Three Dollar Quill

Am I doing any better with the brain fog? I don't know. I feel fine right now, but also I'm not really pushing myself to work on anything (with one weird exception). Probably that will be helpful for recovering.

The weird exception is, I've been pulling on a thread regarding patterns in interval sizes in scales, and I found an approximation to somewhat specific logarithms, which seems consistent, but I'm not sure if it's useful. Basically, for a concrete example, in a scale that evenly divides the octave, the number of steps in the octave will be roughly the square root of three times the number of steps in the fifth. The only way I can see this being "generally" useful is if it's much easier to get rational approximations to the square root of a rational number, as opposed to rational approximations to the binary logarithm of a (different) rational number. I haven't had the focus to look up whether this is even the case. Although, most music involves relatively coarse divisions of the octave, so it does seem to take a while for the inaccuracies to mean anything. Like, the approximation I mentioned before is good enough until 49edo.

Anyway, I didn't have anything else to talk about, so I'm going to end this now.

Good night.