The definition of the word "music" is hotly contested, not least because the word has such strong connotations and use beyond the subject itself.
Music as sound: One common definition of music is to label it as "organized sound" or more ornately, "the artful organization of sound and silence". This definition is widely held to from the late 19th century forward, which began to scientifically analyze the relationship between sound and perception.
Music as subjective experience: Another commonly held definition of music holds that music must be "pleasant" or "melodic". This view is used to argue that some kinds of organized sound "are not music", while others are. Since the range of what is accepted as music varies from culture to culture and from time to time, more elaborate versions of this definition admit some kind of cultural or social evolution of music. This definition was the predominant one in the 18th century, where, for example, Mozart stated that "music must never forget itself, it must never cease to be music."
Music as a category of perception: Less commonly held is the cognitive definition of music, which argues that music is not merely the sound, or the perception of sound, but a means by which perception, action and memory are organized. This definition is influential in the cognitive sciences, which search to locate the regions of the brain responsible for parsing or remembering different aspects of musical experience. This definition would include dance. The Boulanger's established a school of thought centered around this concept which included the idea of Eurhythmics, which is gesture guided by music.
Music as a social construct: Post-modern theories argue that, like art, music is defined primarily by social context. According to this view, music is what people call music, whether it is a period of silence, found sounds, or performance. Famously John Cage's work 4' 33" is rooted in this conception of music.
Because of this range of definitions, the study of music comes in a wide variety of forms. There is the study of sound and vibration or acoustics, the cognitive study of music, the study of music theory and performance practice or music theory and ethnomusicology and the study of the reception and history of music, generally called musicology.