The interval which encompasses 4 degrees of a diatonic scale. It is usually close in size to the frequency ratio 4:3, which is ~498.0449991 cents. It was considered to be the primary consonance (called "diatessaron") by the ancient Greeks, and probably other ancient peoples before them, possibly as early as the Sumerians.
In the usual 12-EDO tuning, the perfect 4th encompasses 5 semitones, and is thus exactly 500 cents. Note that in all tunings of the important meantone family, the 4th is larger than the 4:3 ratio.