Several of you noted in Online class discussion #1 that harmony seemed to tie disparate musical lines together — if they all corresponded to the harmony, the piece still felt coherent, no matter how many different ideas were going on.
Another thing that harmony does is provide color or shading to a melody. If the same note in the melody is supported by different chords (different harmonies), then it will feel different.
The short video below (only 2 minutes!) is a cute demonstration of how quickly harmony can change in a piece of classical music — it happens much more often than you might expect coming from a pop music-trained ear! The video’s creator has labeled different harmonies with roman numerals (I, V, II, etc) because this is the way that musicians label chords when discussing music theory, but he has also assigned each harmony a different character. You’ll see different combinations of notes played at the same time (harmony or a chord) visually represented by a smiling, frowning, or conniving face.
The piece being played is the exposition of Wolfgang Amadeus Mozart’s Piano Sonata No. 16 in C Major, K.545, I. Allegro (1788).