The origins of music and science go far back in time, perhaps even earlier than modern human beings. Perhaps more importantly, the connection between music and science appears to be equally as ancient. We will explore this history with two instruments. The Greek lyre is a stringed instrument that was thoroughly studied by the Greek mathematician, Pythagoras in about 600 BC. The second instrument was only recently discovered and dates back to the time of the Neanderthals and appears to be a flute made out of an animal bone.

Both the flute and the lyre are fairly sophisticated instruments upon which a melody can be played. Thus, they are called melodic instruments. The other main group of instruments is called percussion. This group includes drums, cymbals, and triangles, for example. They can be used for great dramatic effect in a piece of music but cannot really sustain a melody. Now, off hand, one might think that percussion instruments are easier to make than melodic instruments and would have been developed first. This may be the case, but, interestingly, the physics of melodic instruments is actually simpler than that of percussion instruments. In light of this, it is not surprisingly that the science of musical instruments started with melodic instruments.

For this same reason, we will also begin our study of music and instruments with melodic instruments and only later delve into the more complex physics of the percussion instruments.

Not too long ago, a remarkable discovery was made: an animal bone was found at a Neanderthal camp site. The significant feature of the bone is that it has fairly small very circular holes drilled into it. It obviously took some time and skill to create these holes, which immediately raises the question: why did the Neanderthals spend the effort to make them? The pattern of the holes is also striking: they are in a line but they are not equally spaced. This bone can be seen at: www.greenwych.ca/fl-compl.htm.

Although the conclusions are controversial, it appears that the bone is, in fact, a musical instrument as the arrangement of the holes is the same as that of a modern flute. If correct, this is a profound insight because of the many implications. It implies that:

• Music has been around a very long time and predates modern humans.
• The Neanderthals created and appreciated music.
• They were capable of skilled craftsmanship.
• They used their technical skills to make musical instruments.
• They had some level of reasoning to choose a particular hole spacing.
• They used the same harmony and musical scale as we use today!

This last point is as subtle as it is significant and we will need to learn a bit more about musical scales and instruments before we can fully appreciate it. However, it does hint at the conclusion that Western music and harmony is not a purely cultural creation but has its roots in some basic physics that applied to the Neanderthals just as much as it applies to us. It also encourages us to examine more closely the connection between physics and music.

Actually, the idea that it might be interesting to apply scientific analysis to music and musical instruments it not particularly new. In fact, it was thought of at least back to the time of Pythagoras. Pythagoras was, as far as we know, the first person to seriously study mathematics, science and music. Most everyone as been exposed to the Pythagorean Theorem sometime in High School. This is just one of the many results and accomplishments of Pythagoras.

The popular instrument of the day in Pythagoras’s time was the lyre. It consisted of frame on which were strung four strings and each string was adjusted to produce a certain pitch when plucked. Pythagoras was intrigued by this instrument and wanted to understand exactly why the strings were set at particular pitches and why these pitches followed a particular scale. However, before we continue, we must introduce a bit of music theory – about the only music theory that we will need for the rest of the course!

When we start to examine music and music theory one of the most significant observations is that not all pitches are used. Consider a violin: you can move your figure along the string to produce a continuous range of pitches. However, in any musical composition, you only play from a certain group of pitches called notes. Depending on the type of music, Western, Arabic, Asian, India, etc. there may be many or few notes that are used, but the point is that there is a definite collection of pitches that are played. For special effects, musicians may slide from one note to another covering a continuous range of pitch, but this is not really part of the melody or harmony. This set of notes is organized into what is called a musical scale. Again, the particular notes that comprise a scale vary from culture to culture, but organizing the notes into a scale is universal.

All scales share another feature: they are specified only over a small range of notes called an octave. Most everyone is familiar with the names of the notes on the piano: C, D, E, F, G, A, B, C. These are the "white" notes on the piano, and anyone who has taken piano lessons probably started out by playing this sequence. However, there are many more than eight white keys on the piano, so what are the names of the rest of the notes? If you every look at a piano keyboard you would notice that the pattern of white keys and black keys repeats up and down the piano. In the same way, the names of the notes repeat up and down the keyboard. With this in mind, the sequence of notes above form a scale, called the C major scale. Once you reach the end of the scale, it simply repeats as you go higher or lower. Furthermore, the range from one C to the next is called an octave. We will discuss all of this in much more detail in the next few sections, but it is helpful to get some sense of what is coming up.

Returning to Pythagoras, as mentioned above, he was intrigued by the fact that scales exist and he wanted to know why Greek music was based on a particular kind of scale, in other words, why did Greek musicians use a particular sequence of notes for their musical scale. These questions that Pythagoras asked launched a way of thinking and analyzing the world that has produced a tremendous body of knowledge that Pythagoras could never have dreamed of. Indeed, Pythagoras’s method of understanding the musical scale eerily foreshadowed the sequence of steps that led to the development of Quantum Mechanics and modern physics.

For historical correctness, I need to point out that what we know about Pythagoras is rather indirect, mostly coming from what other people wrote about Pythagoras. It is known that he did study intervals and scales and came up with the "Pythagorean" intervals.