I've been trying to make harmonies most of my life.
My parents met while singing, and my mom in particular is able to fashion her own part, harmonizing with the melody, with no music in front of her. She knows enough music that she often can predict where the melody is headed, and she hears which intervals will work best with that melody. She's also strong enough to hold her own note in the midst of people singing something different. I inherited this ability from her (though it's a lot easier for me to do if I know the melody).
Though I started in vocal music as a soprano, I'm more of a second soprano to first alto now. I prefer harmonies. The melody is tied down, restricted in where it can go for the song to remain recognizable; the harmonies can go wherever they choose note-wise and rhythm-wise: they just need to complement the melody.
It's about more than music, though. I search out the harmonics in subjects. I can learn something, but I'd rather learn it from a new view or see it through a different lens. I want something that makes the knowledge deeper and richer. I want more rootlets tying new information into the body of existing things I already know. I look for parallels to join in and reinforce (or reinterpret) my knowledge.
Not all harmonies are comforting. Dissonance, one note jarring against another, creates a tension that can then be resolved. That tension heightens awareness of the notes, though. There can be greater relief when dissonance resolves into a placid third interval than if only a third was played from the beginning. Varied harmonies can showcase different perspectives of a note, different glances at the same piece of information.
I search for harmonies. When I see truth in nature, I look for a way that insight can help me understand God better--or my marriage, or my kids, or even how to cook a next entree! If there is misunderstanding, I like to find the common ground between warring parties, trying to help them understand each other's perspective. A melody is singular, but the harmony possibilities are endless.
Harmonizing takes practice (and that willingness to fail). Many of my harmonies are horrible; many of my attempts go nowhere.
I'm still compelled to keep looking.