I figured out the clock system for Otvei, but I haven't made words for each term yet. It uses a 24-hour clock, with 6:00 am being the start of the day (0:00 in Otvei). I'm still using 60 seconds per minute and 60 minutes per hour to make conversion easier. I also divided the day into different sections.
24 hour period (day)
...subdivides into 12-hour periods:
6 am to 6 pm (daytime)
6 pm to 6 am (nighttime)
...subdivides into 6-hour periods:
6 am to 12 pm (morning)
12 pm to 6 pm (afternoon)
6 pm to 12 am (evening)
12 am to 6 am (night)
...subdivides into 3-hour periods:
6 am to 9 am (early morning)
9 am to 12 pm (late morning)
12 pm to 3 pm (early afternoon)
3 pm to 6 pm (late afternoon)
6 pm to 9 pm (early evening)
9 pm to 12 am (late evening)
12 am to 3 am (early night)
3 am to 6 am (late night)
Here's a picture (kind of large):