A clarinet has no even harmonics. What would produce no odd harmonics?
Producing "only" even harmonics is equivalent to producing all harmonics.

Say your original signal contains all harmonics:

1f, 2f, 3f, 4f, 5f, ...

Now remove all the odd harmonics:

2f, 4f, 6f, 8f, 10f, ...

The original 1f has been removed, so now you will hear 2f as the fundamental, and 4f will sound like the 2nd harmonic, 6f will sound like the 3rd harmonic, etc.  You're back to 1f, 2f, 3f, 4f, 5f, ... except an octave higher.  I think this might be something that happens in instruments, like "overblowing"?  But I'm not sure.  Anyway it will just produce a harmonic sound an octave higher, but with a different timbre.

Somewhat related: https://dsp.stackexchange.com/a/6178/29