I think that, in the beginning of a new phase in music history, aesthetic choices are driven by strong contrasts. This might be because it is strong stresses in general that tend to cause a new phase in the arts. For example, Monteverdi lived at a time in which there were stark philosophical, theological and intellectual oppositions. Gary Tomlinson reviews these in the beginning of his book on Monteverdi, Monteverdi and the End of the Renaissance:
One way of describing these oppositions is with the terms "scholasticism" and "humanism." These two ways of viewing the world were not new, but the opposition between them became especially keen in the later 16th century. Scholasticism, a characteristically Medieval world view, relied on authority and faith and absolute truth arrived at through deductive logic. Apart from the Scriptures and writings of the fathers of the church, the main authorities were people like Aristotle (who largely invented deductive reasoning in six treatises dating from the 4th century BC) and his 13th century AD follower, St. Thomas Aquinas.
The humanists, on the other hand, driven by monumental changes in the world such as the voyages of discovery of Columbus and others that opened up entire new hemispheres, emphasized things like moral and political philosophy that dealt with the pragmatic realities of the real world. This involved the growing importance of rhetorical persuasion. In the words of Petrarch, an early humanist, "It is safer to strive for a good and pious will than for a capable and clear intellect." The need for society to respond quickly to rapidly changing circumstances depended on swaying and channeling the passions to result in right action.
Now let's relate this to music. The world that Monteverdi was born into was the world of the ars perfecta as I mentioned before in this post. The style of ars perfecta emphasizes smooth consistency over contrast. There were a series of rules governing how melodies moved and how dissonances were introduced and resolved the whole point of which was to create a kind of contrapuntal perfection. The pinnacle of this style can be found in the work of Palestrina. Here is brief Psalm setting as an example:
This is what we would often characterize as "beautiful", that is, it is consonant, smooth, flowing and so on. But, of course, this is only one kind of beauty and the stresses and oppositions in the later 16th century led to a very different kind of beauty, one based on contrast and expressive intensity. Monteverdi was one of those who developed this new kind of writing to a high level.
One example of the kinds of contrasts that Monteverdi created can be found in his madrigal "A un giro sol" from the Fourth Book. The text of the madrigal is based on a contrast between the pleasantness and charm of the exterior world and the inner misery of the poet. This made it ideal for the creation of corresponding musical contrasts. There are many rhythmic contrasts between flowing representations of the waves and the winds and the more chordal sections, but the biggest contrast is a harmonic one, at around 58 seconds in this clip, where the poet breaks in to say "I alone" am in despair. From G major, the harmony instantly changes to E major (dominant of A minor), a huge contrast at this point in music history! These kinds of contrasts were simply out of bounds in the older style. Let's listen to the Monteverdi madrigal:
And listen to all those lovely minor second dissonances in the last part! Beauty, you see, can be heightened through the skillful use of dissonance and contrast.