Tolumnia species are native to the Caribbean, where they get frequent rains, but lots of warm breezes to quickly dry them out. The trick is to mimic that.
They are not big plants, so the mount does not have to be large. I have them on 2" x 4" and 6" x 9" pieces of cork or Epiweb, on bark-free maple branches collected from my yard, in wooden baskets of loose coconut husk fiber, and in 1" clay pots with no medium.
When you mount, it's better to place the moss over the roots, not under them, but in the case of tolumnias, I recommend against using moss, as the roots prefer to dry more rapidly than it allows. Instead, I spread strands of coco fiber over them, stapling it to the cork bark until the plant grabs hold.
Ray Barkalow, Orchid Iconoclast
Using science and logic to advance orchid growing
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