I thought they might mean rectifier also but the OP said he's using WE 396 and likes the sound. A double diode has no "sound" per se. A 396 is a 9 pin miniature tube base and the 6H6 is an 8 pin octal with key. Also the pin out of the 6H6 would not match a typical 5AR4/GZ34 or 5AU4 so it wouldn't be a typical rectifier sub. If looking for an "audio" tube then the 6N6P Russian 9 pin would be the most likely sub. Also - from the MP site:
Signal tubes:
Soviet 6H6 (stock), 6n11, 6H30, E88CC, 6922, 6DJ8.