This piece (We Can Still Stop Her by Michael Giacchino, Inside Out OST) has a strange beat. It seems 4/8 at first, but something isn't right: it takes 9 bars for the melody to repeat, but it's two repetitions of the melody. Does that mean that the piece is in a 18/8 beat instead? Or is it a simple 4/8 with occasional 2/8 bars inserted?
I would interpret the beginning section as 9 beats of 2 quavers each arranged as alternating bars of 4/4 and 5/4. Writing it as 9/8 or 9/4 would imply three groups of three (triple time) which doesn't match the rhythm.
Listening to it I'd have put it into 9 (or maybe 4+5 if 9 always means compound, and it definitely doesn't have a triplet feel). This puts it in 3/4: http://www.musicnotes.com/sheetmusic/mtd.asp?ppn=MN0153795