Final answer:
The term that describes the expressive alteration of tempo in music by speeding up or slowing down is 'rubato.' It allows for a more personal and emotional interpretation of a piece.
Step-by-step explanation:
The term for a perceived beat that speeds up and slows down for expressive effect is rubato. Rubato is used by musicians to add emotional depth to a performance by slightly altering the tempo. This technique involves taking liberty with the time value of notes, stretching and compressing them to create a more personal interpretation of the piece. This is very different from the strict time-keeping role of a metronome, the off-beat accents of syncopation, or the gradual increase in volume known as a crescendo.