Defining music is as difficult as defining art. It is a problem that has been tackled at various times by philosophers, lexicographers, composers, teachers, students and various other musicians. The word has been used to mean various things from "any euphonious and pleasing sound" to a printed document showing how a piece is to be performed (as in sheet music). The question of what the art form we now call music actually consists and does not consist of is, however, something still argued about today.
The word itself comes from the Greek mousikę (tekhnę) (μουσικη (τεχνη)) by way of the Latin musica. It is ultimately derived from mousa, the Greek word for muse. In ancient Greece, the word mousike was used to mean any of the arts or sciences governed by the Muses.
Later, in Rome, ars musica embraced poetry as well as what we now think of as music. Our current understanding of music as being something which is abstract and has nothing to do with language (but something which may be combined with it in song) is relatively modern.
In the European Middle Ages, musica was part of the mathematical quadrivium - arithmetics, geometry, astronomy and musica. The concept of musica was split into three major kinds: musica universalis, musica mundana, musica instrumentalis. Of those, only the last - musica instrumentalis - referred to music as performed sound.
Musica universalis referred to the order of the universe, as God had created it in "measure, number and weight". The proportions of the spheres of the planets and stars (which at the time were still thought to revolve around the earth) were perceived as a form of music, without necessarily implying that any sound would be heard - music refers strictly to the mathematical proportions. From this concept later resulted the romantic idea of a music of the of the spheres.
Musica mundana designated the proportions of the human body. These were thought to reflect the proportions of the Heavens and as such, to be an expression of God's greatness. To Medieval thinking, all things were connected with each other - a mode of thought that finds its traces today in the occult sciences or esoteric thought - ranging from astrology to believing certain minerals have certain beneficiary effects. Rather than being ridiculed as unscientific, Medieval thought should be seen as a system that is constistent in itself, and is reflected in the religious or spiritual thought of many other cultures - for instance that of India- some of which are very much in vogue in Western society today.
Musica instrumentalis, finally, was the lowliest of the three disciplines and referred to the manifestation of those same mathematical proportions in sound - be it sung or played on instruments. The polyphonic organization of different melodies to sound at the same time was still a relatively new invention then, and it is understandable that the mathematical or physical relationships in frequency that give rise to the musical intervals as we hear them, should be foremost among the preoccopations of Medieval musicians.
An oft cited definition of music, made by Wynton Marsalis among others, is that it is "sound organized in time." Apart from objections that "organization" is not required, this definition is seen by many as being too broad. The fifteenth edition of the Encyclopaedia Britannica pinpoints the problem by saying that "while there are no sounds that can be described as inherently unmusical, musicians in each culture have tended to restrict the range of sounds they will admit." Organization would seem to be a crucial restricting criterium in this context, after all.
It might be added that as well as cultural background, historical era is also a determining factor in what is regarded as music. What would be accepted as music in Indonesia may be dismissed by many westerners as just "a din." What would today be accepted as music in the west without the blinking of an eye, would have been ridiculed in the 17th century. And what would be music to The Sex Pistols' Sid Vicious, who is said to have commented, "you just pick a chord, go twang, and you've got music," would almost certainly not have been music to William Congreve, who wrote that, "Musick has charms to sooth a savage breast" (The Mourning Bride, 1697). All of which is to say that there can be no absolute definition of music that will be accepted by everybody.
Many people do, however, share a general idea of music. The Websters definition of music is a typical example: "the science or art of ordering tones or sounds in succession, in combination, and in temporal relationships to produce a composition having unity and continuity" (Webster's Collegiate Dictionary, online edition). There are a number of potential objections to such a definition.
While some may find this definition too restrictive, arguing that "unity" and "continuity" are unnecessary, it is likely that more will find it too broad, thinking of music as being made of pitched sounds, and containing melody, harmony and rhythm. The idea that music must contain these elements is widespread, but there are several examples of what would be widely regarded as music, which lack one or more of them. Plainsong for instance, or monophonic music in general, has no harmony. Much percussion music lacks both harmony and melody; it is true that drums are tuned, but their pitches are indefinite, and they cannot be said to produce a melody in the traditional sense. If one takes rhythm to mean a regular pulse underpinning music, then many kinds of modern electronic music can be said to lack rhythm.
Some attempts to define music concentrate on the method of producing it. Even though some of the first "instruments" in prehistory must have been rocks and bits of wood, it is only in the past one hundred years or so that the idea that music could only be produced by a singer or a traditional musical instrument (such as a violin in Europe, a sitar in India or a koto in Japan) has been challenged. Erik Satie challenged what constituted a musical instrument, and therefore a musical sound, when he wrote the ballet Parade which included a part for a typewriter. His justification was that since the typewriter made a noise, it was a musical instrument. In a lighter vein, Leroy Anderson also wrote music that included a manual typewriter, played with strict rhythm.
The composer John Cage challenged traditional ideas about music in his 4' 33", which is notated as three movements, each marked Tacet (that is, "do not play"). The implication, as expanded upon by Cage himself, is that the background noises which are normally a distraction from the music (the humming of the lights, the shuffling of the audience, the sound of traffic outside) are to be regarded as the actual music in this case.
This is contrary to the usual view that music is, if nothing else, deliberate. Furthermore, Cage does not state the length of the piece - the duration of the first performance (given by David Tudor seated at a piano) was arrived at by consulting the I Ching, but it is not stated in the score (although whenever the piece is performed nowadays, the original duration is usually maintained). The total time of silence is 273 seconds, which has a parallel in the temperature -273 degrees Celsius, absolute zero. This is pure coincidence, however.
Some people deal with the challenges posed by 4' 33" by simply refusing to consider it as music.
Of course, even in conventional music, the "silent" gaps between notes are part of the music. The pianist Artur Schnabel, when asked what made him a great pianist, said "The notes I handle no better than many pianists. But the pauses between the notes? Ah, that is where the art resides!" There is also at least one piece of music, a string quartet, in which the players stop suddenly while the sheet music shows a long rest at the end. When skillfully performed, the silence at the end is quite obviously part of the music. In Franz Joseph Haydn's Symphony No. 45, Farewell, the entire composition anticipates the silence at the end as the musicians one by one stop playing and walk from the stage.
The American composer La Monte Young took this line of thought to an extreme by suggesting that even sound itself was not necessary for a piece of music to exist. In Composition 1960 #5, one of a series of similar pieces, he instructed the performer to "Turn a butterfly (or any number of butterflies) loose in the performance area," the piece being considered complete when the butterflies have flown away. The choice of a butterfly is significant in that it is perceived as a silent animal. During the performance, there will be background noises, just as there are in a performance of 4' 33", but this is not the thrust of the piece. Rather, Young is interested in the theatrical element of music.
Young's point in this instance is that when one goes to a performance of a piece of music, seeing the musicians perform is as much a part of the music as hearing them, so why not remove the hearing element altogether? In this sense, his interest is similar to that of Mauricio Kagel, who carefully notates the theatrical element of performance in his works (although he usually maintains a significant sonic element also).
The academic discipline of ethnomusicology focuses on music as an act of performance - as opposed to classical western historical musicology, which is mainly concerned with analyzing "works", that is music in its abstract form as written down in a score or other mode of notation.