I think I got the idea. Anyway, diagram time!
Spoilered for huge. Seriously.
Side view of the basic idea. (Stolen from the wiki)
█*██*██*██
█%>█%>█%>█
^██^██^███
When water hits the red pressure plate, it activates after 100 ticks. It will then (when it's active after the 100 ticks) toggle the red gear assembly. In the meantime, the yellow pump pumps the water to pink pressure plate. a hundred ticks after the water has left the tile, the plate deactivates and immediately the gear assembly restarts. Then the cycle starts anew.
Top view, everything. (As in Thundergates, Jyppa's fort. Note: the pressure plates are on the level below.)
Day cycle
███████████████
█^%-.%-^%-^%-^█
█|███████████%█
█%█ █|█
█^█ █^█
█|█ █%█
█%█ █|█
█^█ █^█
█|█ █%█
█%███████████|█
█^-%^-%^-%^-%^█
███████████████
The pressure plates are connected to (the mechanisms on the level above connected to) the pumps of the same colour. The white dot can be left empty and the white pump is not connected to anything. The red pressure plate is the Day++ one and is linked to the 'resistor' (a bunch of mechanisms to drain enough power so the cycle doesn't keep on working all the time, but only when the resistor has been activated (not enough power to the pumps). This is when the connecting mechanism, linked up to the red pressure plate, is toggled due to the red pressure plate being activated after an entire day has passed.) at the week cycle.
Week cycle. The colours here have nothing to do with the colours of the Day cycle.
█████████
█^%-^%-^█
█|█████%█
█%█ █|█
█^█ █^█
█|█ █%█
█%█████|█
█^-%^-%^█
█████████
Again, the red pressure plate is connected to the resistor. This time the one of the Month cycle. The rest should be apparent.
Month cycle.
█████████
█.%-^%-^█
█|█████%█
█%█████|█
█^-%^-%^█
█████████
Same explanation: red pressure plate linked to the resistor of the Year cycle.
Year cycle. I just made a small modification: It's also a 14-long cycle. This will allow the red pressure plate to be linked up to an adder, which will then be able to count the years and visualize them through some kind of means. At least, if it works like I think it should. If you don't want this, just remove the two white pumps and the red pressure plate. Note that this will need a different layout because of the fact that there can only be one channelled tile (with the plate) between each pump.
███████████████
█^%-.%-^%-^%-^█
█|███████████%█
█%█ █|█
█^█ █^█
█|█ █%█
█%█ █|█
█^█ █^█
█|█ █%█
█%███████████|█
█^-%^-%^-%^-%^█
███████████████
Does that look like it could work? Also, I think it would be clearer if you named the Day cycle the Hours cycle (because it just is a cycle of hours), the Week cycle the Days cycle, the Month cycle the Weeks cycle and the Year cycle the Months cycle. It will also make your notes more logical.
Now, let's say you want an automated entrance. And it only opens from the 1st of Opal to the 10th of Opal. You need to link up the pressure plates of day one of the month and day two to
an OR logic gate. The same goes for every pair of days. You'll be left with five pairs of days which activate when it's either of their pair. Then link up pairs of outputs. If you at one point have an odd number of outputs, just link the last one up to the higher tier. Continue to link them all up, until you only have one output left. Next, link this output to
an AND logic gate, along with the pressure plate of the month you want the door/bridge/... to be opened. Link the output of the AND gate to
a NOT gate and the output of that to the bridge. When it is OR the 1st OR the 2nd OR the 3rd... AND Opal, the bridge will NOT be toggled (meaning: open). If you want the bridge to be opened automatically in different months, link the months' pressure plates via OR gates until you only have one output left and link that with an AND gate to the output of the days, and then via a NOT gate to the bridge. If it wasn't clear: Diagram time!
Let's say you want the entrance opened in time for the caravans to arrive. They come between the 1st and 15th of Granite, Hematite and Limestone.
Days: 1 2 3 4 5 6 7
┌-┘
AND-┐
| |
W 4 | |
e | |
e 3-┘ OR--------┐
k | |
s 2-┐ | |
OR--┘ AND---NOT---[bridge]
1-┘ |
|
┌-----OR------┐
| |
┌---OR---┐ |
| | |
Months: 1 2 3 4 5 6 7 8 9 10 11 12
G S F H M G L S T M O O
r l e e a a i a i o p b
a a l m l l m n m o a s
n t s a a e e d b n l i
i e i t c n s s e s d
t t i h a t t r t i
e e t i o o o a
e t n n n n
e e e e
Note that the NOT gate is necessary when using a bridge, because the default state of it is open. This way, when the conditions are met (it is one of those days in one of those months) the AND gate will give an 'on'-signal, which corresponds to an opened bridge. If the conditions are not met, the AND gate sends an 'off'-signal. The NOT gate negates that signal and so the bridge gets an 'off'-signal (default state, i.e. open) when the conditions are met. If you're using things which are closed by default (e.g. doors, floodgates, grates...) the NOT gate obviously isn't neeeded.
That is the general way. Let's say you want to open the special foods stockpile in the week before and the week after your real life birthday. Or mine, in this example: 31/07, which corresponds to 28th Limestone (last day of the seventh month to make it easier/applicable to DF). The week before is the last week of Limestone and the week after is the first of Sandstone. This is a relatively easy example: I link week 4 to Limestone with an AND gate, and link week 1 with an AND gate to Sandstone. The output of those AND gates are linked to an OR gate (it's in either the last week of Ls OR the first week of Ss). The output of the OR gate is then linked to the door.
For a more complicated example, let's take the day I signed up here: 11/11 or 11th Opal. Again, the week before and after something has to happen. This means from 4th Op to 18th Op. Handily, week 2 (8th to 14th) is smack in the middle of the period. So we can link that one up directly to an OR gate. Then you link up the separate days with OR gates until you've only got one output left. This gets linked to the other input (the first comes directly from week 2) of an OR gate. Then link this with an AND gate to Opal and the output to something else.
BIG NOTE: I haven't tried any of this. It's all how I think it should work. It could be that it's all wrong. I'm going to test it myself, and hope it's all right. If somebody sees an error, please feel free to tell. This here is all FOR SCIENCE! and purely hypothetical. For me that is. There are others who've done one of these things. And both of these, but separately. I've done neither, and hope to do the combination of logic gates and a clock together. Anyway, if somebody already has done something like this and sees some fatal flaw in my plan, don't hesitate to tell me. Or just anybody who thinks he can help out.
... I think I overdid my post a bit. But I hope it was helpful. And correct. I think it is, but I'm not entirely sure.
EDIT: I made a bit of a mistake in my examples. I kind of forgot the way the clock itself worked: not with 28 days, but with 4 times seven days...
EDIT2: Corrected some mistakes regarding colour-coding and logic of the clock.
EDIT3: Made a mistake in the cycles: the pumps without a delay should be right next to each other (in case of the day and year cycles), and directly after the pressure plate which isn't linked to anything. I tried making it the way I had drawn it originally, but things went awry. The water went too fast for a couple of pumps and then it slowed back down. I'm fixing it, and hoping it will work. which it does. Victory!