Imagine you numbered each note of a scale, and then played the mathematical sequences on the notes like they were music. What would 1, 2, 3, 4, 5, 6, 7, 8, 9,… sound like? What would it sound like if you automatically jumped back down an octave every time you passed a multiple of 7? You may find this tool useful for actually listening to the sequence of numbered notes you generate.
What would the sequence of square numbers sound like? What about prime numbers? What if you kept the tone of the notes the same, but varied the length of the notes? How long would the sequence of notes that started with a half-note, but then halved the length of each subsequent note, take to play?
What would π sound like?
Math Thinking 
Dude this is too AWESOME!!!!
David,
There is a lot here to think about. I haven’t thought so much specifically about mathematical sequences and their connection to musical scores, but I can see how it’d be helpful. I wonder where this would fit into my “Math and Music” course outline:
http://hyperbolicguitars.wikispaces.com/Math+%26+Music+Course
Thanks for the interesting idea!
-mike
It probably could, but the emphasis is different. My problem uses music as a representation for a mathematical idea, your course is mostly focused on the mathematics inherent in music itself. With my idea, there are a lot of different possible representations, music is just intended as a hook to make exploring the ideas behind sequences different.
In terms of your course, it would be interesting for students to use some of the mathematical ideas taught and design (and play!) their own musical instrument as a culminating project.