## Search found 57 matches

Sun Jun 28, 2020 2:30 am
Forum: Just Intonation notations
Topic: developing a notational comma popularity metric
Replies: 441
Views: 25177

### Re: developing a notational comma popularity metric

Suppose we raise π(p) to some power? In its case the power would probably be > 1. I could see this being the right thing. That composers actually use higher primes in a pattern which is based not on their size but their index in the sequence of primes, but then not a linear weight on these indices ...
Sat Jun 27, 2020 4:11 am
Forum: Just Intonation notations
Topic: developing a notational comma popularity metric
Replies: 441
Views: 25177

### Re: developing a notational comma popularity metric

That thing has an SSL certificate that's expired by about a week... If you're not comfortable visiting that link, volleo6144... No, there really wasn't anything I was worried about, really; it's just that ... the site's admins probably haven't cared in a week, or they'd have ... done something. ---...
Fri Jun 26, 2020 11:24 pm
Forum: Just Intonation notations
Topic: developing a notational comma popularity metric
Replies: 441
Views: 25177

### Re: developing a notational comma popularity metric

I'm not sure I understand exactly what you mean: 1:343 abs(n - d) = 343 - 1 = 342 1:341 abs(n - d) = 341 - 1 = 340 1:343 abs(sopfr(n) - sopfr(d)) = 7 + 7 + 7 = 21 1:341 abs(sopfr(n) - sopfr(d)) = 11 + 31 = 42 It looks like abs(sopfr(n) - sopfr(d)) maybe does a better job, but I don't see a "heavy [...
Fri Jun 26, 2020 11:57 am
Forum: Just Intonation notations
Topic: developing a notational comma popularity metric
Replies: 441
Views: 25177

### Re: developing a notational comma popularity metric

Ah ha! I see now. The usage of . as a multiplication symbol is not intuitive to me. That thing has an SSL certificate that's expired by about a week... Also, coming from a pure math background, it might be helpful to note that various metrics often only use a number's square instead of its absolute...
Fri Jun 26, 2020 4:03 am
Forum: Just Intonation notations
Topic: developing a notational comma popularity metric
Replies: 441
Views: 25177

### Re: developing a notational comma popularity metric

I feel like there's gotta be some pithier and clearer term for "they sort the same"... like, mutually monotonic? Anyway, that's a good observation re: 29:1 and 31:1's popularity order being switched (vis-à-vis their prime limit). That could mean either: b. the weight on primes may need to be more c...
Thu Jun 25, 2020 4:20 am
Forum: Just Intonation notations
Topic: developing a notational comma popularity metric
Replies: 441
Views: 25177

### Re: developing a notational comma popularity metric

It sounds like maybe you were thinking our candidate function would map a comma to a value that was meant to look just like the value of a rank, e.g. it might try to map 11:1 to something really close to 6 because 11:1 is the 6th most popular comma. That could work too, but it seems like an extra s...
Wed Jun 24, 2020 11:32 am
Forum: Just Intonation notations
Topic: developing a notational comma popularity metric
Replies: 441
Views: 25177

### Re: developing a notational comma popularity metric

This didn't occur to me when I wrote the above, but I'm pretty sure that there would always be a number of 2's and 3's you could find which could get n-d down to 1, though it could be a huge number of them. Størmer's theorem effectively states that there are only finitely many superparticular inter...
Tue Jun 23, 2020 6:25 am
Forum: Glyph design and Handwriting
Topic: Magrathean diacritics
Replies: 159
Views: 14133

### Re: Magrathean diacritics

Re: the tina smileys, I do plan to add those to the forum eventually. I have added Sagittal smileys before so I know how. Would it be helpful to have them sooner than later? I think our discussion at the moment is not being hindered dramatically by lacking them. See, I believe that is in fact the c...
Tue Jun 23, 2020 12:24 am
Forum: Glyph design and Handwriting
Topic: Magrathean diacritics
Replies: 159
Views: 14133

### Re: Magrathean diacritics

The "u" term heavily penalizes commas with many primes on one side but only one or two, or zero, on the other, such as our yellow 2 [5831:5832], 4 [3024:3025], and 5 [2400:2401] tinas. So "u" is the only thing differentiating 7/5 from 35 etc, but not very well. I'd like to understand why "t" isn't ...
Mon Jun 22, 2020 10:15 am
Forum: Glyph design and Handwriting
Topic: Magrathean diacritics
Replies: 159
Views: 14133

### Re: Magrathean diacritics

I did this for the yellow tina candidates (the ones we've mostly agreed on): I notice the relatively large value 44.155 that the 13:77n got. This appears to be the result of 0.005(13640319 - 13631488). I should have been more explicit about what I meant by n and d: I didn't mean in the actual ratio...