Search found 55 matches

by volleo6144
Mon Sep 21, 2020 9:46 am
Forum: Just Intonation notations
Topic: developing a notational comma popularity metric
Replies: 427
Views: 21826

Re: developing a notational comma popularity metric

and that there's nothing special about the middle exponent of 3 that generates Mills' constant, so there are many similar constants. Yeah. The reason why the version with 3 is the most well-known is because the 2-version might not actually lead to the sequence starting 2,5,29,853,727613 with each e...
by volleo6144
Mon Sep 21, 2020 1:58 am
Forum: Glyph design and Handwriting
Topic: Magrathean diacritics
Replies: 159
Views: 12303

Re: Magrathean diacritics

Actually, I can see some serious floating-point overflow and underflow issues with the form: N2D3P9 × 2^(2^(ATE-DATE)) × 2^(2^(AAS-DAAS)) float overflows at 2^128 = 2^2^7 or ATE=16*, and double overflows at 2^1024 = 2^2^10 or ATE=19*. You'll be fine—I'm sure no comma that has 3 11 as a factor in ei...
by volleo6144
Fri Aug 07, 2020 6:30 am
Forum: Just Intonation notations
Topic: developing a notational comma popularity metric
Replies: 427
Views: 21826

Re: developing a notational comma popularity metric

JavaScript has a primitive value called NaN, which stands for "Not-a-Number". I was using the type check "typeof candidate === 'number'" to confirm that results of the antivotes calculation were all numbers, as opposed to nulls, undefineds, or NaNs. Hilariously, in JavaScript, "typeof NaN" returns ...
by volleo6144
Sat Aug 01, 2020 4:03 am
Forum: Just Intonation notations
Topic: developing a notational comma popularity metric
Replies: 427
Views: 21826

Re: developing a notational comma popularity metric

Yes, welcome back @volleo6144 ! Although I feel you've been here the whole time, offering your silent support :) Mostly. I guess I was just, like, pretty sure I didn't have much to say that you hadn't already figured out, or something. As your example shows, c x with c<1 decreases with increasing x...
by volleo6144
Fri Jul 31, 2020 10:34 am
Forum: Just Intonation notations
Topic: developing a notational comma popularity metric
Replies: 427
Views: 21826

Re: developing a notational comma popularity metric

We also have the change-of-base identities, which make the logarithm-based ones equivalent to \(log_cx\) and \(log_xc = \frac1{log_cx}\), with different c's. And if we're allowing c<1 in the latter, we also ought to allow c<1 in \(c^x\), which has a similar effect of only allowing the penalty to be ...
by volleo6144
Sat Jul 18, 2020 4:22 am
Forum: Equal Division notations
Topic: A proposal to simplify the notation of EDOs with bad fifths
Replies: 95
Views: 23734

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

Dave Keenan wrote:
Sat Jul 18, 2020 1:09 am
#A9A9A9 darkgrey (poorly named) Dark grey is more like this: #373737
And this isn't even the weirdest part: grey #808080 is darker than darkgrey #A9A9A9.
by volleo6144
Fri Jul 17, 2020 1:07 am
Forum: Equal Division notations
Topic: A proposal to simplify the notation of EDOs with bad fifths
Replies: 95
Views: 23734

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

I love the way you go to the trouble of hiliting the EDOs in your posts with the correct colours too. :) Yeah. It's especially nice that many of the colors are on vertices of the RGB cube (where all three values in the triplet are either 00 or FF), and most of the ones that aren't are the more comm...
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: 95
Views: 23734

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: 427
Views: 21826

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: 95
Views: 23734

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:...