Simply stated, the fundamental is the lowest and loudest frequency of a single string vibrating as a whole. It is the pitch by which we identify the letter name of the root, which is also known as the tone 1 scale degree. In Physics, a node is the exact point on a vibrating string where there is no vibration and therefore no sound! On the bass, the nut and the bridge are nodes.
Ratio is the relationship between the length of one whole string to the number of equal parts that it can be divided into. For example, a one-to-two ratio (1:2 ratio) means that one whole string has been divided into two equal parts. Now, if we consider the fundamental to be one string vibrating as one part, that would be a one-to-one relationship or a 1:1 ratio. This 1:1 ratio is also known as a unison interval. For this lesson, our fundamental reference frequency will be E, tone 1 at the nut and bridge of string 4.
Harmonics, also called overtones or partials, are higher frequencies produced by the vibrations of a string divided into any number of equal parts. Harmonics occur because strings not only vibrate as a whole, but they also vibrate in parts or fractions such as halves, thirds, fourths, fifths and so on. Now, whenever a fundamental is sounded, on any instrument whether it is sung, plucked, struck, blown or bowed, there is an entire harmonic series of frequencies that naturally vibrate with it at the same time. This harmonic series is a specific order of frequencies that climb like a ladder through a predictable series of intervals. And each harmonic step of the ladder is a precise multiple of the fundamental frequency.
Notice that tone 8, the 1st harmonic, is a 1:2 ratio that is produced by dividing the string into two equal parts directly over the 12th fret node. The node is the exact point that divides the string into equal parts. This forces the string to vibrate twice as fast as the tone 1 fundamental and to sound one octave higher in pitch, tone 8. Also notice that the same harmonic may be sounded on each side of the 12th fret: the nut side or the bridge side. For example: tone 15, the 3rd harmonic, may be sounded directly over both fret 5 and fret 24 because both frets are the same distance from the 12th fret! Also, notice that some of the harmonics occur directly above frets while other harmonics are in-between the frets or fractions such as 1/4. The reason for this has to do with just temperament, mean temperament and equal temperament, but that’s another lesson.
To produce a loud and clear harmonic on your bass, touch the string very lightly at the node. Do not push the string down toward the fret. Strike the string near the bridge with force. The string will then vibrate in smaller equal parts and this will produce the sound of the harmonic. New strings and perfect intonation, an adjustment at the bridge which assures that fret 12 is at the exact middle of the string, will also help. Be sure to quickly lift your finger off the string after sounding the harmonic, so that you don’t dampen the vibrating string.
Tone 12, which is tone 5 in the second octave, is the 2nd harmonic and has a 2:3 ratio that is produced by dividing the string into three equal parts directly above the fret 7 node. Fret 7 is 1/3 of the strings length. Since it is impossible for a string to vibrate in two unequal parts, the remaining 2/3’s of the string divides itself in half which produces three equal string lengths or parts!
As long as you continue to divide the string into smaller and smaller equal parts, an ever higher and higher series of harmonics will be produced. The sounds of which will be limited only by your strings, hearing and technique. Some harmonics are easy to play, others take more practice.
The important idea to take away from all this, is that the individual timbre (tam-burr) or tone quality of your bass results from the presents or absence of particular harmonics and their relative volumes. It is this balance between the fundamental and its harmonics that makes one bass sound different from another, even when the fundamental pitch they play is the same. In other words, no two basses, no matter how similar, have the same blend of harmonics or the same tone. Each bass is unique!
To learn more about the Bass, please visit: http://www.12tonemusic.com/bass/facts/
Image © C.Chris Peters 2010