Project 9: Vibrational modes of strings and music
Essentially all forms of music on Earth can be notated on a five-line staff. This fact should surprise you given that music is an art form that developed independently in different regions and by different peoples of the globe. Indeed, this observation demonstrates the existence of something universal—governed by the laws of nature—underlying all music (pitches). This universal phenomenon is the mechanism of vibration in strings and tubes. You will start by using a guitar to understand the characteristic vibrations (standing waves) of strings. Once you have understood standing waves, you will be in a position to appreciate the existence of two distinct approaches to pitch tuning: just intonation (natural scale) and well-tempering. So, which of the two is logically superior? This is a question that has no answer. In today’s world, Western piano music uses well-tempering. This is because Bach—who could be called the father of Western music—believed that well-tempering, which allows modulation, was particularly beautiful (admits superior music expressions). Logical thought processes thus reveal many outstanding options. However, our goal is for you to appreciate that, in cultural problems and problems of daily life, the question of which to deem more beautiful is ultimately one that depends on individual personality and sensitivities.