I installed an accurate once-a-day signal (in the meeting hall and in the duchess' bedroom) - opens a hatch exactly once every day, precise to the step. Yeah, another clock-capable oscillator. The basic repeat period is 600 steps, i.e. half a day. It just needs to feed a one-two counter to generate the daily signal, and i had one of those lying around already. It runs on a single minecart (of course) and needs no power:
..^╗ ..╔╗
..║▲0 ..║╚0
0▲╝║▲0 0╗╝║╔0
0▲║║▲0 0═║║═0
0▲║╔▲0 0╝║╔╚0
.0▲X .0╗║
..╚╝ ..╚╝
Ramps/ Track
buildings
0 - Wall
▲ - Ramp, all of them impulse ramps
^ - Pressure plate that generates the output signal (twice a day)
X - Floodgate to stop the cart if desired
The cart bounces north-south on each of the three-ramp series most of the time: it is thrown into the array from the side at notable speed, thus collides with the limiting wall before accelerating along the line. The cart will thus start out at the very limit of the tile, practically scraping on the wall. The EW ramp between the opposing ramps accelerates the cart to the side once everytime it passes, but only for a single step, and the speed is instantly cancelled after leaving the tile (those are both checkpoint effects).
Thus, on each passage, the cart is displaced ~4900 length units to the side. A ramp tile is a bit over 140.000 units wide, so it takes 29 passes until the displacements carry the cart off the row of ramps. The cart goes through the northern resp. southern loop and passes to the other ramp array, at sufficient speed to bang into the wall and start the full displacement cycle on that side as well. With the small extra loops, the total time consumed for every full cycle comes to precisely 600 steps.
I didn't bother to take a picture, it ended up rather untidy, and it's pretty much impossible to explain without the diagrams anyway.