The crossfade is a procedure in
sound editing which allows the editor to make a smooth transition between two
tracks: very simply, the volume of the first track is gradually reduced to zero while that of the second is increased from zero. This may be done by
manually controlling two volume slides at once, or by a specialized slider that automatically causes one track to
fade out as the other
fades in. The crucial component(s) here will be some sort of
variable resistor. Or, of course, like everything nowadays, by computer.
The actual smoothness of the transition depends very much on what the two tracks are you are trying to meld together. Two sounds differing greatly in timbre, pitch or volume, or two musical tracks in remote keys or with very different rhythms will make an almighty mess while the crossfade is in progress. Rather than seamless, the result may be more like putting chicken and meringue in the same bowl.
Problems might also arise if either track has big fluctuations in volume that negate your skill in gradually adjusting those sliders. However, only classical music and war soundtracks (i.e. random loud explosions) tend to have that sort of dynamic range. In the first case, anyone attempting to fade one piece of classical music into another does not deserve to live. In the second case, you don't really want to achieve a smooth transition anyway.
It might be thought that the crossfade is a modern phenomenon of the electronic age. However, many classical composers realized the effect of crossfading without the benefit of a mixing desk, merely by hairpins (or crescendo and diminuendo markings, as they are usually known).
Beethoven was, to my knowledge, the first, in the first movement coda of the Ninth Symphony. The passage begins with the woodwind developing a little phrase of semiquavers over an angular, syncopated string accompaniment. Gradually the strings grow louder and move higher up the scale, while the dynamic of the woodwind remains the same. At the strings' zenith, they have completely submerged the woodwind which are virtually or completely inaudible. But then the fade happens in reverse: the strings gradually subside and the woodwind become the leading part again.
Strictly speaking this is not a crossfade since we don't begin with 100% woodwind and 0% strings, but the effect is similar. The passage seems tailor-made for a dramatic subtext such as a dissenting voice surviving in the face of persecution, or a little bird being drowned out by a passing stampede of buffalo, or something. Anyway, it's very effective, so go and have a listen. (I know, yet another Beethoven advertisement, but he was quite good.)
Another striking example occurs in Mahler's 6th Symphony: three trumpets sound a major chord and then diminuendo down to nothing, whilst three oboes crescendo up from nothing (and later diminuendo). At the mid point when the clear, open trumpet timbre is just yielding to the sharp, plangent oboe timbre, the chord changes from major to minor. If the passage is properly played, you get a continuous change of tone colour; in conjunction with the shift of tonality, the effect is staggering, and is actually one of the main motifs of the symphony.
Finally, the works of Charles Ives offer a wide choice of crossfade-like effects. Ives was fond of writing pieces of music which consist of several different pieces of music going on at the same time in different keys and rhythms. The technical name for this is polytonality or polyrhythm, but really it's just two pieces going on at once. Hence Ives often found himself in the position of fading one group of musicians in or out against another -
sometimes deliberately imitating the sounds of several bands playing in the same vicinity. An interesting discussion by Michael Tilson-Thomas of Ives' Symphony no.4 mentioning the various fade effects (for which "subterranean percussion" are required!) can be found at http://www.musicweb.uk.net/Ives/WK_Sym_4.htm .
Other classical masters of crossfade-like techniques are Wagner -- known as the "master of transitions" -- who in Das Rheingold engineered a double transition between normal orchestral sound and an ensemble of a dozen anvils, and Jean Sibelius.