Hoo, boy. Try 15¢ worth of vinegar (the active component of ketchup) before you
try $2 worth of ketchup. To make it stronger, put some salt in it.

Regardless of what chemical cleaning method you use, I strongly suggest that
your last step is boiling the rope in water and then pulling it straight out of
the hot water and allowing it to self-dry which it should do within 60 seconds.

It won't stay clean very long, you know. Google on protecting copper or brass,
there are many posts on this subject.

GWE

Larry Green wrote:

I wear a copper bracelet made from 1/8" (3 mm) diameter chain links (as
opposed to the more usual copper band). During the summer the bracelet
will turn green within an hour if I am outside and sweating as the salts
react with the copper.

I have tried lemon juice and vinegar to clean it but by far the best
cleaning 'solution' I have found so far is tomato ketchup. I simply
squirt some into a small bowl, lay in the bracelet and then push the
ketchup around with my finger to make sure it fills all the voids.
Thirty minutes later I take an old toothbrush and give the bracelet a
good scrub with the ketchup to get the oxide build up off the inner
faces of the links. A rinse under a warm tap followed by a quick rubbing
with a few drops of liquid dish soap to remove all traces of the ketchup
followed by a second rinse and then drying with a paper towel and the
bracelet looks like brand new again.

The bracelet will take several weeks to tarnish under normal conditions
but sweat will 'turn' it within an hour!

I would suggest you try coating your rope with ketchup and then rubbing
it with a toothbrush (or other stiff brush) after a suitable 'soaking'
period. I think you will find that the ketchup will penetrate deep into
the 'grooves' of the rope and the stiff brush will remove the oxide
build up your soaking methods have left behind. The nice thing is it is
environmentally friendly and you don't have to worry about splashing
nasty acids all over yourself as you scrub at it with the brush.

HTH.