I'm kinda always looking for compact clocks to power hoppers, as I use waterstreams for most item transports. I usually build the clock in the attached picture, which has the beautiful property that it's fast and 1-wide tileable and needs only access to one side of the dropper. However, it works at double hopper speed and becomes very noisy if items come in slower.
I came up with a hopper based clock that also needs access from only one side, which is often important for compact builds. But that one is too slow, it works only at half hopper speed (I think 7 redstone ticks compared to 4, to be precise).
Is there another elegant clock that is
(a) pretty much silent.
(b) works approximately at hopper speed and
(c) can power a hopper from one side, and
(d) allows a solid block over the hopper (for water elevators)?
I played around with your setups a bit and discovered that you can slow down the observer clock by adding more observers, the monstrosity in my second screenshot runs at less than one pulse per second.
The one in the first screenshot seems to run at about half the speed of the original, for some reason it runs unevenly, tick-tick---tick-tick---tick-tick---
The repeater seems to be needed, without it the piston just keeps pushing the observer back and forth instead of cleanly retracting it when the dropper empties.
I guess I was counting dropper ticks rather than looking at what the clock itself was doing, the uneven ticking must be because the clock is still a bit too fast for the dropper and if the dropper isn't ready it skips a pulse and waits for the next one?
Yes, the repeater is necessary because otherwise the piston gets powered by the top observer and gets a bud from the other observer, I guess.
Still, more weirdness: If I power a dropper through a 4-observer chain, it runs exactly at hopper speed (4 redstone ticks).
However, if I power the dropper with the same 4-observer chain attached to the piston with the comparator, it runs faster (3 redstone ticks I think). After removing all differing blocks (piston, repeater, comparator) the other clock continued to run faster. I think while a traditional 4-observer clock (much like a 4-hopper clock) pulses 1 signal sequentially through the observer, here we get 2 independent signals circling in, see 3rd picture: Observer 1 is first triggered when observer 2 is pushed in, then observer 2 is triggered independently because it was moved. You can see this with the redstone resource pack that 2 observers are powered at the same time.
Consequently we need 8 observers to pulse the dropper with hopper speed. Maybe not as compact as I hoped, but a solution nevertheless