Search found 81 matches

by volleo6144
Wed Jun 24, 2020 11:32 am
Forum: Just Intonation notations
Topic: developing a notational comma popularity metric
Replies: 493
Views: 211811

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...
by volleo6144
Tue Jun 23, 2020 6:25 am
Forum: Glyph design and Handwriting
Topic: Magrathean diacritics
Replies: 213
Views: 125723

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...
by volleo6144
Tue Jun 23, 2020 12:24 am
Forum: Glyph design and Handwriting
Topic: Magrathean diacritics
Replies: 213
Views: 125723

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 under...
by volleo6144
Mon Jun 22, 2020 10:15 am
Forum: Glyph design and Handwriting
Topic: Magrathean diacritics
Replies: 213
Views: 125723

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...
by volleo6144
Mon Jun 22, 2020 1:55 am
Forum: Glyph design and Handwriting
Topic: Magrathean diacritics
Replies: 213
Views: 125723

Re: Magrathean diacritics

It seems wrong to include your "u", as all the other terms are logarithmic, or kind of logarithmic, but "u" is linear. So relative to all the other terms, "u" is exponential. "u" is scaled to one prime 5 for every 1000 difference in the ratio (the 1:1001 &quo...
by volleo6144
Sun Jun 21, 2020 4:55 pm
Forum: Glyph design and Handwriting
Topic: Magrathean diacritics
Replies: 213
Views: 125723

Re: Magrathean diacritics

q + 0.75r + 0.1s + 0.05t + 0.005u q: Sum of Prime Factors > 3 r: Tenney Height = log 2 (n×d) s: prime limit t: abs(SoPF>3(n) - SoPF>3(d)) u: abs(n - d) [...] Lemme know what y'all think. I'll run it against the tina candidates if I get an endorsement. I did this for the yellow tina candidates (the ...
by volleo6144
Sat Jun 20, 2020 2:45 am
Forum: Notations for other tunings
Topic: Notation for George Secor's High-Tolerance Temperament
Replies: 13
Views: 13292

Re: Notation for George Secor's High-Tolerance Temperament

A fourth message defining the fifth itself and noting a number of commas of the temperament appears here , which is linked to from the sagittal.org homepage. In order for this temperament's commas to have a 12edo keyspan of zero, 8:11 has to be an augmented—not perfect—fourth (:(|): = P1; :/|\: = A1...
by volleo6144
Fri Jun 19, 2020 10:37 pm
Forum: Developing Educational Resources
Topic: How best to use directed comma names
Replies: 26
Views: 22386

Re: How best to use directed comma names

If we put a nickel in a jar every time one of us edited each other's post instead of quoting it, we'd be... well, we'd probably have about a 7C by now. ...You mean, like, 240edo nickels? (Also I just love doing things 5.5 times...) I think the apotome should be called "3A". If :/||\: is 1...
by volleo6144
Fri Jun 19, 2020 10:23 pm
Forum: Developing Educational Resources
Topic: Naming commas and other intervals: a compilation of various sources
Replies: 84
Views: 50119

Re: Naming commas and other intervals: a compilation of various sources

The algorithm shown in the paper only disagrees with the "Sagittal" algorithm it describes for five primes below 100: Pr DRComma SagComma -- ------- -------- 17 1 /17 k 17 / 1 C (DR = :~|: / SAG = :~|(:; sum = 12edo3C) 59 1 /59 M 59 / 1 L (DR ~ :'::/|): / SAG ~ :.::(|\:; sum = 7edo3A) 67 1...
by volleo6144
Fri Jun 19, 2020 4:16 am
Forum: Glyph design and Handwriting
Topic: Magrathean diacritics
Replies: 213
Views: 125723

Re: Magrathean diacritics

Modified the table a little: abs3exp 1/(14-x)-1/14 ×154 1/(14 1.5 -x 1.5 )-1/(14 1.5 ) 1054 1/(14 2 -x 2 )-1/(14 2 ) 6468 0 0 0 0 0 0 0 1 0.005494505495 1 0.0003715239113 0 0.0000261643119 0 2 0.0119047619 2 0.001089600817 1 0.000106292517 1 3 0.01948051948 3 0.002102165925 2 0.0002455527666 2 4 0.0...