p1569
viewtopic.php?p=1570#p1570

[Edit: From December 2006:
See my next post in this thread (on the next page).]

From October 2007:
viewtopic.php?p=1373#p1373

What do you take away from these as the reason(s) why 11:49C was chosen over 11:25C for ~~| ( )? And are they still valid? I have my own reading/theory but I don't want to influence yours.