05-08-2012, 12:02 PM
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A couple of the named species should never be included in a tank with Tiger Barb, and some others attain a fair size which will need a larger tank if they are included with the TB. I'll assume the TB are definite.
Black Phantom Tetra are not compatible with any barbs. This tetra, like all those in the Rosy clade of Hyphessobrycon, is quiet and sedate. Barb are quite the opposite, all species are active, as are the common danio species, so this alone is not a good match. And the extended fins of the Tetra will almost certainly get nipped by TB.
The other tetra might work in a larger tank, but within the confines of a 40g (presumably 3-feet in length?) a decent group of TB (minimum 8 as has been mentioned to hopefully control their feistiness) is going to own most of the space, and some of the other Tetra get large, 2-3 inches for some. Either of them on their own, with a group of 8-9, would be fine in this tank. All are in our profiles with data on size, tank size, etc.
Of the fish named, in the 40g with TB, Zebra Danio are the best, and a group of 8-9.