Credit for inspiration from MrFake, in An Advanced Repeater.
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^ and ^ are both 1-7 water plates linked to the gears of the same color. This time I've planned the necessary access doors and stairwells ahead of time instead of adding them haphazardly. Build order: upper pump, lower pump, gears, pressure plates.
The green pressure plate produces an OPEN signal exactly once every 200 steps (once 2 water have been put into the system). Tested and confirmed. Hopefully the base component in a dwarven clock that doesn't drift over time.
Using the same principles one can construct a repeater which produces a signal on any multiple of 200. The following is a tested design for a 400 step repeater:
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A compact version, sharing some power transmission gears:
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600 step repeater:
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One way to initialize it is by putting 1 water on the red, blue, and cyan plates, then a 2nd water on the red and cyan plates, and finally a 2nd water on the blue plate.
I've now tested a period doubler with a 600-step repeater, giving a 1200 step repeater:
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The first two rows together form a 600 step repeater. The signal from the second row is fed into the third row, which acts as a period doubler, making a 1200 step (daily!) repeater. I have an idea for a monthly repeater, using a 1000-step repeater doubled twice to 4000, delayed by 200 steps to 4200, then doubled another three times to 33600 steps (1 dwarf-month). The only bit I'm having trouble with is that extra 200 step delay in the middle. I'll put my design here when I have something which might work.
Hmm. If I have this right, I might have figured out how to add exactly 100 steps to any repeater's period. I must test this design:
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If this works as I expect, it should be a 300 step repeater. If so, then I should be able to build a 1000 step repeater, double it to 2000, add a hundred to get 2100, then double it 4 times to get 33600 (one dwarf-month). Testing in progress!
Update: saving and reloading while a gear is hanging above an inactive gear deconstructs the upper gear on reload, even if it should be supported by neighboring machinery. Once it's rebuilt, the machine will work correctly, until you have to save the game again. I've redesigning all my devices to prevent this problem from coming up, and, incidentally, making it easier to power some of these devices using windmills. As you can imagine, this involves quite a bit of digging and rebuilding things in my test area.