Well, yes - it's a ZX81 with 16Kb of RAM.
Theoretically it should be possible to get beeper sound from it (not as complicated as from ZX Spectrum 'though, as far as I know), however I have never managed to hear the sound (not EAR, but MIC port).
The sound from the port is SO silent that actually impossible to hear. I don't know if my ZX81 is broken (but I tested 2 issues - and nothing) or maybe it was typical for ZX81. But in this case - how the hell they were able to save programs on tape????
There are several "music" demos with one channel only. And I heard them only from emulator.
Maybe if somebody wrote any beeper engine for the machine (or port one from Spectrum into ZX81) then it would be good for music. But You have to test Your MIC port if You hear anything with SAVE "name" command, at all.
Maybe Shiru could port his Huby engine into ZX81 but I actually don't know if there is a point, because I really hear nothing from my ZX81s.