What is the term for a complete musical idea or phrase upon which a musical composition is created?

The term that describes a complete musical idea or phrase, which serves as a foundational element upon which a musical composition is created, is "theme." In music composition, the theme is typically a distinctive melody or a combination of musical elements that encapsulates the essence of the piece. It can be developed and transformed throughout the work, providing coherence and unity to the composition.

The other terms relate to different aspects of music: a riff is usually a catchy or repeated phrase often found in popular music; a motive is a shorter musical idea, usually just a few notes long, that can be developed within a piece; and "cello" refers to a string instrument, not a compositional element. Thus, "theme" is the most accurate term for a complete musical idea used in the creation of a composition.