What is music?

Music is often defined by contrast of sounds. Some definitions of music place it explicitly within a cultural context by defining music as what people accept as musical.
Broadly, here are some groups of definitions:
Those that define music as an external, physical fact, for example "organized sound", or as a specific type of perception Those that label it, according to context, as a social construction or subjective experience Those that label it as an artistic process or product, with the related psychological phenomena Those that seek a platonic or quasi-platonic ideal of music which is not rooted in specifically physical or mental terms, but in a higher truth. The definition of music as sound with particular characteristics is taken as a given by psychoacoustics, and is a common one in musicology and performance. In this view, there are observable patterns to what is broadly labeled music, and while there are understandable cultural variations, the properties of music are the properties of sound as perceived and processed by people.
Traditional philosophies define music as tones ordered horizontally (as melodies) and vertically (as harmonies). Music theory, within this realm, is studied with the presupposition that music is orderly and often pleasant to hear.
John Cage is the most famous advocate of the idea that anything can be music, saying, for example, "There is no noise, only sound," though some argue that this somewhat fascistically imposes the definition on everything. According to musicologist Jean-Jacques Nattiez (1990 p.47-8,55): "The border between music and noise is always culturally defined--which implies that, even within a single society, this border does not always pass through the same place; in short, there is rarely a consensus.... By all accounts there is no single and intercultural universal concept defining what music might be."
In support of the view that music is a label for a totality of different aspects which are culturally constructed. Often a definition of music lists the aspects or elements that make up music. Molino (1975: 43) argues that, in addition to a lack of consensus, "any element belonging to the total musical fact can be isolated, or taken as a strategic variable of musical production." Nattiez gives as examples Mauricio Kagel's Con Voce [with voice], where a masked trio silently mimes playing instruments. In this example sound, a common element, is excluded, while gesture, a less common element, is given primacy.
The platonic ideal of music is currently the least fashionable in the philosophy of criticism and music, because it is crowded on one side by the physical view - what is the metasubstance of music made of, if not sound? - and on the other hand by the constructed view of music - how can one tell the difference between any metanarrative of music and one which is merely intersubjective? However, its appeal, finding unexpected mathematical relationships in music, and finding analogies between music and physics, for example string theory, means that this view continues to find adherents, including such critics and performers as Charles Rosen and Edward Rothstein.