Re: the proposition for a related image which goes up to prime 23, I think it gets kind of messy past 16 because the harmonics stop being in order. I certainly agree we shouldn't replace what we've got (up to 13) with it. If you think it would be handy to our higher-limit brethren, I won't stop you from making it. But I also agree it would be low priority.
Oh, that's excellente!Done. Let me know what you think of the new edit, between horizontal rules?Also, I thought that maybe until we have a full-fledged interactive calculator ready for this notation — like we have for the precision level notation, in spreadsheet form — we might want to add a note explaining what to do with the bolded 3-exponents. I had totally forgotten about those, and also the bolding isn't exactly enough to help them jump off the page atcha to remind you they're there.
One nitpick, and this is my fault: I was wrong to suggest that it goes up to 23 unbroken. It skips 21. Oh and I see you observed and reported this yourself in the next post. But the text in the intro post still suggests otherwise.
Those instructions are quite helpful, yes. They give you an instant answer for the nominal+sharp/flat for any single otonal pitch up to 23. The generalized instruction would explain that, say you're notating 7/5, then you'd need to sum the 3-exponents for those two. I.e. the 7-comma's 3-exponent is 2, and the 5-comma's 3-exponent is -4, but the 5 is in the denominator so you flip the sign to 4, so the sum is 6, so you'd notate that off of the nominal -6 away from your 1/1, which in the case of G would be Db.
But don't agonize over it. The calculator will be immensely helpful for this sort of thing.
Oh, another thing: you determined the Prime Factor notation, as you say in the intro, "The symbols were obtained as follows: As we came to each new prime, we determined its Olympian symbol." To be clear, you mean you determined its Olympian symbol with your 1/1 set to G, right? It might be nice to mention that, if so.