I have

If you can't deal with it, the only way is to get a new crank and chainring.

Does anyone know how to check if the BB is causing the uneven chain tension?

Some dude with a beard does...

https://www.sheldonbrown.com/straighten-chw.html

Everyone except those riding with very expensive, precision manufacured track components has to deal with some variation in tension around the rotation of their cranks. From your description though it sounds like you have too much of it to be safe, and your chain definitely might fall off. But to be sure, try and derail it yourself, BEING REALLY CAREFUL not to AMPUTATE YOUR FINGERS. As long as your chainline is good and you can't derail it by hand, it might be rideable for now.

I had this problem with a conversion once. Turned out I had a bent rear axle.

Thanks everyone, I will try and analyse the problem again from the info you have given.

Looks like a distant cousin of the crank I used to have. Probably the ring was mated to the arm off centre.

In other news, it is pretty likely that the ring will separate from the arm (well, develop play first...) sooner or later, especially if you're heavy and/or skid. Mine fell apart even though I'm light and never skid. These things don't stand up to brutal back-and-forth forces. Mind you, even the ultra-expensive CF cranks fall apart under brakeless fixed riders.

Long story short: best plan would be to get a new crank and transplant this one into a singlespeed bike where it could live longer. Or ride it into the ground and come up with a plan after that.

BTW, it's easy to check that the chain tension problem comes from the crank and not a bent rear axle. If the chain's loose/tight cycle is in synch with the crank rotation, it's the crank.

Having elinated the BB, this must be the problem. How i wish i had got better crank arms (spider and chainring bolts etc)! I think this would have been more versitile in terms of adjustments (chainrings, chainline and tension). Morale: get a circular chainring setup. This chainring setup is just too low spec for use without any chain tensioning device (derailler etc) that could even out the bumps. Yes, before anone says so, I know I can't have a chain tensioner, and don't want one anyway! For a £100 ($194.217) experiment it has done its job. I am a convert to the fixed gear. When I have mashed the cogs and skid-stripped the tires to the ground I will re-build better, newer smarter!

Looks like that was originally a road double, with the inner ring removed those things aren't very strong. A kid completely crumpled one at the sprints in chicago last year, very nasty. I won't use cranks like that any more after seeing that failure.

Not a road double, just a cheap singlespeed crank, kind of like this Dotek $20 special I got from my LBS

hmm, guess the holes are for some kind of bash guard, I thought they looked too small to be for another chainring

Yep. This is a cheap and cheesy swaged crank, not suitable for fixed-gear use.

Swaged cranks are not designed to withstand the two-way torques of fixed gear use, and even if it was concentric, it would not be suitable, because the small diameter swaged joint between the arm and the chainwheel is liable to fail.

I learned this the hard way 30 years ago, when I had a Sugino Maxy crank on my Raleigh International. Going down a hill, the chainring suddenly started to slip and spin around the swaged connection. I was a fair ways from home at the time, and it wasn't easy getting home. I could pedal on the flats, but as soon as I got going up even a slight grade, the chainwheel would slip. It was sort of like driving a car with a toasted clutch.

That's a very cool looking frame, by the way.

Sheldon "Forged Not Swaged" Brown

I can imagine how that must've sucked. I rode 20km once with a bent fork and wheel. The bike wouldn't track straight at all.

Thanks sheldon. I'll just have to find a forged crank arm spider then. Maybe a good chance to go to 165mm?

Good luck finding a 165mm for cheap. Older road cranks can be had for pennies. The 600 crankset I run on my conversion cost me $20, plus another $20 for the chainring.