Final answer:
The melody accompanied by harmony that supports it without introducing new melodic lines is called homophony. This texture enriches the primary melody with harmonic accompaniment, frequently utilizing various instrumental timbres.
Step-by-step explanation:
The texture of a melody accompanied by other voices that are producing harmony but are not primarily of melodic significance is called homophony. This type of texture in music involves a primary melody with accompaniment which enriches the sonic environment without instigating new melodies of equal importance. The accompanying parts provide harmonic support and enhance the overall sound without overshadowing the main melody. In homophonic textures, elements like rhythm, language, or harmony can be combined to create a rich tapestry of sound. Pieces composed with homophonic texture may also employ varying timbres from different instruments, adding to the distinctiveness of the piece without compromising the primary melody.