I need to bring two branches of a palm tree/bush together. So I need a knot that is secure under tension but can also be progressively tightened. What knot would you recommend?
While I could think of a number of ways to tie a string the way you want, a cam buckle strap would be super simple and (more importantly) damage the bark considerably less. Even without a cam buckle, I would still advise tape before string. Professionals use strips of loose fabric to spread the load across the bark as much as possible.
I agree with the prior answer that a rope should not be your permanent solution here, given that it will ultimately damage the tree. However, I think you can mitigate this for short-term use of rope, until the tree has stabilized itself and no longer needs human help, in one of two ways, possibly both:
- Chafing gear. Use scraps of other material as a pad between the rope and tree. A tarp or other strong fabrics might work, but I think the best thing here is to run the rope though sections of old garden hose before tying your knots.
- Frequent re-adjusting. Every couple weeks, remove your rig and re-do it in a slightly different place, allowing any friction damage that has occurred to heal. (It sounds like you already plan to do this.)
Given that, I think the rig you want is some form of trucker's hitch, which is not really a single knot but a combination of multiple knots. Working together, the different knots form a virtual ratchet strap that holds itself under tension.
For a couple how-to's, here's some links: https://www.animatedknots.com/truckers/index.php and https://www.wikihow.com/Tie-a-Trucker%27s-Hitch. Normally Animated Knots is quite good, but in this case I think they didn't do well in showing the distinct parts. Wikihow's drawings can be hard to interpret, but give a decent idea of what is going on.