That's what it is supposed to be. No mention of "staggered." The OP said:
"I created a document in Photoshop that is alternating 1px vertical solid black then white lines."
Got it.
I interpreted it as an alternating 'pixel' instead of an alternating 'line.' My bad.
Pixel staggering would be an even bigger mess no doubt over the OP's staggered line. Might be fun though.
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Okay, I tried this on a couple of 3880's. I did both the staggered pixel I made and the lines JPG in the above OP's post.
What I noticed was the OP has a very long format. Don't know if it was resampled in the Epson driver for a better page fit, or if he printed it that long on a sheet? On mine, it seemed to compress the lines on a 8.5x11 inch page and really doesn't show a good line, line, line. More like a blur, blur, line, blur due to the size. I made mine a 8x10 format and it looks fine other than some bizarre darkening near the last 3/4" of all prints from either 3880 (??). I did them on a K3 inkset and a K7 piezo both. The K7 is darker black than the K3, but I didn't print as a QTR software, just out of the Qimage software for all. I can see the staggered jaggies of the staggered pixel I mode in both, although the lighter Epson K3 inkset seems sharper maybe due to lighter ink coloration against the K7.
I did the same on a Canon and the Canon does seem sharper than either Epson, just the ink seems a bit lighter and more blue too so it might appear sharper. I see some transport individual line darkening too where it might have slipped a bit in the rollers though, but it is slight for one pixel. No darkening at the end of the print like the Epson shows above either, other than the OP's JPG showing the irregular lines due to possible re-sampling to fit the page. I'd redo the OP's image to fit smaller than the test page personally.
Aside, I see the Epson K3 just spit out a clogged nozzle too on about 4 colors as I just did a normal print job and it showed horizontal banding. Damn Epson! Why they clog during printing a job is frustrating!
Running an Auto Clean cycle now along with a 2 hour wait before re-testing the nozzle check...
SG