Math/Music: Structure and Form

Homework Assignment #3

Due Wednesday, October 6, START of Class


Homework should be turned in at the BEGINNING OF CLASS. You are certainly encouraged to work on assignments with other classmates, although the solutions you turn in should be YOUR OWN WORK AND WRITING. Please cite any references (websites, Internet, etc.) that you may have used for assistance with the assignment.

Note: Please list the names of any students or faculty you worked with on the assignment.


Music is the mediator between the spiritual and the sensual life.
Ludwig van Beethoven

  1. Listen to the CD Math and Music 2: Tonality and the Evolution of Polyphony, available on Moodle. Liner notes for the CD are available here. You may be tested on some of this music so be sure to read the liner notes and listen carefully. One approach to effectively absorbing the music is to make brief notes about each piece, listing significant details as you listen.

  2. Read and complete the circled exercises 1 - 3, 5, 7, 8, 12 - 15 in Chapter 4 of The Music Kit, 2nd ed., Workbook, Tom Manoff (handout from class on 9/27.) You are encouraged to play those exercises asking to be played. It's important to hear the notes on the page.

  3. Read and complete the circled exercises 1, 3, 5 - 9, 11, 13 (part 2 and 4 only), 14, 15 in Chapter 5 of The Music Kit, 2nd ed., Workbook, Tom Manoff (handout from class on 9/29.) As with Chapter 4, you are encouraged to play (or sing!) those exercises asking to be played. The music for the famous Ode to Joy (question #11, part 2) was distributed in class during the unit on rhythm (the triple dots of Verdi's Requiem is the first page.)

  4. On music staff paper, write out an ascending chromatic scale (one octave) using sharps in both the treble clef and the bass clef beginning on the note F. Looking at the resulting set of notes, which two letter names are used only once?

  5. Write out an ascending whole tone scale (one octave) using flats in both the treble clef and the bass clef beginning on the note A flat.

  6. Write out an ascending natural B minor scale (one octave) using only sharps in the treble clef.

  7. Write out an ascending harmonic F minor scale (one octave) using only flats in the bass clef.

  8. Notate all the intervals (include major, minor, perfect, etc.) between successive notes in the first 8 bars of Dona nobis pacem (Ch. 5, question #13, part 2.) You may do this on the Ch. 5 handout or if you would like more space, you can copy it over onto your own staff paper.

  9. List all the keys (eg. C major) in which the theme to Close Encounters of the Third Kind will be played on only the white keys of the piano keyboard. For what keys, if any, can the theme be played only on the black keys?