I'm thinking about installing a Shimano FC-M410 square-taper crankset onto an old miyata triplecross frame. According to shimano's manuals, I need a BB-UN26 / UN26 (-E) bottom bracket that's 113 mm wide.

The thing is, websites don't seem to differentiate between the blank, E-type, and K-type bottom brackets. Should I be worried? What exactly is the difference between these BB's? Will a K-type work?

Your question is messing me up.
Your Miyata takes an English BB. Is that the (-E) referance?
The frame is 68mm wide there.
Your cranks are NJS square tapered. Standard Shimano taper.

My bet is something like this would work: https://cgi.ebay.com.sg/SHIMANO-BOTTO...mZ200302176719

I don't know what 'K-type' is.

Maybe this helps: https://www.sheldonbrown.com/bbtaper.html

Maybe it has to do with symetry or asymetry of the spindle? E.G, for 113mm spindle perhaps one type has a slightly longer or shorter right side than the other (with corresponding shorter or longer left side). Such a difference would affect chainline a bit. Thats just a guess though. Also. don't some Mountain bike FDs mount via a clamp to the BB rather than seat tube? Perhaps that's relevant?

E= E type derailleur mount
K= Chain case mount
EK= E type derailleur and chain case mount

Alright, I get it now. Thanks a bunch.

One last question, the 113mm width was for a 50mm chainline. If I install a 110mm BB, will that get me a 47.5mm chainline? They don't say specifically in the manual for the m410, but I looked at some other crankset manuals and it seems like there is a 3mm difference in BB widths to switch from 47.5 to 50mm. I'm learning guys!

I am far from being knowledgeable on this but when I built up my wife's bike, the crank arm manufacturer provided a range of BB sizes depending on the type of frame and dropout spacing. I ended up trying three different sizes until I found one that worked. I did l learn that the different sizes are not proportionate to each other, meaning a 110 spindle is not 1.5 mm shorter on each end compared to a 113.

novice here

would you mind explaining that a bit more

https://sheldonbrown.com/harris/derailers-front.html

"E-type" Shimano units have a bracket that is held on by the bottom bracket retaining ring. These also use a special braze on to stabilize the derailer."

Bill

Thanks for the link and info

E type FD's are usually only found on very low end bikes or full suspension bikes that don't have a conventional seat tube with a place to mount a FD with a clamp. I suspect they come on low end bikes because the assembly is so easy: the whole thing is installed along with the bottom bracket and crankset. There's no adjustability in terms of angle or up/down, but if you want fast assembly that's a good thing. To be clear, though, there are high end full suspension bikes that, because of their frame design, have to use an E type FD (I can see someone with a $5000 mountain bike chiming in on this). And therefore there are higher end E type FD's available as well.

As far as I can tell, no one knows definitively. I've certainly never been able to find a reliable predictor of chainline based on spindle length. It's trial and error. Most likely, you'll get something totally workable.