Made my own (using different sized 'hardware cloth' = mesh of whatever size needed bought by yard/meter in hardware store), using lumber for a frame and stapling mesh to it...

My theory is that poorly constructed US tax laws regarding inventory make buying much of a variety of hardware cloth difficult. One fourth and 1/2 are available and other than expensive mail order, I've found nothing else at least around me. There is insect screen of course.

Regarding the poster's question, is 1/12th not about as small as you want to go? It is about 2.1 mm.

I got wire mesh and made one for myself.

I looked everywhere but could not find 1/16 hardware cloth. I got a screen top for a reptile cage that was 1/16 sturdy wire mesh from a local big box pet store.

It was a bit spendy at roughly $15 (US), but I recon it should last a good long while. It has worked perfectly so far and I would recommend it.

I use a regular kitchen strainer, the one I have is below. Held up to a measuring tape, to my eye the screen appears to measure exactly 1/16th" though I can't swear to that. This one is small so you can only do a few handfuls of turface at a time, but it was cheap and it works for me since I don't need tons. You could probably find a larger one with the same screen.

https://www.target.com/p/colander-mesh-1pc-threshold-153/-/A-17006366#lnk=sametab

Or one of these. I bought it at Goodwill store for 50 cents.

@Pete, 1/12th gives a great result, but it results in wasting about 1/4 of a bag of the turface. I think 1/16th would still give me larger particles for the gritty mix while wasting less material.

Try a gold panning / mining supply store.

Josh