Twin Earth plays music with a definite heavy/psych bent by weaving spontaneous riffs, rhythms, and noise around a predetermined, core melodic base -- much like jazz units work standards. Borne of the defunct DC lo-fi garage-pop band Ambassador Now! and a distaste for the obvious, the three members now in Twin Earth almost overwhelmingly preferred the rudderless jams produced during their rehearsals to standard song "craft."
After trolling for a second guitarist to help expand the sonic possibilities of the threesome, they somehow found a soul mate in Franco, possessor of huge ampage. All four members of the band listen to, and are thusly influence by, a wide range and genre of music, from Radiohead and Brian Jonestown Massacre, to standard rock fare like Led Zeppelin and Black Sabbath, from avant-metal bands like Sunn 0))) and Lightning Bolt to Brian Eno, Velvet Underground, and Os Mutantes, and psych-inflected bands like Can, Hawkwind, early Pink Floyd and Spacemen 3.
Music, like any other artistic medium, is not (or should not) be directed or affected by a set of absolutes; as with any creative endeavor by any truly creative persons, it should challenge those who experience it, in some capacity--whether positively or negatively. Like visual art, music does not have to be a cyclical experience as it usually tends to be, it does not have to be the same experience every time, either for the listener or the performer. It can be hurried and frantic, deep and contemplative, painted or assembled. The rest is just pandering.