**Trigger warning for sexual violence
One of the worst decisions the US has ever made was to force women to pass on the genetics of likely the worst person they've ever met on to the next generation. The real problem should be that these numbers are way too high. We need to be banning rapists.
So technically you could fit 360 sidereal days into one of Earth's rotations around the sun without the need of any intercalation. Here, I did the math for you.
The only lunisolar system I've ever seen capture this perfectly is actually the zodiac wheel.
Every lunar phase through the constellations is like a month and with the sun, it's like a season.
The solstices and equinoxes are exactly 180° degrees apart. It's perfect as far as I can see.