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I've now tested a period doubler with a 600-step repeater, giving a 1200 step repeater:
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Now I just need to figure out how to halve the frequency of a repeater without doubling the number of components, and I'll be able to build a perfectly precise dwarven clock.
 +
 
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Experiment in progress:
 
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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.
+
The first two rows together form a 600 step repeater. The signal from the second row is fed into the third row, which, in theory, should act as a period doubler, making a 1200 step (daily?) repeater. If this system works, it may be possible to make a monthly repeater with about twice as many components as this. Without a period doubler, a monthly repeater of this type would require 28 times as many components as a daily repeater.
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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!
 
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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'm 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.
 

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