Alright, done!

Dave Keenan wrote: ↑Sat Sep 05, 2020 10:50 am
Here's the full val I used, up to the 59-limit, if you'd like to double-check it. Graham Breed's tool (

http://x31eq.com/temper/net.html) seems to be not working for me, but it wasn't hard to find it myself.

Code: Select all

```
⟨ 8539 13534 19827 23972 29540 31598 34903 36273 38627 41482 42304 44484 45748 46335 47431 48911 50232 50643 51798 52513 52855 53828 54437 55296 56357 56855 57096 57565 57794 58238 59676 60058 60610 60789 61645 61809 62289 62751 63050 63484 63904 64041 64704 64832 65085 65209 65931 66612 66831 66939 67152 67466 67568 68069 68360 68644 68922 69014 69283 69460 ]
```

I checked it up to prime 59 and I concur.

I just noticed that what I sent you previously was actually up to the 281-limit. I suspect my confusion must have been related to the fact that 281 is the 60th prime, and the final index of a zero-indexed array of length 60 is 59. *shrug*

Point is: I'm filtering inconsistent metacommas out myself now, so you don't have to worry about it.

I decided to filter them as a final step, that is, I didn't filter them since I didn't think inconsistency of a metacomma should affect whether it counts toward the metametacomma choice.

None of the most common metacommas per bucket were inconsistent anyway, though.

Man, this *really* would have been a great thing to pair program on. I think I struggled a lot on exactly the kind of stuff you could have guided me through.

I'm going to list results per whole tina bucket, only including those within the top 20% of the maximum occam in the given bucket, as you did before.

The following comes from the badness metric being LPEI. Shortly will follow the LPE results too.

So according to these results, the 10241/5n narrowly edges out the 121/1225n:

CANDIDATES FOR SEMITINA 2
[
["10241/5n", 13],
["121/1225n", 12],

The one you

yesterday declared the winner for 2 tinas wins here too:

CANDIDATES FOR SEMITINA 4
[
["1/5831n", 12],

Of course the 1-mina wins:

CANDIDATES FOR SEMITINA 6
[
["1/455n", 37],

The 4-tina agrees with your most recent summary of the results per bucketing by actual metacomma size:

CANDIDATES FOR SEMITINA 8
[
["3025/7n", 17],
["49/1045n", 15],

Same goes for the 5-tina:

CANDIDATES FOR SEMITINA 10
[
["2401/25n", 15],

Of course we have our 2-mina:

CANDIDATES FOR SEMITINA 12
[
["65/77n", 23],

The 7/425n barely ekes out a victory here too (as it did for the actual metacomma size based bucketing):

CANDIDATES FOR SEMITINA 14
[
["7/425n", 12],
["143/1715n", 11],
["1729n", 10],
["119/11n", 10],

Interesting. The 77/13n does not win here. You recently wrote:

Being the tina complement of a mina might be just another rule that trumps any of these considerations. Which I'm fine with. (I may go back and edit that list of considerations I drew up recently to include this one last thing, which we did talk about a bit in the earlier days of this project). What do you think?

CANDIDATES FOR SEMITINA 16
[
["187/175n", 16],
["385/19n", 13],
["77/13n", 13],

The 9-tina was a landslide victory and again agrees with actual metacomma size based buckets:

CANDIDATES FOR SEMITINA 18
[
["1/539n", 34],

Alright, then how about metametacommas? There are actually 19 of them, not 18, since I include the one from the unison to the result for the most common metacomma for the half-tina dot. Please let me know if you specifically intentionally wanted to exclude that metametacomma for some reason. In this case it is the 77/185n. That results in there being a tie for the most common metametacomma: the 77/185n, with 2 occamms (that's occurrences as meta-metacomma), one from 0 to 0.5 as just described, and one from 9 to 9.5 (the metametacomma from 6 to 6.5 is not actually the 77/185n here, because the 2125/7n was found to be the most common metacomma in the 6.5 bucket). The other metacomma is the 21385/11n, which occurred between 3 and 3.5 and 5.5 and 6. Between these two I certainly prefer the 77/185n, though this particular metametacomma technique didn't give an obvious winner.

Alright, how about with the badness metric being LPE? (Without error, it's not a full-fledged badness metric, only a complexity metric, but since we're using it in a position where metrics up to badness get used, I think I'll just treat it as one.)

The answers, thankfully, are remarkably similar:

For the 1-tina, it's again super close between the 10241/5n and 121/1225n. This time they tie.

CANDIDATES FOR SEMITINA 2
[
["10241/5n", 12],
["121/1225n", 12],

For the 2-tina, the 1/5831n still wins, though it's a bit closer this time.

CANDIDATES FOR SEMITINA 4
[
["1/5831n", 11],
["35/1573n", 9],

(skipping the 3-mina)

Very similar for the 4-tina, again, just a bit closer. Beginning to wonder if the fact that including error in the badness metric very slightly increases the victories of the most common metacommas, or in other words consolidates them turning up, means it's doing a good job.

CANDIDATES FOR SEMITINA 8
[
["3025/7n", 17],
["49/1045n", 16],

Same exact result for 5-tina.

Skipping the 2-mina.

Here the 7-tina gets actually a slightly stronger victory, running against the pattern we've seen so far, but it's the same victor.

CANDIDATES FOR SEMITINA 14
[
["7/425n", 13],
["119/11n", 11],
["143/1715n", 11],

Again our preferred 8-tina does not win, but again it's close.

CANDIDATES FOR SEMITINA 16
[
["187/175n", 16],
["77/13n", 15],

And again a landslide victory for the 9-tina.

Alright, and so then what do we see for the metametacommas? This time, not a single dupe. 19 different metametacommas. Now, I do notice that we have several ties for most common metacomma per semitina bucket, so I could re-run that and try each one tied for first. But I suspect this won't be worth the trouble as this method isn't seeming super fruitful. And/or you'll say that because 77/185n turned up previously both in a direct badness search, in my bucketing-by-actual-metacomma-size search, and its competitors almost never show their heads anywhere, we should just go with it.

Here is the list I think we should go with:

0.5 tina: 77/185n

1 tina: 10241/5n

2 tinas: 1/5831n

3 tinas: 1/455n

4 tinas: 3025/7n

5 tinas: 2401/25n

6 tinas: 65/77n

7 tinas: 7/425n

8 tinas: 77/13n

9 tinas: 1/539n

This is is still 37-limit. The whole tinas are 19-limit. There are 7 superparticulars out of the 10.