Take a peep at the image. Take a listen to the recording. Guess what they have in common. Multiples.
We’ve been studying fractions the past two weeks and asking questions using the Question Formulation Technique in order to build a deeper understanding of multiples. You can view the questions we will tackle by viewing them on a Google Doc we created.
The definition for a multiple is the product of two counting numbers. But what does that really mean?
One thing we’ve learned that is that common multiples show us when events overlap in the space of time. Take the picture above. You’re looking at a screen shot of an open-source software called Audacity. (You can legally download it for free for a Mac or PC and use it to create music!)
The patterns you see represent waveforms of sounds. Students used tones, plucks, drums generated by Audacity as well as sounds they made and recorded!
Look at the regularity of the shapes. The song in this post has sounds coming in at multiples of 2, 3, 4, 5, 6.
There is also a “click track” playing at a tempo of 120 beats per minute.
One thing we’ve noticed that is that music sounds “right” when the sounds used are multiples of the click track. For example, if you count by the multiples of 2, 3, 4, 5, and 6 you will get 120! We tested this by changing a click track to 123 beats per minute, and we could hear the music getting out of sync.
We’ll reach out to mathematicians and musicians next week to ask them some of the questions we’ve come up. Undoubtedly, there will be more questions to ask and answer. We look forward to sharing our “music” with you and will create a short film sharing what we’ve learned through this project.