I know what you're saying to yourself. "If only I could get rid of that awkward base-10 numbering system, I could finally get my life together - maybe learn to play violin." Good news! I have your solution. Based on a variant of the dozenal system of notation (covered at length at www.dozenal.org), I've put together a base-12 clock. It keeps traditional units for years down to hours, simply converting the numbers to their duodecimal equivalents.
Minutes work a little differently, since simply converting the minutes to their base 12 equivalent actually made the clock a lot more awkward. Instead, I implemented 72 shorter minutes which works better in most ways.
I have to say, the pebble API is a delight to use, and an all digital watch makes this kind of kooky project completely feasible. It was interesting to notice how deeply embedded the number 12 is in our time system already. Not only are there 12 months and 12 hours, but the hour is broken into twelve 5 minute units. Duodecimal numbers actually work very well in this application.
If you're interested, look for "Dozenal Watchface" in the pebble app store.