Great.Dave Keenan wrote: ↑Sat Aug 15, 2020 10:53 am OK. I agree to using the capitalisation "N2D3P9" in math expressions too.

I remember saying that myself! I'll haven't come across the evidence yet, but in any case, this is true.Good work finding those earlier agreements re the topic of this thread. I think you'll likely find somewhere where I also agreed to not changing the title at such a late stage, despite it being not quite appropriate, because the forum software doesn't change the title of all the posts. You'd have to do that one post at a time.

Okay, interesting.But I note that there aretwosteps to get from a 5-rough-no-pop-rank to a badness metric. The intermediate step is the comma-no-pop-rank [just trying out possible terms here] whose job is to distinguish between commas that notate the same 5-rough pitch ratio (as well as those for different 5-rough pitch ratios). This includes a consideration of abs3exp and/or apotome-slope. This is useful independent of a badness measure, in determining which commas deserve symbols.

What else gets included in a "badness measure", then? I found this: "A "badness" measure is typically a combination of a complexity measure and an error measure. But we have two kinds of complexity measure in this case." I wasn't aware that a badness measure was an established concept, let alone was I aware that it had conventions, and I also don't know what an error measure is in general or what it would be in our case.

What use would the intermediate no-comma-pop-rank have? You say it would be useful independent of a badness measure, but if the badness measure is what we would use to determine which commas deserve symbols (Magrathean accents), then I now know of zero uses for the no-comma-pop-rank-or-whatever in and of itself.

I cannot answer until I understand more about badness.So we could choose to make the title of this thread come true by continuing on to that — then start a new thread for the badness, which includes a consideration of the error (in cents or fractions of a tina, or other ina).

If we start a new thread for comma-no-pop-rank, what should we call it?

Indeed, messy.The use of the adjective "notational" is messy. Sometimes it refers to the comma and sometimes the popularity. A notational comma is a comma used for notation (i.e. a comma that is used as the value of an accidental or diacritic symbol) as opposed to say a vanishing comma or tempered-out comma. It doesn't make sense (to me) to talk of a notational pitch ratio or notational 5-rough ratio. They aren't used for notation, they need tobenotated. They are notated ratios, not notational ratios. But it does make sense to me to talk of the "notational popularity" of such (non-comma) ratios, i.e. how often they turn up needing to be notated, as opposed to say how often they occur as intervals between notes, or how much people like to hear them in chords.

Agreed that ratios aren't "notational". I used "notatable" here, though I think I prefer your "notated". And even more so I prefer "notational popularity of ratios".

Agreed. I will try to be consistent henceforth in using "no-comma-pop-rank" and "5-rough-no-pop-rank".Hence "comma-no-pop-rank" could also be "no-comma-pop-rank", where "no" is short for "notational". But "5-rough-no-pop-rank" could not be "no-5-rough-pop-rank". Hence using the form "comma-no-pop-rank" to make the similarities and differences clear relative to "5-rough-no-pop-rank".

Well, first thought is: since N2D3P9 includes prime-limit, I could just grab the N2D3P9 of all 127-limit ratios. And then the 5-exponent would have to between -9 and 5 because `\frac{5}{3}^9` is ~99.23 and `\frac{5}{2}^5` is ~97.65 and if you go any bigger than 9 or 5 respectively then you'll exceed 130. I could repeat this logic for each prime. That's still pretty dumb; I'll still filter a bunch of >130 results in the end, and it'll be millions of N2D3P9's to check, but I think (?) I've crunched harder numbers on this topic ...BTW, Can you think of an easy way to generate a list of all the 5-rough ratios with an N2D3P9 of 130 or less? The idea would be to sort them on N2D3P9 and see which ones we have comma-symbols for (in primary roles only). Some would have more than one symbol, but are there any early in the list that havenosymbol?

Where'd you get the 130 number from? Is that the N2D3P9 of your least favorite comma in Sagittal?