Which term can describe a musical performance that has a broken and melodic quality?

The term that describes a musical performance composed of a broken and melodic quality is arpeggio. An arpeggio involves playing the notes of a chord in succession rather than simultaneously, creating a flowing and melodic effect. This technique can generate a sense of movement and can be found across various musical genres.

Con brio translates to "with vigor" or "with spirit," and while it indicates an energetic performance style, it does not specifically refer to the broken melodic nature described in the question. Ostinato is a term used for a repeated musical phrase or rhythm, which does not inherently convey the broken or melodic characteristics described. Con moto means "with motion" and suggests a lively tempo but again does not specifically capture the essence of arpeggio playing. Therefore, arpeggio is the most fitting choice for a performance characterized by a broken and melodic quality.