Topics in Mathematics: Math and Music

Final Project

The most important thing in our world is emotional connections—to people who are far away and to people who are near; humanity is our community, and music binds it together. Music addresses people's internal imagination and memory through sound; it helps to understand things from the inside. That's what music is for.   — Yo Yo Ma
The final assignment for the course is to complete a final project consisting of a musical composition and performance demonstrating some of the mathematical concepts learned this semester. The aim is for you to combine your creative and analytic abilities to produce a short piece of music. You can be the composer, or the performer, or both. The project may be completed individually or with one other classmate. For instance, one person could be the primary composer and the other could be the performer. It is ok to ask a peer outside the class to perform your piece.

A brief, typed report should accompany your composition explaining the mathematical connections and rationale in your work. You will also give a brief presentation describing the work and its mathematical connections immediately before its performance. You might discuss your inspirations for the piece, creative impulses, special features, etc. The last two class periods of the semester will be allocated for you to work on your project and to receive feedback.

Your final project is due on May 11 and should consist of the following four items:

  1. A brief presentation about your composition (2 – 3 minutes).
  2. A performance of your composition (4 – 6 minutes).
  3. The musical composition itself, turned in on staff paper.
  4. A brief typed report (2 pages) explaining the mathematical connections in your piece and the ideas you are trying to convey.

The performances will take place from 8:30 – 10:30 am on Friday, May 11 in Brooks Concert Hall.

Timeline of Due Dates and Presentations:

  1. April 26: Brief description of your piece (type, musical style, performers, general mathematical concept, etc.) as well as at least 8 bars of music.
  2. May 1 and 3: Final Project work days (during regular class time).
  3. May 3: Title of piece and names of all performers.
  4. May 11: Performances/Presentations in Brooks Concert Hall.
  5. May 11: Musical composition and 2-page typed report due.

The Composition Itself: You are required to turn in your composition on staff paper. You can write it by hand or you can use one of the many computer programs available to assist you. One good, free option is the program MuseScore which is easy to use and has the additional bonus feature of playing back your composition so you can hear what you've composed. Another good option is the user-friendly program Noteflight. The music department has a few copies of Sibelius, a leading, user-friendly software program that also allows you to hear your piece as you compose it. However, there are only two computers in the music library that have the software.

Note: You are encouraged to speak with me at any point during the composing and planning process of your work. I would be happy to look at rough drafts of your composition or discuss possible ideas for your piece.

Questions or Concerns You Might Have:

I've never composed before. Where do I begin?
There is no easy answer to this question. First, decide what instrument(s) you are writing for (e.g., piano, voice, violin, tuba, percussion, etc.). Are you going to have more than one part? Your choice 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 counter-melody or play around with your original to create more music. This is a good place to utilize some of the ideas regarding musical symmetry (see Ch. 5 of the course text).

Other things to consider: What is the overall structure of your piece? How do you musically distinguish different sections of your piece? What is the feeling or image you are trying to convey? Be creative. Always be conscious of rhythm, which, if used effectively, can bring your work alive. Variety in tempo, rhythm, dynamics, tonality, style, etc., is a great way to make your piece interesting.

What are some of the mathematical ideas I could use in my composition?
You could use virtually anything we have discussed in class or from the text: creative rhythms, polyrhythms, symmetry (reflections, translations, rotations), the golden ratio, Fibonacci numbers, change ringing, permutations, group theory, 12-tone music, magic squares, minimalism, phase shifts, etc. Use your imagination, be creative, and apply some of the mathematics you've learned. Some previous student compositions are described in Section 8.4 of the course text.

Warning: Do not try to throw in a little of everything in your piece. Focus on one or two primary concepts to generate your music.

How will I be graded on this project? What if my piece sounds "terrible"?
First of all, music sounds different 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; we are not voting for our favorites. You will be graded on your ability to complete the assignment and on the way you incorporate mathematics into your music. 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 and have fun!

Should I practice my piece beforehand?
You bet! You should plan to rehearse several times before the actual performance. Practice, practice, practice. Treat this as a performance, because it is! 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 organizing effectively to ensure that your performance goes off smoothly. For instance, 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 are available on May 11, etc. This takes extra time and planning. Another good reason to practice repeatedly is that your piece must be 4 – 6 minutes in length, so a run-through beforehand is a good way to judge the length of your work. You may also find things that you want to change in your piece after hearing it played live a few times.

What should I wear?
Look nice! This is a performance and you should dress accordingly. Even if you are not performing your piece, you are still giving a brief presentation beforehand. What you wear effects the quality of your performance and presentation. Be sure to take a bow after your piece is finished. Also, you are welcome to invite friends, peers, family, faculty, etc. to our special concert.