12 x 60 clock and calendar

The 12 hour clock is beautiful. Yet we have 24 hours per day.

Should we keep the hour the same length, then we could split the day into day and night, or morning (am) and evening (pm).
You could then have a format similar to ISO 8601 replacing the T separator, to indicate which half day with A for AM and P for PM, which would still result in correct lexical ordering.

2019-08-18A08:00 and 2019-08-18P08:00

Calendars usually count a day as a whole rotations of the earth with respect to the sun. We could reuse the 12×60 clock for the calendar, counting half days instead. We’d then count double the number of days per month.
Odd numbers would be AM and even numebrs would be PM.

2019-08-36T08:00 and 2019-08-37T08:00

Extra days for 31sts  could be indicated by another signal, such as a light.

This approach doesn’t feel like an improvment over current calendars.
It’s presented here to illustrate that a variety of approaches have been considered, tested and decided against.