Is there a common name for periods between Medieval and 19th century?

The History of the period from the end of Medieval period to 1950 or so is often referred to as Modern History. The period from 1950 to present under this scheme is termed post-modern, or contemporary history.

Supposedly the contemporary period is supposed to designate a period still largely within living memory, and thus the boundary will move forward over time. However, personally I think the dividing line at 1950 is actually a very good place to keep it, so I hope it stays there. A typical person living in 1940 was not living a life too much different than one in 1500. There were more machines around in 1940, but people still related to each other in the same ways. If you needed to know something, you asked around to find the local expert, or you went to the library. If you needed to communicate with someone, most likely you wrote a letter. Today we have information at our fingertips that puts the most magnificent 20th Century library to shame, and we expect to be able to communicate with anyone we want instantly.

So personally I think split at 1950 is a good one. I don't like the names so much ("contemporary" is more recent than "modern"? What brand of English is this?), so I'd prefer if we used something more like Renaissance and Computer Age, but the current time split is good.

Yes, there is a name that can describe the period between The Fall of Constantinople in 1453 and the beginnings of The French Revolution in 1789.....it's called Modern History or more specifically, Early Modern History.

Typically, Early Modern History begins with either The Fall of Constantinople or the birth of the Renaissance in Northern Italy. The 1500's, have often been called, "The Age of Exploration"-(referring to the Iberian imperial powers, namely, Spain and Portugal), though the 1500's was also the time of The Protestant Reformation and the eventual emergence of Northern Europe as a major historical presence. The 1600's, is usually considered to be The Golden Age of the Dutch, though it was also the time of the Scientific Revolution. The 1700's, was the well known Age of Enlightenment, though the latter part of the 1700's would also plant the seeds of Revolution in America and France as well as to help to rebirth.....the system of Democracy and Liberal values.

All of these major above mentioned periods were largely characteristic and representative of Early, Pre-Industrial.....Modern Western History.

You could call that period the Age of Exploration, but it's really a couple different periods (at least by my thoughts):

• The Renaissance. The "rebirth", a time when Europe started rediscovering a lot of the wisdom of the Romans and Greeks, started in some sense with Erasmus in the 1300s but really began to kick off when Eastern Christian scholars from the communities which were being overrun by Muslims in the 1400s began to flee westward, particularly to Italy. 1453 and the fall of Constantinople is a pretty good year to set the start of this, but as with all of these "periods", there was quite a bit in flux. The Renaissance didn't really reach England until the early 1500s, for instance.

• The Schism. Martin Luther nailed the tenements to the door of his church in I believe 1519, but the thing that separates this from previous schisms within Christianity isn't that it was attempted but that it succeeded. There was a big split in southern France in the early 1300s, for instance, which inspired an entire crusade (the Albigensian Crusade) to crush it. The Reformation and the Counter-Reformation were pretty huge deals in European history.

• The Early Enlightenment Period. At around this time, perhaps because the warring church factions finally gave natural philosophers the cover they needed to explore controversial issues in some depth, perhaps because the Renaissance sparked a bunch of new ideas in its own right, perhaps because of a combination of things, you begin to see people like Nicolas Copernicus and Galileo Galilei begin to react against some of the wronger ideas people had at the time. Those two avoided persecution for various reasons (Copernicus because he only had De Revolutionibus published posthumously, Galileo because, famously, he renounced his scientific achievements in court), but several others, particularly Giordano Bruno, did not.

• The Later Enlightenment Period. As you get past the mid-1600s and onward, the power of the Church to stop science subsided a bit and there was a bit of a backlash against it as well. Gibbon's Rise and Fall of the Roman Empire, for instance, flat-out blamed Christianity for destroying the Empire. Rousseau came around later on in this period and stated that, contrary to the idea that the natives in places like America could only be saved by Christian intervention, it was the natives themselves who were living a superior life (this was the birth of the "noble savage" trope, at least as far as I know).

• The Industrial Revolution. This, like the Renaissance, occurred at lots of different times depending on what country you're talking about, but the IR was most certainly under way by in England by the time the French Revolution occurred.