You'll find this timeline helpful.
Theories about mathematics and music came particularly from the Pythagorians. Pythagoras (c. 570 BC – c. 495 BC) developed a physical theory of music. He observed the properties of vibrating strings and experimented with a single-string instrument, a “monocord”, to demonstrate his theories. His purpose was to show how the notes of the monocord correspond with the planetary spheres.
He also discovered the simple numerical relationships between the notes of the harmonic series. Music and its harmonies for the Pythagorians, were the means for understanding the universe and our relationship with it.
Music in Greece was almost entirely monophonic, that is, a single line of music, perhaps accompanying poetry or recitative. Instruments included the small harp-like lyre and cithera. Music's range was generally within a single octave and the problems of harmony were not considered.
By the time of the Renaissance (about 1400 - 1600, beginning in Italy), music had become quite complex, enabled by the ability to write it down and study the theory of composing.
Churches and monasteries became centres of learning and the force behind the creation of much religious music. This was often in the form of polyphony, multiple lines of interrelated music. This form reached its peak in the 17th century with the music of J.S. Bach.
Monarchs were often great sponsors of music and commissioned lavish works to entertain their court. Folk music continued to be passed by word of mouth and was considered to be relatively insignificant and not worth writing down.
"Real" music was even then still aimed at revealing the glories of the universe, rather than as a means of self-expression. This approach, current since classical Greece, changed dramatically and almost completely with the advent of the Enlightenment (late 17th and the 18th centuries) and music's own Classical and then Romantic eras. Thence came the great individualistic composers, expressing their own inner selves as opposed to the inner workings of the universe.
At the turn of the 20th century, composers attempted to throw off the shackles of the preceding age and free music from what they saw as the constraints of classical and romantic forms, which seemed to dominate the whole realm of music.
Hence there came the breaking down of all rules and sense of music as a journey which ends back safely back home. Serialism, music concrete, neo-classicism, minimalism, ambient music are just some of the genres that are in this whirlpool of new ideas. In the 21st century composers are adapting digital technology for their own needs and working on space-age projects that Dr Who would feel at home with.
Despite this use of technology, there is a move today towards the clarity of the distant past and music as a means of exploring reality. This time that reality is more to do with what is going on in the microcosm of the composer's inner universe than in the outer cosmos. This represents a reaction to existentialsm, materialism, the clockwork universe and meaningless modern art.