Math/Music: Aesthetic Links

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 compose and perform a short piece of music based on some of the concepts 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 or peers 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 8 - 9 minutes total (7 minute minimum). It is very important to heed this time limit so we can schedule all the performances during class time.

Your final project 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 (due May 4).
  4. A brief typed report (2 pages) explaining the mathematical connections in your piece and the ideas you are trying to convey (due May 4).

The schedule for your presentation/performance is available here.
The performances will take place in Brooks Concert Hall on Mon., April 30 and Wed., May 2, and will conclude in Hogan 514 (the choir room) on Fri., May 4. Your report and actual composition are not due until May 4 even if you give your performance at an earlier date.

Timeline of Due Dates and Presentations:

  1. April 18: Brief description of your piece (type, musical style, performers, general mathematical concept, etc.) as well as at least 8 bars of music. (Class on the 18th will be devoted to working on your composition.)
  2. April 23 and 25: Brief in-class practice presentation about your piece (possibly including some of your music).
  3. April 27: Title of piece and names of all performers.
  4. April 30 - May 4: Performances/Presentations
  5. May 4: Musical composition due along with a 2 page typed report explaining the mathematical connections in your piece and the ideas you are trying to convey.

In-class Work: We will devote several classes specifically toward working on your composition. On April 18, you will pair up with a classmate and share your description of your piece as well as some of its music. We will play a few examples in class and provide constructive feedback. On April 23, half the class will give brief presentations about their pieces, possibly including some of their music written thus far. On April 25, the other half of the class will give presentations. Time will be allotted for feedback. These two days are also intended to give you practice speaking in front of the class.

The Composition Itself: You are require 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. 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. I have been using the free software Lilypond which is fairly simple to use (on a PC or a Mac), although familiarity with a computer programming language would be helpful.

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 we have discussed regarding musical group theory. Deciding on the overall structure of the work first may help you in the composing process. Be sure to be conscious of your rhythm, which, if used effectively, can bring your work alive.

Note: Variety in tempo, rhythm, dynamics, tonality, feeling, etc., is a great way to make your piece come alive. Be sure to think about the overall structure of your piece. How do you musically distinguish different sections of your piece?

What are some of the mathematical ideas I could use in my composition?
You could use virtually anything we have discussed this semester: musical group theory, change ringing, 12-tone music, magic squares, minimalism, the golden section, etc. Some of the specific mathematical concepts available include symmetry (reflections, translations, rotations), group theory, permutations, patterns, phasing, creative use of rhythm, the Fibonacci sequence, etc.

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 nor are we voting for our favorites as in American Idol. 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! Use your imagination and use some of the mathematics you've learned this semester/year.

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 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 repeatedly is that your piece must be no longer than 6 - 7 minutes, so a run-through beforehand is a good way to judge the length of your performance.

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, Montserrat mates, family, etc. to your performance.