You may remember “My Grandpa Al Reacts to Dubstep,” a Youtube video in which a grandson catches the mystified expressions of his grandfather’s first hearing of Skrillex.
The grandpa humorously inquires if he’s hearing instruments (“Not to be nasty, but is that considered music?”) Al’s reaction to Dubstep is completely understandable, as he is listening for simpler musical elements, like lyrics and melody. For the thousands of years that our species has been musical, we’ve been organizing, categorizing, and discussing sound. Dividing a musical experience into its constituent parts, like harmony, melody, or rhythm, is how we relate our experience of a concert to a friend. However, our musical vocabulary is still rushing to catch up with the parts of electronic music that are less easily described, like the filter sweeps of “First of The Year.” To a musical audience who grew up listening solely to the simpler elements, electronic music can seem dissonant or repetitive. Fans of electronic music, however, know that they are listening to a much broader scope of sound composed in many new dimensions. To understand how to appreciate these new dimensions of music, we must first observe the physics of sound.
The material world is elemental, meaning that at some level, the particles that comprise you, your dog, and your laptop are all the same substance. The ancients Greeks philosophized on this concept, conceptualizing that very tiny particles comprised the world at large. Sound can be similarly considered, in that very distinct and different sounds are made of a fundamental substance. To better understand how electronic music is brought into existence, the waveform, (or graphic representation of air pressure conditions), must be distilled into its constituent parts. The motion of a vibrating string is a wonderful vessel for conveying some fundamental properties of sound.
Watch a video of a vibrating string:
Think of a single string, stretched tightly and secured at both ends. When this string is fixed, as on a guitar, a melody can be produced by the strategic placement of fingers on strings. “Fretting,” or moving one’s fingers up and down the bridge of a guitar, alters the way in which a string may vibrate, necessarily affecting a change in the sound of the string. If you imagine a point at the center of a vibrating string, then the waveform is simply the up-and-down motions created over time.
Remember the sine wave image from the oscilloscope? When the valleys and hills (called peaks and troughs) of the waveform are close together, like the waveform above, they produce a higher frequency than a waveform whose peaks and troughs are farther apart. The changing frequencies of a guitarist’s melody are just changes in the vibrational patterns of the fretted string, distinguished by the distance of waveform peaks. We interpret these low, middle, and high frequencies as correspondingly low, middle, and high pitches.
Consistencies in vibrating string patterns were explored nearly 2,500 years ago by Pythagoras, the legendary Greek mathematician. Using an ancient ancestor of the guitar called the monochord, Pythagoras discovered that when specific waveform alignments pleased the ear, the harmonious sounds could be attributed to a mathematical basis.
The monochord is comprised of two strings, equally tuned, stretched across a sound box for amplification. One of the strings is a constant drone, ideally operating on a single frequency, and the other string has a moveable bridge that makes the pitch changeable. By moving the bridge exactly in the middle of the second string, a string half the length of the original is created. Pythagoras noticed that the resultant sound of this configuration of strings was not only pleasing, but it could also be represented by the whole number ratio of 2:1 (as the drone string vibrates on a length twice as long as the second string). Pythagoras deeply explored the relationship between whole number ratios and vibrating string lengths, and constructed an early music theory based around the harmonious frequencies they created.
A unit of frequency is measured in Hertz (abbreviated as Hz), and represents the amount of waveform cycles, or vibrational oscillations up and down the length of string, per second. To put this in a mathematical perspective, imagine that the fundamental pitch of the drone string of our monochord is tuned to an A, which takes place at 440 Hz. This means that the pitch of A (A4 on a piano) is 440 oscillations of the waveform moving up and down the length of the string each second.
When the second string is divided in half with the moveable bridge (see above image), the Pythagorean ratio of 2:1 produces a frequency difference an octave higher than the original. So if our original string vibrated at 440 Hz, dividing the second string in half with the moveable bridge will produce a vibration exactly twice that of the original. A vibration at 880 Hz (or 880 oscillations of the waveform up and down the string per second) will be heard, which corresponds to the pitch of A an octave above the original. Move the bridge again, creating a string only a fourth the length of the original, and an A that oscillates at 1760 Hz, twice that of 880 Hz, will be heard.
So if this series is supposed to be about electronic music and understanding production techniques, you might be wondering why we’re talking about strings. Electronic music is a relatively new phenomenon taking place in a digital age, and it can be confusing to immediately jump into the 1’s and 0’s of computer synthesis. An understanding of what sound waves are and how they interact is essential to understanding how electronic instruments operate. We are beginning to assemble the tools for synthesis by examining the smallest building blocks of sound. So stay tuned for next week’s series: Part II: Harmonics and Basic Waveform Patterns.