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Many songs will start with only a few number of instruments, and after a specified amount of time has passed a new instrument is added, and this is repeated until all instruments for the song are playing its rhythms. Sometimes this is also done when finishing the song, but in reverse order.

Does this style of opening a piece has a name?

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I do not have an answer, but if you get the chance to hear Gavin Bryars piece en.wikipedia.org/wiki/Jesus'_Blood_Never_Failed_Me_Yet go for it, it is a beautiful example of gradually adding instruments to accompany a simple looped sung phrase. So moving. –  dumbledad Dec 21 '13 at 14:52
    
I've seen the phrase "terraced entrances" used to describe this, but cannot find any formal definition of the phrase I'm afraid. Hard to believe there's not a formal term for this. –  Lee Kowalkowski Jul 22 at 14:12

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Technically, this is less about form and more about orchestration. People can use instruments to denote a shift or division or a new section in the piece, though they don't have to.

Orchestration is the art of timbre.

When instruments enter one at a time, their entrances are described as "staggered". The fact that the instruments enter halfway through the piece is an orchestrational one. Canons and Rounds do not apply in this context if the staggered voices do not also enter through imitation as well.

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I think this is more near to the answer I search. I will accept it if no more answer come in a few days. –  PhoneixS Dec 23 '13 at 15:50

The closest term I found for this was a canon. Not exactly the same, but pretty close. A canon pretty much when one voice has the melody and some duration later another voice comes in playing the same melody and then the pattern continues for more voices. A round is also a type of canon that may be slightly closer to what you are thinking of.

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Development, or buildup? Crescendo is when the music gets louder. Development is nearer to what you ask.

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I don't think you'll find an exact term for this, but what you are referring to is "texture." In the type of piece you describe, the texture starts "thin" and then layers or builds to a "dense" texture. For the reverse(at the end of the piece) you could describe the texture as "thinning out" or "layering out." If there is one instrument, the texture is monophonic, two is biphonic, and 3 or more polyphonic.

More info on texture here: texture on Wikipedia

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