Okay. I had a sleep on it. And I think I get it now.
It could be said that a primary goal of yours is that you really really really want there to be something out there whose preferred name is "the 5C". It's not enough for that to be an accepted alternative. You worked really hard to convince people to start calling the syntonic comma the 5C and that was hard enough. You have strong doubts that we'd ever convince people to use "1/5C" and "1/5C down", and while I'm often lapse into not being mindful of this consideration, when I am mindful of it, I must admit I wouldn't expect the general public, burdened by convention, to go along with it.
In what sense are your preferred names "directed" if you still need to put "down" after them to give them a direction other than up? That was the case with the original undirected names with the colons.
I see I already asked that, and you responded
Right. And what I responded was, in bold text:
cmloegcmluin wrote: ↑Sat Jun 20, 2020 4:20 am
The purpose of encoding the direction into the name is to disambigutate the orientation of the comma's prime content with respect to whether you are moving up or down by it.
Which I can see I got grumpy about you not responding directly to... but it looks like implicitly I came to realize that you didn't so much disagree with that idea as much as wish to deprioritize it. Which I eventually went along with. But I see that I've naturally circled back to this personal fixation of mine, because though we agreed your way was better before, it didn't fully sink in for me.
So there are two aspects of a comma involving direction: the direction of its prime content (which 2,3-free primes are in the numerator, and which are in the denominator), and its direction itself (is it positive or negative when written as cents), and I clearly have a deep-seated desire to separate the information about these two types of direction, encoding the former in the comma name, and the latter by accompanying it with the word "(up)" or "down". I suppose it's my engineering instincts which draw me to this clean implementation. But I recognize now that there are more important considerations than cleanliness. The users of this system will not be amenable to this approach, and our mandate is to devise a system which people (read: actual composers, not technico-aesthetic nerd hobbyists like myself) will actually take to.
And so I've come around, again, to the approach of using the comma name to represent both the direction of the prime content as well as the direction of the comma. We could say, then, that each size category (except the unison) has a pair
of bounds mirrored by the unison, e.g. that a kleisma is any comma in the range -11.73¢ to -4.5¢ or 4.5¢ to 11.73¢.
So then what of that one massive worm, the case of the ambiguous 5-limit MS+A counterexample to the naming scheme?
(get it, prim:-)
Mostly I say: eff it. We shouldn't make decisions that affect how practical Sagittal's accompanying comma naming system is on such ludicrous counterexamples.
I almost set out to write a script this morning that would see if there were any simpler counterexamples to worry about, but then I had the thought while grinding my coffee... why can't we just use the 2-exponent as a tie-breaker?
In other words, why not name them like this:
[336 2 -146> = 1/112...625MS+A
[-342 2 146> = c112...625MS+A
Then we could also say:
[-336 -2 146> = 112...625MS+A
[342 -2 -146> = c1/112...625MS+A
I think there might still be ties possible. You'd have to find a comma where when you flip the sign on both the 2-exponent and the 3-exponent (while not flipping the signs for the 2,3-free prime content; otherwise you'd just have flipped the whole thing) you end up in the same size category. That'd mean that the combination of 2-exponent and 3-exponent on its own would have to be really small, e.g. the 3s, [-84 53⟩, ~3.6¢. But keep in mind that since in this counterexample scenario we don't have recourse to octave-reduction, we still have to find some 2,3-free prime content to accompany such a thing which is also itself comma-sized.
I found many, many examples. Here's just one:
[0 0 0 -1 2 0 -1⟩
That's 121/119, ~28.855¢, what we'd call the 121/(7⋅17)C. So this:
[-84 53 0 -1 2 0 -1⟩
at ~32.470¢, is the hc121/(7⋅17)C (that's right, it's the hypercomplex one... there're two other simpler 121/(7⋅17) commas before we reach this one which has the property we're after). So then, according to my code now, this:
[84 -53 0 -1 2 0 -1⟩
at ~25.240¢, is also
the hc121/(7⋅17)C. And the point here is, that even we used the 2-exponent as a tie-breaker, we'd still have a problem.
I'm open to suggestions on how to break the tie at this point. Maybe we just say that the one whose 3-smooth content is super is the simpler one, i.e. the one which adds the 3s is simpler and the one which subtracts it is the more complex?
Dave Keenan wrote: ↑Wed Dec 09, 2020 5:17 pm
It seems bizarre to me, to consider "5C" a simplified form of "1/5C".
It now seems bizarre to me, too, in the face of the unmovable object which is the community's refusal to accept "1/5C down" over "5C".
Please spell out your preferred version of that sentence about
The same one I came to prefer before: "The right barb
is therefore defined as the 55 comma (55/54), i.e.,
the 11M diesis (33/32) plus
the 5 comma (80/81), where the upward and downward left barbs cancel."