The art of speeding up and slowing down the tempo of a piece in order to add emotion is called .

Rubato

Explanation:

Rubato–flexible hurrying or slowing of tempo to add emotion–was favored over strict tempo, and composers would even mark this into their scores.

Now, instead of following a set tempo through an entire movement of a piece, the tempo changed throughout the movement. And, not surprisingly, composers even began to add emotion words to their tempo markings. For example, a strict allegro might be replaced with allegro agitato, that is, brisk and agitated.

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