Search found 58 matches

by volleo6144
Thu Jul 16, 2020 12:49 am
Forum: Equal Division notations
Topic: A proposal to simplify the notation of EDOs with bad fifths
Replies: 100
Views: 25337

Re: A proposal to simplify the notation of EDOs with bad fifths

There are only finitely many (non-"b") EDOs of each color except grey, with the last one of each being: Black: 1 Gold: 42 (5n stack ends at 30 / 35 ) Green: 83 (22n stack ends at 66 / 88 ; 27n stack ends at 54 / 81 ) Blue: 259 (17n stack ends at 136 / 153 ) Magenta: 724 (29n stack ends at 377 / 406 ...
by volleo6144
Tue Jul 14, 2020 4:10 am
Forum: Just Intonation notations
Topic: developing a notational comma popularity metric
Replies: 463
Views: 25977

Re: developing a notational comma popularity metric

But I can't quite figure out myself how taking the log of poapfar would be equivalent to a soapfar. It sort of makes sense, because of shifting from multiplicative space to additive space, but there's something about it being broken across primes that makes me thing that can't be true. Because the ...
by volleo6144
Mon Jul 13, 2020 1:09 pm
Forum: Equal Division notations
Topic: A proposal to simplify the notation of EDOs with bad fifths
Replies: 100
Views: 25337

Re: A proposal to simplify the notation of EDOs with bad fifths

But I have a better criterion. I realised that what makes a second-best fifth worth considering for notation, is when it is not much worse than the best fifth. A convenient cutoff is where the error in the second-best fifth is no more than 4/3 of the error in the best fifth. Putting it another way:...
by volleo6144
Mon Jul 13, 2020 3:28 am
Forum: Equal Division notations
Topic: A proposal to simplify the notation of EDOs with bad fifths
Replies: 100
Views: 25337

Re: A proposal to simplify the notation of EDOs with bad fifths

Here's a proposal for precise colour boundaries at fifth-sizes which are noble fractions of an octave. I haven't always given the noble ratios in lowest terms. I've left them in a form where the denominator refers to EDOs of the colours on either side of the boundary. Boundary (fifth error) Colour ...
by volleo6144
Mon Jul 13, 2020 1:25 am
Forum: Equal Division notations
Topic: A proposal to simplify the notation of EDOs with bad fifths
Replies: 100
Views: 25337

Re: A proposal to simplify the notation of EDOs with bad fifths

Ah. Thanks for that. How about a limit on abs(group-10)+steps_per_CD? Seems maybe okay; this essentially means drawing two diagonal lines parallel to the two diagonals with 72 on them. If this limit is 12 (as the value for 72 ), then ten EDOs on the sharp side (42, 49, 56, 63, 70, 54, 61, 68, 59, 6...
by volleo6144
Sun Jul 12, 2020 11:29 pm
Forum: Equal Division notations
Topic: A proposal to simplify the notation of EDOs with bad fifths
Replies: 100
Views: 25337

Re: A proposal to simplify the notation of EDOs with bad fifths

What's a reasonable criterion for deciding which "b-grade" ETs should be included on the periodic table? Some maximum value for EDO-number multiplied by absolute error in cents? I'm thinking we should only include 23b, 30b, 35b, 37b, 42b, 47b and 59b. Note: any non-"b" EDO will have EDO × error < 6...
by volleo6144
Thu Jul 09, 2020 4:21 am
Forum: Administrative, forum or website issues
Topic: New [over]...[/over] bbCode, and short forms of several existing bbCodes
Replies: 8
Views: 738

Re: New [over]...[/over] bbCode, and short forms of several existing bbCodes

On my end, the smilies aren't mangled per se, but just ... now they're superscripted forms of the ASCII smiley code; a peek into Firefox developer tools shows that's literally all they are: : /|\: instead of the actual smiley :/|\: / ↑. Anyway, with the increasing use of [ pre] tables, it might be i...
by volleo6144
Sat Jul 04, 2020 2:00 am
Forum: Equal Division notations
Topic: A proposal to simplify the notation of EDOs with bad fifths
Replies: 100
Views: 25337

Re: A proposal to simplify the notation of EDOs with bad fifths

Thanks for that. I've nudged the purple/rose boundary in this post to include 59b in purple. In fact, I thought, why not define the boundary as the noble number that is the limit of this fibonacci-like sequence 4\7 , 15\26 , 19\33 , 34\59b , 53\92b , 87\151bb , 140\243bbbb , 227\394bbbbbb , ... i.e...
by volleo6144
Fri Jul 03, 2020 1:06 am
Forum: Equal Division notations
Topic: A proposal to simplify the notation of EDOs with bad fifths
Replies: 100
Views: 25337

Re: A proposal to simplify the notation of EDOs with bad fifths

By the way, thanks for correcting my pronunciation of "a-POT-o-me". I had been pronouncing it "AP-o-toam" like "microtome" all these years! Yeah, me too. What's so special about a 692.2¢ fifth that makes it the boundary between purple and rose? Nothing. Any value between 15\26 ≈ 690.91 ¢ and 19\33 ...
by volleo6144
Mon Jun 29, 2020 12:00 pm
Forum: Just Intonation notations
Topic: developing a notational comma popularity metric
Replies: 463
Views: 25977

Re: developing a notational comma popularity metric

No, not a lot else. It's really just the 3-exponents. (for schismas and schisminas, apotome slope and abs3exp are essentially the same thing). Yeah, pretty much. The definition of a comma's apotome slope is equivalent to "the comma's 3-exponent minus its size, where the size is measured in 7eda (~7...