[C_J_H]

It seems logical that if space is not continuous [1] and relativity works roughly as we think it does, time couldn't be continuous either. If that's the case the shortest unit of time would intuitively be the planck length divided by C.

It would be interesting if the 'wavelength' of time gave rise to higher-order harmonics that we could actually observe.

[1]https://en.wikipedia.org/wiki/Planck_length

[gizmo686]

Do we have solid evidence (theoretical or otherwise) that space is not continuous.

My understanding is that the only fully accepted implication of the plank length is that it is the smallest measurable unit of length. Attempts to probe smaller regions result in black holes (do to the increasing energy necessary to probe small units of length; and the fact that energy is mass, and therefore exerts gravity).

[T-A]

Correct. And to date, all data remains consistent with space being continuous. This was big a couple of years ago:

https://phys.org/news/2015-03-einstein-scientists-spacetime-...

(the news piece focuses on foam, but the constraint applies generally to any kind of discrete structure where derivatives get replaced by stencils).