Topics in Mathematics: Math and Music

MATH 110   Homework Assignment #5

Due Friday, April 6, 5:00 pm

Homework should be placed in the black folder outside my office, Haberlin 305. All problem numbers refer to From Music to Mathematics: Exploring the Connections. Unless otherwise indicated, all parts of a problem (e.g., a., b., c., etc.) should be completed. You are encouraged to work on these problems with other classmates, and it is ok to use internet sources for help if it's absolutely necessary; however, the solutions you turn in should be YOUR OWN WORK and written in YOUR OWN WORDS. Be sure to cite any references, websites, Internet sources, etc. that you may have used for assistance with the assignment.

Important: Please list the names of any students you worked with on the top of your assignment.

Equal temperament is a lot easier to use than Just Intonation, but I find it lacks expressiveness. It sounds dead and lifeless to me. As soon as I began working microtonally, I felt like I moved from black and white into color. I found that certain combinations of intervals moved me in a deep physical way. Everything became clearer for me, more visceral and expressive. The trade-off is that I had to be a lot more careful with my compositions, for while I had many more interesting consonant intervals to chose from, I also had new kinds of dissonances to avoid.
Robert Rich (composer)

Section 4.1 (pp. 126–127)
Problems:   4, 5, 6, 8, 9

Section 4.2 (pp. 132–133)
Problems:   4, 5, 6, 9

Section 4.3 (pp. 140–141)
Problems:   1, 3, 5, 6, 7, 9

Note: A major 10th is an octave plus a major third. For example, the interval between middle C and E' (an octave above the first E above middle C) is a major 10th.

Section 4.4 (p. 144)
Problems:   1, 2, 3, 4