I have been hearing that math and music are strongly connected for quite some time. I’m always interested in integrating art into my classroom, so I have been listening. The only problem is that I have utterly no clue about music. I definitely cannot read music, have never played an instrument (except for the recorder in elementary school, but I accidentally snapped that in half…), and feel like Fall Out Boy is a genuinely good band. Luckily, the internet was there for me.
We just did the straw graphs, and then all the wrap-up needed for them to be extra familiar with the graphs of sine, cosine, and tangent. They know not just what y=sin(x) looks like, but also why it looks like that. Now they’re working on what happens when the graph is y=4sin(x), or y=sin(220x), or y=sin(x)+1 (which sidenote, I do not believe has a musical meaning).
The first introduction to sine shifts was watching this video. They agreed it was pretty cool. This also helped us to discover that the larger the wave’s amplitude, the louder the sound, and the higher the pitch, the greater the frequency of waves. This was a great class because most of them know more about music than I do, so we were all teaching each other.
Then we followed the NCTM illuminations plan pretty closely. They found the frequencies of the notes in two octaves on a piano. *SPOILERS* In addition to reviewing geometric series, they discovered that the frequency of an A note in the higher octave is twice the frequency of an A note in the lower octave.
Things got exciting when we graphed a lower A, a higher A, and then a B note. I asked them to observe what how these graphs compared. The two A notes are harmonious – they would sound nice played together, and their graphs intersect in even intervals:
An A and a B note are too close to each other. They would clash when played together, and their graphs reflect that, kind of hitting each other randomly, as a student put it “just off”:
For an excellent example of dissonance in jazz, listen to City of Glass by Stan Kenton. It’s on Spotify!
I’m really glad I finally did this. I feel like I understand music more, and the students have something concrete to tie the very abstract concepts of sine graph shifts to.