Please note my recent correction to that table. I realised the denominator limit was 23, not 17, due to 25/19 and 25/23 having N2D3P9 ≤ 136.Thanks for crunching the numbers and preparing that table of min and max prime exponents for me. That's exactly everything I need to get the answer to your question without really having to think about anything... just hammer out a little code.
I get N2D3P9(121) ≈ 37, N2D3P9(1225) ≈ 60. I can't figure out what you're doing wrong.Out of curiosity I asked what N2D3P9 had to say about the 121k vs 1225k issue. Interestingly, while 243/242 has lower SoPF>3 than 19683/19600 (22 vs. 24), it has higher N2D3P9 (≈16 vs. ≈12). We'll wait on the comma-no-pop-rank metric though to make a call on that front.
Interesting. But I can't see that sort of history being of much interest to others. I'm thinking of the writeup as a Xen Wiki entry for N2D3P9. I'm imagining a reader who has seen the term somewhere but knows nothing about it. They want to know: What is it good for. Why should I believe it is fit for those purposes? How do I calculate it? And maybe: Who came up with it and when? How did they come up with it.?So as you know I'm currently reading my way back over this topic from page 1 and taking notes about the different threads we pursued (including the blue threads of death... ). So far we've each only almost given up once apiece (I seem to recall almost giving up three times myself, you maybe only twice). It's occasionally agonizing how close you or I come to wbl1 before my code gave us some confidence that we couldn't do better.
Bugger all. Although we did throw away some data on 3-exponents from the Scala archive data, because initially it was the full pitch ratios with their individual counts, before I crunched them down to 5-rough. I think the full data is in a spreadsheet somewhere in this forum. That's data on what 3-exponents people use in pitch ratios. But I assume the average (signed) 3 exponent will be close to zero.I still have no idea how we're going to weight abs3exp and apotome slope. What objective data do we have to model that after?
We're more interested in: When choosing what comma to give to some symbol, how much are we willing to allow the 5-rough-no-pop-rank to increase in order to have a comma that doesn't require so many sharps or flats to go along with it.
I must admit to similar wicked thoughts myself.Besides of course Sagittal commas, which if — and this is a big "if" — we no longer cared about our reputations, we could just fit it to those and call it day.
I see no harm in looking at that.I could imagine it might be something to the effect of: for ratios of a given N2D3P9 rank, what does the distribution of apotome slopes look like? Does this comma under consideration fall on the better or worse side of this distribution?
The other thing we should do is look again at George's comma complexity metric.
I'm thinking we'll have to multiply N2D3P9 by some number raised to the power of the apotome-slope, rather than add something.
I'm biased towards using apotome-slope alone, where George took a kind of mean between that and abs3exp. Of course the two are indistinguishable for commas as small as tinas.
I'll soon be off hiking for a few hours.