Additive Process

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Ruth Crawford Seeger is one of many American composers that explored the boundaries of what music could be. Her string quartet is one quite interesting process that became much more common in the 20th century, an additive process. An additive process is when a composer uses some sort of mathematical operation (usually addition) to develop materially, in this case rhythmically. While this piece is a serial piece, there are some really interesting processes occurring here. Lets listen. (Play Whole Excerpt)

Notice how the first violin plays 1 note, followed by 2, then 3 then 4, 5, 6, then 7 and so on. (Play this excerpt)

In the other strings they play in octaves cycling through a series of pitches, first 20, then 19, 18 17, 16 ect. (Play this excerpt)

Notice as the first violin line gets longer the space between he two lines gets smaller. Things you would notice if you kept going through the piece is that the lower strings get louder over time while the first violin is  getting softer. Cues like this are helpful to figuring out what types of processes are being used. 

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Sources

Crawford-Seeger, Ruth. String Quartet. USA. 1931 (IMSLP)