Medieval

When we explore Medieval music, we are dealing with the longest and most distant period of musical history. Saint Gregory is credited with organizing the huge repertory of chant that developed during the first centuries of the Christian church, hence the term Gregorian chant. He was pope from 590 to 604, and the Medieval era continued into the 1400s, so this period consists of almost a millennium's worth of music.
One of the principal difficulties in studying Medieval music is that a system for notating music developed only gradually. The first examples of musical notation date from around 900. For several centuries, notation only indicated what pitch (or note) to sing. The system for notating rhythm started in the 12th or 13th century.
Gregorian chant is monophonic, meaning music that consists of only one melodic line without accompaniment. The beauty of chant lies in the serene, undulating shapes of its melody. We do not know who wrote the melodies of Gregorian chant. Like folk melodies, the music probably mutated as it was passed down through generations and eventually reached its notated form.
Polyphony, music where two or more melodic lines are heard simultaneously, did not exist (or was not notated) until the 11th century. Unlike chant, polyphony required the participation of a composer to combine the melodic lines in a pleasing manner. Although most Medieval polyphonic music is anonymous--the names of the composers were either lost or never written down at all--there are composers whose work was so important that their names were preserved along with their music.

Renaissance Period 1400-1600 A.D.

In the mid-1500s, a prominent bishop commented that music composed
for the church should reflect the meaning of the words so that the listeners
would be moved to piety. This concept seems like a no-brainer today,
but it was a fairly new idea at the time. To suggest that Medieval
composers had no desire to write "expressive" music would be unfair.
But, it was the rediscovery of ancient Greek ideals in the Renaissance that
inspired many musicians to explore the eloquent possibilities of their art.
The increased value of individualism in the Renaissance is reflected by the
changing role of the composer in society. Unlike most of their Medieval
predecessors, the great masters of the Renaissance were revered in their
own lifetimes. The technique of printing music, while slow to evolve,
helped in the preservation and distribution of music and musical ideas.
Sacred music was still predominant, though secular music became more
prevalent and more sophisticated. The repertory of instrumental music
also began to expand significantly. New instruments were invented,
including the clavichord and virginal (both keyboard instruments) and
many existing instruments were improved.
Masses and motets were the primary forms of sacred vocal polyphony.
Secular vocal forms included motets, madrigals and songs (generally
accompanied by lute or a small instrumental ensemble or "consort").
Instrumental pieces were usually short polyphonic works or music for
dancing.
Compared with the Medieval style, Renaissance polyphony was lush and
sonorous. The era between Josquin Desprez and Palestrina is known as
"the golden age of polyphony." Imitation--where one melodic line shares,
or imitates the same musical theme as a previous melodic line--became an
important polyphonic technique. Imitation was one method composers
used to make complex music more easily comprehensible and give the
listener a sense of structure. Imitative polyphony can be heard in the
masses and motets of composers from Josquin onward and is featured in
instrumental music by Byrd, Gibbons, and the Gabriellis.