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.

Section 5.1 (pp. 180–182)
Problems:   1, 2, 3, 5, 6, 8

Hints: For #2, follow the example shown in the text in Figure 5.3. The inversion should be tonal (stay in the given key), reflected about the starting pitch A. For #3, the opening note is an A♭. This follows because the opening note of the Subject is a C, a whole step above B♭. To invert about B♭, we go down a whole step from B♭ to A♭. For #6, the tonal inversion begins on a G (a third below B♭ but still in the given key), while the exact inversion will begin on G♭ (a major third below B♭). For #8, notice the two examples are in different clefs.

Section 5.3 (pp. 199–200)
Problems:   1, 2, 5, 7, 8, 9

Hints: For #8, you are to construct the group multiplication table for the symmetries of an equilateral triangle. This is a 6 by 6 table, similar to the one we constructed for the symmetries of the square. First, find the two triangles corresponding to the rotations R₁₂₀ and R₂₄₀ (assume a clockwise rotation). Then, use these and the triangles shown in Figure 5.27 to create the full multiplication table for the group.

In addition to the problems listed above, listen to CD #3: Symmetry in Music, available on Moodle and read the liner notes for the CD, available here. You will be tested on some of this music so be sure to read the liner notes and listen carefully, following along with the score wherever possible to understand the symmetry. The music for many of the pieces is in the course textbook or included in the class lecture notes on symmetry in music. One approach to effectively absorbing the music is to make brief notes about each piece, listing significant details as you listen.