Wormwiggler, Currant, speed, troll direction, depth, ball weight, location of downrigger, etc... all play a part in "singing", just like Mac said!

I can tell you that once you find a combination that matches your target species, boat, rigger, etc... STICK WITH IT! I generally carry 4 sizes of rigger balls, usually located in the belly of my boat. 8 lb., 10 lb., 12 lb., and 15 lb. balls are present for fishing different bodies of water from lakes to tidal sounds. As you probably know, these locations require different sized balls for their given conditions, (tide, depth, species, etc..). By changing out a lighter weight for a little heavier model, I GENERALLY reduce or eliminate the line singing. This isn't always the case, but it usually gets it done!

Using the newer superline rigger line is an alternative that seems to work. I installed it on my Big Jon electric riggers for fishing spring kings at 200ft. I have only been using it for a month and thus far remains very effective! Disadvantage to the superline, is that it's not as durable as good old wire.

I can get away with 8 lb. balls trolling for lakers on local lakes with little to no line singing. Change the speed and or depth + - .5 mph or 20 ft. and it starts to sing. Either I ignore it, or just clip on a heavier ball. This is a simple fix usually not targeting just slower speeds for deep water lake fish. Changing weights has worked in such heavily tidal areas like the Florida Keys, Puget Sound, coastal Oregon, and the coastal waters of Alaska, (where I currently fish.)
I know many fishermen on MFF don't troll in the salt, but there's plenty of leasons salt water folks can pass on. One preventable saltwater tip for line singing is trolling with the tide, instead of against it. Trolling against a tide is "usually" ludicrous, and not advised for salmon. Trolling with the tide is much more effective, unless your at "slack" tide when the fish are aggressively feeding. Point is, no matter how many pounds of lead you place on your rigger, that tidal flow will still make your line sing! One small adaptation I tried with huge success was the addition of ball retriever. Ball retrievers, assist you in "retrieving" your ball back to the boat. The contraption is really just a cleat, string, and a pulley like mechanism that fits around your rigger line between the water and your rigger. You simply pull the retriever through the cleat and your ball comes closer to the boat, (especially helpfull for those who use the longer boom riggers.) I know I'm off track, but hear me out. Once your rigger weight is deployed to the desired depth, you can pull the retriever in JUST A LITTLE to eliminate pesky wire noise. If that little trick doesn't work, try a bigger ball.
I really can't find a real reason "why" rigger lines would chase fish away from your line?

That rhythmic whining seems to have a negative effect on me! I can tell you that some seals are programmed to follow boats with downriggers! Puget Sound Washington seals seem to associate downriggers with fish.

I had several seals follow my boat and wait for me to fight a fish. Once the fish are off the clip, the seals sneak in and grab the struggling fish either in one bite or tussle with you for several minutes, (until they come up for air!) Don't know where I was going with this, other than if a seal hears it under water, I imagine a fish would too!
I do believe that your riggers polarity has more of an effect on fish than wire noise.

You may know this.... or not! Check your riggers status using this sites helpful hints.
http://www.apexlures.com/blkbox3.htmlWormwiggler, Good luck with the singing or you can always get a good stereo to cancel out the noise!
Mac, I use depth track downrigger line on my old Big Jon electric riggers. IT'S GREAT STUFF and so far..... Quite!!!
http://www.cabelas.C0M/information/Boating/CabelasDepthTracDownriggerLine.html Are you purchasing one of those Ridgeback rattlers? They look like a space ship from an old 60's movie.

You have to give a report on those! -Barleydog