Daniel Crawford is working on an interesting problem; how can we represent data about climate change in other ways. Each note he plays represents the average temperature for a year, with higher pitched notes representing higher temperatures. While I wouldn’t call this piece very musical, it is a very interesting and useful way to represent data about average temperatures.
Once people understand that our world is getting warmer, and significantly so, the next step is to wonder why. I’m interested to see what it would sound like if they overlaid these graphs with graphs of the average parts per million of various gases known to be associated with the greenhouse effect, and played by different instruments.
Listen to the two songs linked below, and ask yourself, is this the message we should be sending our children?
After the horrible rape case in the now infamous town of Steubenville, I have been thinking about what could possibly have made this act seem justified by the boys who committed it, and although I do not think we can lay all of the blame on popular media, as it is a reflection of our culture, some of the blame must lie there.
I listened to this song, at the request of my son, and I was quickly horrified. It reminded me of a song I knew growing up, and how my uncritical mind had been deceived into liking this song, until a friend quietly pointed out (while I was singing the song) what the lyrics to the song meant.
I remember the moment that opened my mind, and started me thinking about music more critically.
My friend and I were walking from Koerner Library to the Student Union building on UBC campus, as part of our weekly Safewalk shift, and I started to hum, and then sing. As I got to "how easy it would be to show me how you feel", my friend interrupted me and asked, "Do you know what those lyrics mean?" I stopped singing, and said, "Uh…" I was slightly embarrassed. "That song is about pressuring girls to have sex with their boyfriend," she continued, "Are you sure you want to be singing it?" I paused, and ran through the lyrics in my head, and realized just how right she was.
I will admit that at the time I had more than my fair share of naïveté, but I believe that this is a common experience for many to not think very critically about the music to which they listen (or any media which they consume, for that matter).
I certainly know that young children, like my son, are especially unlikely to think critically about music. I wonder where my son learned of this song, and who introduced it to him and I wonder if they talked about the meaning of the song. I am especially worried that songs like this will influence his developing perspective on women, and his later relationship to them.
I would like my son, and all other boys, to grow up to be men of which we can be proud. Please, if you are exposing children to music or any other media, please, please think about what music to which you expose them, and ask yourself, if this child accepted the message of this music whole-heartedly, would this make them a better person?
I’m always on the look-out for ways of finding connections between mathematics and other areas of knowledge. Music is one of the areas of knowledge that I know has some similarities with mathematics, and so I’ve been brainstorming ways one could incorporate music into a mathematics classroom. Here are a few examples.
A musical scale is an example of a sequence (of notes) and could be used to show the idea the order of objects, related to the order of numbers. As each note in an ascending scale is played in sequence, students should be able to hear that the notes have a order, and then you can relate this order to the order we associate with the counting numbers.
Introducing students to patterns can also be done nicely with music, either with notes, or with percussion instruments. Here are two sample patterns. One simple activity to do with students here is to have them produce their own different types of patterns.
You can also use music to develop some conceptual understanding of skip counting. Often children are taught to count by 2s and 3s but do not necessarily understand what this means. Obviously one should use manipulatives and other techniques to develop this understanding, but here’s an example of how skip counting sounds in music. This example could also be used as an introduction to simple linear functions as well at a later grade.
You could introduce students to fractions by comparing relative sizes of different notes. In the example below, the music starts off with 16th notes, followed by 8th notes, quarter notes, half notes, and finally a whole note. Can you hear how obvious the difference is between the notes?
Music notes themselves are sound waves, which if you have an oscilloscope, you can visualize directly as you listen to a note. A pure note has a relatively simple associated wave, but notes as played on a music instrument are almost always composed of multiple harmonics (or waves of different frequences added together). This is an example of a capture from a digital oscilloscope. What do you think the seemingly random waves that appear between the notes are from?
You can also visualize the volume of the notes (by opening up an audio recording of some music being played in a program like Audacity, for example), and notice an interesting drop-off that occurs. If you measure this drop-off closely, it should match an exponential decay function.
Notice also what the volume of the notes over time looks like when we zoom in on one of them.
Imagine you played one note on the piano at one constant speed, and another note at a different constant speed. After how many notes would you play both notes at the same time? This is an application of the lowest common multiple (provided you express the number of notes played per unit time in lowest terms). Below is a video where one note is being played at a rate of 120 times per minute, and in a different recording, the same note is being played at a rate of 150 times per minute. Do you notice something interesting when both recordings are played simultaneously?
Another area where mathematics comes into play is in the ratio of the wavelengths of different notes. Karen Cheng does an excellent job of explaining how this relates to why we appreciate some music more than other music.
Hopefully these short examples give you some examples of how mathematics and music are related. In another post, I intend to look at musical instruments, and how mathematics can be used to construct them.
* Musical scores created with Noteflight. This program has a free demo one can use without signing in, but if you want to save your work, you will need to sign up for a free account.
** If you are viewing this post in your email, none of the videos will be visible, so I recommend reading it online here.
“The problem, often not discovered until late in life, is that when you look for things in life like love, meaning, motivation, it implies they are sitting behind a tree or under a rock. The most successful people in life recognize, that in life they create their own love, they manufacture their own meaning, they generate their own motivation. For me, I am driven by two main philosophies, know more today about the world than I knew yesterday. And lessen the suffering of others. You’d be surprised how far that gets you." [Emphasis mine] – Neil Degrasse Tyson