There are various "degrees" of "mourning". Generally, the most noticeable change is refraining from hearing music, which, BTW, is not a minhag mentioned in the Shulchan Aruch. It developed years later and has become a common minhag. ([After the destruction of the Bet Hamikdash, one should NEVER listen to music. Few follow this halacha.](https://judaism.stackexchange.com/q/2169/759)) Generally, the strict laws of mourning are similar to those done during the 9 days such as not eating meat, not drinking wine, etc. I'm not sure that refraining from music would be considered a form of "mourning" in the strict technical sense. Tachanun, BTW, is not said during both happy occasions as well as sad occasions - it's not said in a mourner's house. So Tachanun cannot be used as your example of implying that it's ommitted only because of happy occasions.