Okay, we’re talking science fiction speculative fiction stuff here. Just go with it.
First, almost all rhythm is based on math. Indian ragas are really long, polyrhythmic stuff is difficult to quantize, but it’s all based on math. Rhythm is math. Any alien civ would understand math before going into space… unless they were really lucky and domesticated space dragons or something that just so happened to also live on their homeworld.
Second, pitch is based on math. And here’s the kicker – harmony is a physical phenomenon. That C and G sound good together is not arbitrary – it’s science. G is so close to the second harmonic of C that they sound good together. Harmonics are frequencies that are integer multiples of the fundamental frequency. The fundamental can be arbitrary, but its harmonics will be twice, three, four, five etc times the fundamental frequency. In other words, physics – which doesn’t change much between us and aliens – make the harmonics. Harmonics make the circle of fifths. The circle of fifths makes the chromatic scale. The chromatic scale is on our pianos, our guitars, our synths. Sure, they can tune it differently, use different modes and scales (whole tone scale, anyone?), but more likely than not, they’d have the chromatic scale… If they like harmony, thatis.
Third, the vibrating string, the vibrating membrane, the basic waveforms – they’re based on math. Or rather, physics. Again, we’d have this in common. Would they prefer a sitar over a guitar, or a harpsichord over a piano? Do they want their drums tuned? Do they appreciate raw waveforms, or prefer more advanced synthesis techniques? Taste is different, and their instrument constructions and conventions would be different, but the core of the instruments would likely be the same – no matter the kind of instrument.
This doesn’t mean they’ll like four on the floor beats. Maybe they only like rhythms based on prime numbers. Triplet rhythms might work, but if they’re sophisticated, they might want stuff like 11/8, 19/8, or something even higher. And what are the timbres of their rhythm instruments? If they even make that distinction.
This doesn’t mean they’ll necessarily have music in tune with ours. If they pick a fundamental in between two semitones of our chromatic scale, it’ll sound off-key. And it might not conform to any scale or mode we are used to. If they have and appreciate tonal music at all.
And nothing says their instruments need to be remotely like ours, nor do the techniques need to be the same. I can play part of a Chrono Trigger melody on harmonics on guitar, and often do this inadvertently while just playing. Perhaps they don’t have necks on their instruments, maybe they play on separate strings and/or harmonics. Maybe they play on a single string, which they change the tension of, thus changing the pitch with a more pitch-bend-like effect (our guitars are tuned this way, and played by changing the length of the freely vibrating string). Maybe they use advanced synthesis techniques to create ethereal soundscapes where many aspects of music bleed together into… well, something more sound design than music.
That said, I’m still bothered by how Stargate SG-1, Babylon 5, Star Wars, and so many other shows and movies have alien music that sounds like Earth music. Yes, you can use our scales and tunings. No, you can’t just decide that the aliens’ hat is jazz music or whatever. Composers, take heed.
You know, I should just make some examples.