I love new clock designs, here is my try https://triclock.franzai.com/
The clock in Lord Vetinari’s anteroom didn’t tick right. Sometimes the tick was just a fraction late, sometimes the tock was early. Occasionally, one or the other didn’t happen at all. This wasn’t really noticeable until you’d been in there for five minutes, by which time small but significant parts of the brain were going crazy.
– Going Postal by Terry Pratchett, page 321
Why limit yourself? — make a 24-hour version and you have 86,400 possible times!