“The notes I handle no better than many pianists. But the pauses between the notes – ah, that is where the art resides.”

Interview, The Los Angeles Times, 1969

Source: City of Thieves

An Apology for Idlers.
Virginibus Puerisque and Other Papers (1881)
Context: A happy man or woman is a better thing to find than a five-pound note. He or she is a radiating focus of goodwill; and their entrance into a room is as though another candle had been lighted. We need not care whether they could prove the forty-seventh proposition; they do a better thing than that, they practically demonstrate the great Theorem of the Liveableness of Life.

As quoted in Turning Numbers into Knowledge: Mastering the Art of Problem Solving (2001) by Jonathan G. Koomey, p. 96; since at least 2010 similar statements are also sometimes attributed to Mozart, and a similar remark, apparently one of Ben Jonson, is quoted in "Notes to Cynthia's Revels, in The Works of Ben Jonson: With Notes Critical and Explanatory, and a Biographical Memoir (1875), edited by William Gifford, Vol. 2, in notes to p. 223, on p. 551: Division, in music, is "the space between the notes of music, or the dividing of the tones."
Unsourced variants:
Music is the silence between the notes.
The music is not in the notes, but in the silence between.
The music is not in the notes, but in the silence between them.
Variant: Music is the space between the notes.

[Denyer, Ralph, The Guitar Handbook, 2002, 114, 0-679-74275-1]
Elsewhere

As quoted in If Not God, Then What?
Source: If Not God, Then What? (2007) by Joshua Fost, p. 93

The Cherubinic Wanderer