Complex harmonies refer to musical combinations that involve multiple notes played simultaneously, creating rich and intricate sounds. These harmonies often include extended chords, such as seventh, ninth, or eleventh chords, which add depth and color to the music. They are commonly found in genres like jazz, classical, and contemporary music, where musicians explore the emotional and expressive potential of sound. In music theory, complex harmonies can be analyzed using various techniques, including chord progressions and voice leading. Composers like Claude Debussy and Thelonious Monk are known for their innovative use of complex harmonies, pushing the boundaries of traditional music and inspiring new styles and interpretations.