Mathematics and Music

Final Project

Is not music the mysterious language of a faraway spirit world whose wondrous accents awaken us to a higher, more intense life?
Franz Liszt (19th century Romantic composer)

The last assignment for the course is to compose and perform a short piece of music based on some of the ideas we have discussed over the course of the semester. The aim is for you to combine your creative and analytic abilities to produce a short piece of music. You can be the performer or you can ask a peer to play your piece. Before the performance, you should give a brief presentation explaining the mathematical connections utilized in your work. You may also talk about your inspirations for the piece, creative impulses, special notation, etc.

Note: Your presentation and performance combined should be no longer than 7 - 8 minutes total (5 minute minimum).

Your final project should consist of the following items:

  1. A brief presentation about your composition (2 - 3 minutes).   Schedule
  2. A brief performance of your composition (5 minutes).
  3. The musical composition itself.
  4. A typed report (1 - 2 pages) explaining your work. (due Monday, May 1)

Click here to see the schedule and location for your presentation/performance. These will take place during the last three classes of the semester: Wed., April 26, Fri. April 28 and Mon. May 1. Your report and composition are not due until Mon. May 1 (last class) even if you give your performance at an earlier date.

Questions you might have:

I've never composed before. Where do I begin?
There is no easy answer to this question. First, decide what instrument you are writing for (eg. piano, voice, violin, tuba, etc.). Are you going to have more than one part? Your choices may depend on your musical abilities or those of your peers. Next, try writing a simple melody (say 4 - 8 bars long) by sitting at the piano and playing the notes. Write your melody down on staff paper. Is there any obvious symmetry apparent? Do you want there to be? From here, you could compose a countermelody or play around with your original to create more music. This is a good place to utilize some of the ideas we have been discussing regarding musical group theory. Deciding on the overall structure of the work first may help you in the composing process. Feel free to come talk with me about your composition.

What are some of the mathematical ideas I could use in my composition?
You could use virtually anything we have discussed this semester from change ringing to musical group theory to different tuning systems. Some of the specific mathematical concepts available include symmetry (reflections, translations, rotations), group theory, permutations, patterns, geometric series and periodicity (sine waves.) There are probably others as well.

How will I be graded on this project? What if my piece sounds terrible?
First of all, music sounds differently to different people. Just as with art or literature, what can be incredibly moving to one person may have little effect on another. This is not a popularity contest nor are we voting as in American Idol. You will be graded on your ability to complete the assignment. If you fulfill all four requirements listed above (piece, performance, presentation and report), then you will do fine. The goal here is to be creative! Use your imagination and use some of the mathematics you've learned this semester.

Should I practice my piece beforehand?
You bet! If you are not performing, make sure that the person or people who are have rehearsed beforehand. Part of the challenge of this assignment will be to get it organized so that your performance goes off smoothly. For example, if you have more than one performer, you will have to write out the music for each part, find time for them to get together and practice, make sure they can be at class for your scheduled performance, etc. This takes extra time and planning. Another good reason to practice is that your piece must be no longer than 5 minutes, so a run-through beforehand is a good way to judge the length of your performance.