Three Dollar Quill

This post isn't too related to the specifics of this project, but I realized something recently and I want to see if it makes sense as a way to approach projects like this. When it comes to developing a calendar, it's possible to end up considering multiple different kinds of day, month, and year, with intimidating-looking formulas to convert between them. Look at all of the nesting, and the subtraction hidden right in the middle. But if we switch our perspective from "the duration of a celestial event" to "the frequency of changes between instances of the celestial event", then the formula simplifies into a simple subtraction: the "solar day frequency" is equal to the "sidereal day frequency" minus the "orbital frequency". If we think entirely in terms of frequencies, then tidal locking results in a "solar day frequency" of 0, which feels a lot nicer to me than "the day length is... oops, divided by 0".

Looking at the various months associated with the moon, it's my impression that nearly every calculation involved in this can be simplified by considering the frequency instead of the period, and then not converting back until the end (when people would rather see "twenty-whatever days" than "four hundred-ish nanohertz"), or not even really then, simply dividing day frequency by month frequency, rather than month length by day length.

I'm a little tempted to take this in a crank direction of, like, "why don't they put it in these terms?" but for one thing, reciprocal-based formulas do seem to be known, and for another, like, nobody has a reason to listen to me on this beyond "hey, let's try it out", so, like, if you're doing calendar worldbuilding based on this kind of epicycle-inducing rotate-y stuff, give this a shot and see what you think. I will say that this seems much more suited for spreadsheets or some other programming language, than for manual computation, but then, manually computing this stuff is kind of a chore if you're not doing the calculations for their own sake.

Anyway, it's getting late and I should wrap up, just wanted to get some thoughts out.

Good night.