Art music—also known as formal music, serious music, erudite music, or legitimate music (sometimes shortened to legit music) —is an umbrella term that refers to musical traditions, implying advanced structural and theoretical considerations and a written musical tradition. The notion of art music is a frequent and well-defined musicological distinction, e.g., referred to by musicologist Philip Tagg as one of an "axiomatic triangle consisting of 'folk', 'art' and 'popular' musics." He explains that each of these three is distinguishable from the others according to certain criteria. The main tradition in the Western world is usually called classical music. In this regard, it is frequently used as a contrasting term to popular music and traditional or folk music.