Essay Quiz


1		Using graph paper, draw a matrix with the twelve-tone row presented in this chapter. Using numbers 0-11 (C=0, C#=1, D=2, and so on), show the original, the inversion, the retrograde of the original, and the retrograde of the inversion. In the matrix, how many row forms are available?



2		Read Schoenberg's Die Reihe. Also study books by Eric Cone (Set Theory) and Milton Babbitt. Do these mathematical approaches to music intrigue you? Is there any scientific correlation between music and mathematics?



3		Look at Anton Webern's Variations for Piano, opus 27. Locate the row forms near the beginning of the first movement, planned as a double crossover of six notes plus six notes. Try to play this piece as written. Is this possible? If not, rewrite each movement into a standard readable format. Can you play it now?



4		List other musical elements that can be ordered or serialized. Which composers produced totally serialized music?



5		Is it easy to listen to twelve-tone music? An impressive example of twelve-tone programmatic music is A Survivor from Warsaw by Arnold Schoenberg. The story is told by a survivor of the holocaust in Warsaw, Poland. The music includes examples of Sprechstimme. The composition ends dramatically, with a famous Jewish hymn.



6		Research the theremin and the rhythmicon. How did each function? What was the purpose of each? What effect did each have on twentieth-century music?

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