The Sagittal forum

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 ...

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.

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...

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 ...

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 ...

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:...

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 ...

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...

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 ...

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...