Harmony, texture and timbre can define a piece of music as much as the melody and meter can. Tonal harmony is one of the distinguishing characteristics of Western music and it is every bit as important as the melody in moving any piece of music along.
In music, timbre is a term used to describe the quality of the sound. It is also sometimes called tone color. There are both objective and subjective ways to describe timbre but, for most people, the experience is largely subjective. The timbre of the sound of a guitar, for instance, is much different than the timbre of the sound produced by a French horn. While these differences in tone color can be quantified by measuring them with various scientific equipment, aesthetic definitions are usually more important and more descriptive in everyday life.
The term texture, in music, refers to the way that various elements are brought together to create a cohesive whole. The term can also be used in the description of the timbre of an instrument, however. You could say, for example, that the sound of an oboe has a somewhat rough texture to it.