Pitch is only one attribute of musical notes; intensity and duration are also important, and the use of non-traditional combinations of them can give us quite unusual music. Use of unorthodox bars, such as 5/4, barless music, such as in Plainsong, simultaneous use of different bars, can give an "alien" taste to a musical piece.
But considering only pitch, there are different ways to divide the octave. Western music is already at departure of Pythagorean principles, since the introduction of "temperament", ie, of a regular partition of the octave so that the proportion between two adjacent notes is always the same (which requires irrational numbers, basically 2^(1/12)). And while Western music has used the traditional division of the octave into 12 semi-tones, it is possible to divide it otherwise; Arabic music divides the octave into 24 quarter-tones, Balinese music divides the octave into 9 proportional notes, some Western vanguard musicians have used an octave divided into 19 or 31 steps.
All those developments could be mainstream in "alien music". And even if they divide the octave into 12 steps like us, they could use different subsets of them, just like mediaeval music used different "modes" instead of just "major" and "minor", or like several different folk traditions use pentatonic scales, or like Debussy used a 6-tone scale, or Messiaen investigated "limited transpositon modes", or Schoenberg proposed "dodecafonic" or "serial" music.
Is this "meaningful"? It depends; Wittgenstein (in)famously thought that music ended in Brahms (and even in Brahms, he remarked, he could already hear the "noise of machinery"), so he quite certainly thought Wagner was "meaningless". Is Webern "meaningful"? Penderecki? It probably depends on how much an aesthetical conservative/progressist/reactionary the person being asked is.
And, of course, would aliens conceive of a purely auditive art, or would their "compositions" include visual aspects? Olfative? Tactile?
Would their hearing be in the same wavelenghts as ours, or, like giraffes, they would hear infra-sound? Or ultra-sound? Would they be able to hear dog-whistles? If their wavelenghts are different from ours, we could possibly not even be able to hear their "music".
I see that in other answers and several comments that we are underestimating the diachronic aspect of harmony. Reading this page one would probably get the impression that Earthan music does not use tritones. But the tritone is indeed a central part of all "Western" classic and popular music at least since we started the art of counterpoint. Music made exclusively of perfect fifths and octaves would be unbelievably boring for our ears - might even sound "alien" if we allow the idea that aliens are not necessarily more sophisticated than us. Our notion of harmony requires dissonant intervals, and their resolution into consonances. A classic composer would usually end his pieces by resolving a tritone into a perfect third. So tritones, major sevenths, minor seconds, are all part of our tradition, and we actually require them - as long as are they are in their "right place" - to make sense of a musical piece. We would find a piece that ends in a tritone weird, but not much more weird than a piece without any tritones.