A had a bit of an epiphany today. I was sitting thinking about music, trying to come up with some clever thing that could be said about it. Something that would either be profound or amusing, perhaps even both. What came to me was so simple that I almost dismissed it out of hand. Music is all about the concurrent motion of a mass at vastly different scales of time and distance.
Let’s break that statement down a little bit. First, let’s talk about time. Time, as Ray Cummings said in his 1922 science fiction novel “The Girl in the Golden Atom”, is what keeps everything from happening at once. At first, the statement seems trite, even funny. But as you think about it, you realize that it does summarize the fundamental nature of time rather well. Time can be divided into arbitrarily small units called instants that occur one after another. Instants have no duration but serve only to mark a given point in time.
The next fundamental concept is position. At any given time, everything has a position. There are at least three dimensions that we use to specify that position. They are at 90 degree angles to each other and are sometimes referred to as height, width, and breadth. Some initial reference point is given and the position of things can be specified as being a particular height, width, and depth from the reference point, also referred to as the origin. As instants mark a particular place in time, points mark a particular place in space.
Having established instants and points, we can now describe motion. If, from one instant to the next, a thing is located at the same point, it can be said to be stationary. If, however, the thing is at a different point in the next instant, it is said to be moving. Music, indeed all sound, is the result of a mass, moving back and forth at a given rate. The rate at which it is moving is called its frequency. Frequency is usually expressed in Hertz or vibrations per second.
In order to hear the sound, the movement must be transferred, often by air, from the moving mass to our ears. There, sophisticated biological apparatus in our ears transform the movement into electrical impulses that are transmitted to our brains so that we can interpret it as sound.
Now back to my mini-epiphany. When something, say a string, vibrates at a frequency, we hear a pitch. Furthermore, the string vibrates at a number of frequencies all relative to the length of the string. For instance, if the predominant, or fundamental frequency of a string is 440 Hz., the first harmonic is twice that frequency or 880 Hz. The second harmonic is three times the fundamental or 1320 Hz. This continues on to form the harmonic series. A string will produce all of the pitches in the harmonic series, each successive harmonic having a lower volume in the overall sound produced.
This brings us to the point that all of these harmonics are the concurrent motion of the string at different scales of time and distance. When you break it down like that, it doesn’t seem nearly as profound.
Sweet dreams, don’t forget to tell the ones you love that you love them, and most important of all, be kind.