"Tempo rubato [ˈtɛmpo ruˈbaːto] (free in the presentation, Italian for: stolen time) is a musical term referring to expressive and rhythmic freedom by a slight speeding up and then slowing down of the tempo of a piece at the discretion of the soloist or the conductor. Rubato is an expressive shaping of music that is a part of phrasing.
While rubato is often loosely taken to mean playing with expressive and rhythmic freedom; it was traditionally used specifically in the context of expression by speeding up and then slowing down. In the past expressive and free playing (beyond only rubato) was often associated with the terms "ad libitum." Rubato, even when not notated, is often used liberally by musicians; e.g. singers frequently use it intuitively to let the tempo of the melody expressively shift slightly and freely above that of the accompaniment. This intuitive shifting leads to rubato's main effect: to make music sound expressive and natural. Frédéric Chopin is often mentioned in context with rubato (see Chopin's technique and performance style)."
"Accompaniment yields/adjusts to melody"
Definitions of musical concepts (such as rubato) cause misinterpretations if they disregard artistic musical expression. The type of rubato in which the accompaniment is kept regular does not require absolute regularity; the accompaniment still gives full regard to the melody (often the singer or soloist) and yields tempo where necessary:
It is amusing to note that even some serious persons express the idea that in tempo rubato "the right hand may use a certain freedom while the left hand must keep strict time." (See Frederick Niecks' Life of Chopin, II, p. 101.) A nice sort of music would result from such playing ! Something like the singing of a good vocalist accompanied by a poor blockhead who hammers away in strict time without yielding to the singer who, in sheer despair, must renounce all artistic expression.