I think it is a very thought provoking question. In my mind, there is always harmony. If a singer is playing a song on guitar and singing, he is likely singing the melody and playing the harmony in one way or the other. A simple chord progression is the simplist vertical way of looking at the harmony. I used to be a trumpet player and then I was only locked on the melody or what I call horizontal music. It goes from left to right on the page, rising and falling but it is essentially horizontal in nature.

WHen I went off to University to major in music, I found that my way of preceiving music was this, while my classmates that played guitar, organ or piano did not look at it this way at all. Their perception was vertical. Music progressed across a page one chord at a time and if the entire chord was not considered, there was really no basis for the structure of music. Harmony is the Structure, the bones the nuts and bolts that allow the melody to shine forth as the "star" of the song.

Even when I played jazz and would take long "rides" of improvisational qymnastics, at the time I thought I just had an inborn sense of playing things that were related to the melody line, never knowing that it was the harmony that kept it all together. Actually I had a sense of harmony that I was not aware of at all.

Now I sing is a couple of groups, one that does 4 part folk music the other does acapella and do-wop music from the 60s mostly and I am more than ever aware of the rich blessing that harmony does to our music. ALso the ability to hold your part with someone else standing right beside you doing a line that is totally different is a blessing that not everyone has. I think experimenting with harmony with your wife or husband can open rich musical avenues that many of us were unaware existed.