[yencabulator]

> part of it is natural. We roughly divide day and night into 2 parts, so we already need to have considerations for halves.

I forget which country did it but their historical time system counts hours as two halves from sunrise and then from sunset... That sounds a lot better than noon and midnight, to me. We could totally do

  sunrise = 0.00
  sunset = 9.99 -> 10.00
  sunrise = 19.99 -> 0.00

(For some standardized values of "sunrise" and "sunset" that don't slide around over the span of a year.)