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These sites suggest someone around 6'1-6'2 needs a 21-22 inch MTB frame.
http://www.bikeradar.com/beginners/gear/article/mountain-bike-sizing-what-size-bike-do-i-need-40477/
http://www.wiggle.co.uk/h/option/bikesizeguide
http://www.halfords.com/wcsstore/libraries/document/mountain_bike_size_guide.pdf
http://www.evanscycles.com/help/bike-sizing#mountain
These sites (and a couple of others + STW poster) suggest ~19":
http://www.ebicycles.com/bicycle-tools/frame-sizer/mountain-bike/size-sheet?utf8=%E2%9C%93&u=in&r=man&h=1866.9&i=838.2&b=Calculate
http://www.ubyk.co.uk/bike-size-calculator/result.php?unit=imperial&height=187&inseam=84&frame=mountain
What gives?
Seat tube length isn't really a great way to size an mtb, top tube or more so reach nowadays are more important numbers. The other big factor is that people are different shapes so for a given height leg vs torso lengths will vary so what is right for one will be wrong for another.
I guess each bike is different.
I'm just shy of 6'1 and tend to find 18-19" frames comfortable in use. Possibly not the 'ideal' size for me but I've managed up to now like that.
Effective top tube length is what matters on XC bikes, whilst reach is what matters on everything more downhill oriented. You can get very long seatposts (especially dropper ones) so what matters most is being able to drop the saddle low enough for interesting stuff - getting the saddle high enough shouldn't be a problem on a sufficiently long bike.
+1 for what Steveh says
Take 3 people the same height and they will (probably) have different leg, arm and torso lengths to make up that height.
The best way to size a bike is to sit on it.
Next you can get the tape measure and geo/size chart out and see what gives in that respect but seat angle can throw a confusing extra dimension into it (Even on ETT measurements) depending on how much post is showing.
Go try some it's the only way or maybe a full bike fit
Personaly I buy by top tube length not the quoted frame size as it a poor guide to size
I think Transition did a great little video or article on top tube lengths/seat angles recently.