Why Overtones Matter
It is critical to understand the natural resonances of the bass to get the strongest tone and make a plan for fingering strategies in each key. A working knowledge of natural harmonics and sympathetic resonances will allow you to make more sophisticated choices in your playing approach and ultimately improve your sound (and give you a ton of music-geek points). The first step to understanding harmonics requires a little bit of physics – don’t panic! – this is easy stuff and will help with grasping the harmonic concepts. I’m going to explain the practical applications of this from the perspective of the upright bass as it’s more directly relevant to tone shaping. The same natural harmonics can be induced on the bass guitar as well.
When we play a string on the bass the emitted sound is a product of the string-vibration causing the bass to resonant. Essentially the entire instrument needs to vibrate as much as possible to produce the best tone. Pluck a string or play an open string with your bow, watch how the string vibrates. Looking at it you’ll see that is vibrates from the center and tapers to the nut and the bridge. The largest displacement is at the center of the string, with the smallest being at the two ends. If we were to visualize the string displacement horizontally (as if the bass was lying on the floor sideways) it would be shaped like a football.
This displacement is called a wave and vibrates at a specific frequency. Each end where the string is coming to a point is called a node. Whenever we hold a note on the string we are created a new node and changing the pitch. This is because the new wave between the bridge (one node) and our finger (the other node) is smaller than the open string (if the node were at the nut). A smaller wave means a higher frequency, which we perceive as a higher pitch. As we play higher and higher on the neck we increase the frequency until eventually, it doubles. At this doubling point we have the octave (the string is vibrating at twice its standing frequency). The frequency of an open string is known as the fundamental frequency. Integer multiples of the fundamental frequency are commonly known as overtones, partials, or harmonics. For the vibrational explanations I’ll refer to the partial since the terminology lines up with the integer division of the waves. Overtones are the naturally sounding frequencies over a specific fundamental frequency (open string or otherwise), and harmonics are the sounding of the overtone as a note.
The fundamental frequency is the first partial (a vibration ratio of 1:1). Therefore if you played an open A, the fundamental frequency is A. The first overtone is the second partial (a vibration ratio of 2:1) and is the octave. You can hear this overtone by playing the harmonic octave. This is done by placing your finger on the string without depressing it (you’re creating an artificial third node in the center of the string) and then plucking or bowing the string. It will sound at the same pitch as the octave with a depressed string, but will have a different quality to the tone. This works on the bass guitar as well as the upright bass. On the bass guitar this would be induced at the 12th fret. The wave for the second partial (aka first overtone) would look like this (dividing the string into two equal pieces):
The other partials work the same way. These are audible up until approximately the seventh partial, but the first five are the strongest. I would highly recommend Steve Uccello’s lesson on harmonics to get more examples of inducing each pitch on the bass. They correspond to the following intervals (from a fundamental frequency):
First Partial = Fundamental frequency = 1:1 ratio
Second Partial = First overtone = 2:1 ratio = one octave higher
Third Partial = Second overtone = 3:1 ratio = one octave and one fifth higher
Fourth Partial = Third overtone = 4:1 ratio = second octave
Fifth Partial = Fourth overtone = 5:1 ratio = second octave plus one third
Therefore if the fundamental frequency was A, the overtones would be the octave A’(2), E’(3), A’’(4, the second octave) and C#’’.
The overtones from any given string will cause the other strings to vibrate as well if there are shared pitches. To see an example of this, hold down the octave C key on a piano (above middle-C) without making a sound. While holding down that key, play middle C. You’ll hear the octave C ringing. This is because the octave C shares the frequency of the first overtone of middle-C. This is called a sympathetic vibration – the octave C is vibrating because it is in the overtone series for middle-C. To hear this effect on the bass play an open A with your bow and let it ring. It will continue to ring after you’ve removed your bow. Compare this to playing a Db on the A string. Once you remove your bow the note does not continue. This is because there are no sympathetic vibrations with the other open strings for Db.
So why is this important? Well to get the bass to vibrate as much as possible you need to have the strings vibrate as much as possible. There are two ways to maximize vibration: 1) have as long a string length as possible for each note 2) have as many sympathetic overtones for other strings as possible. When you’re analyzing a piece of music you should keep these in mind, especially for parts that require a lot of projection (such as the fortissimo sections in a symphony). Certain notes (and therefore keys) naturally have more sympathetic vibrations and resonant well: C has both the third and fifth partial sharing open-string frequencies; D, G and A each have their third partials sharing open string frequencies; and Eb, F, Ab and Bb all have their fifth partials sharing open string frequencies. Therefore, in order of natural resonances based on overtonal sympathetic vibrations you have:
2) D A and G
3) Eb F Bb and Ab
4) B Gb and Db
The lack of sympathetic vibrations in B Gb and Db makes these “darker” colored keys, it sounds like a blanket has been draped over your instrument.
How should this influence your finger choices? Well if you have to play a loud group of notes you need to maximize the string length. Therefore even if it’s easy to play the piece across the strings in the higher registers you should work out a fingering that increases the overall length of the strings for each note. If you’re playing in a key with less sympathetic vibrations this is even more important. If the key is one without a lot of sympathetic vibration you may need to adjust your bowing, or at least be aware, of how it affects the overall sound of the instrument. Since the note will not ring out well you need to be extra conscious of the weight and speed of your bow. These may seem like minor considerations, but when you think about our role in an ensemble and the art of crafting each note it’s important to consider every aspect of how our instruments work.