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!