What do you mean by "first"? I imagine there is some pattern to the cells you chose to give a thick black border, among the ones highlighed in red for being within 9 tinas in size. And I expect that this pattern is "first" for some definition of first. But I can't figure out what it is.
And I don't understand what it means for a metacomma to "occur" for a tina.
What do you mean by "change"? Do you mean changing some of the comma definitions for the Extreme level, as previously discussed elsewhere?I was not taking any notice of whether commas were exactly notated (without using tina accents), as that is something that could change.
I can't quite parse this sentence. But I thought that taking notice of whether commas are exactly notated is central to our present work in at least some sense.
I think this "without using tinas" concept must be key, but I don't understand what it means.It would make more sense to me if you did it for commas that are not yet exactly notated without using minas (or tinas), since minas are essentially triple-tinas.
What do you mean by "did it"?
Do you mean the commas we already have assigned to and , the 455n and 65:77n, or 4096/4095 and 2080/2079, respectively? I see them both in the table...For example, the table above fails to suggest the obvious definitions for 3 tinas and 6 tinas.
It tells me that the 455n would help us exactly notate 35/13, which is the 5th most popular 2,3-free-class which Sagittal does not yet exactly notate. It tells us that it would allow exact notation of 35/13 since it is the case that we already have a symbol for 169/1. It also tells us that it allows the notation of 3 additional as-of-yet not-exactly-notated commas in this upper slice of popularity. It also tells us that if we want to notate 35/13, we have only one other choice: 1716/1715, a candidate for the 7 tina, which would notate 35/13 relative to 49/11.
I don't see the difference between these two things. I thought they were the same thing. I thought the table I provided addresses that thing.Dave Keenan wrote: ↑Thu Sep 03, 2020 11:01 pm I think you've run with what I wrote here:
and that's fine. The more approaches the better.Dave Keenan wrote: ↑Tue Sep 01, 2020 8:23 am In this post, I noted that the first 2,3-free ratio in the above list that does not yet have a sagittal symbol, 25/11, is a candidate to be notated by a 1 tina accent applied to the existing symbol for 49/11 . That makes 1 tina = 1225/121n which is what George Secor suggested for it. There may be other un-notated but moderately popular ratios that could be notated with tina accents. This might be the best way to assign commas to the accents for 1 thru 9 tinas.
But I'm going with what I wrote later in that post:
... it would be interesting to see that single lowest-slope comma, and its size in cents, listed against each ratio in the above list. Then search for cases where two such commas differ by 9 tinas or less, and consider assigning each tina accent to that correctly-sized difference whose pair of 2,3-free ratios have the lowest maximum N2D3P9.
I think your table is just a different look at the same data. Is it not? You have the LAAS-per-2,3-free-class on the vertical and other LAAS-per-2,3-free-class on the horizontal, with the tinas in the cells. I just pivoted the table so that the tinas are on the vertical and the other LAAS-per-2,3-free-class are in the cells.I've checked my results above, and have attached the spreadsheet I used, with bold outlines on the cells corresponding to the meta-commas I listed.
No worries.I planned to give that list of tinas and their lowest-N2D3P9 metacommas again here, but with the pairs of ranks converted to meta-comma names, so we could compare them to the yellow-highlighted rows in the tables you mentioned from way back. But I ran out of time tonight.
I think I'll need to get my head around the problem a little better before proceeding. Maybe a video call would be good once we're both up.I'd be pleased if you can generate another list of 131 2,3-free ratios, this time with the notational comma for each, that has lowest abs3exp (LATE) (and smallest size, in the case of a tie), instead of lowest absolute apotome slope (LAAS).