Stringed instruments like violins and cellos produce harmonic tone vibrations, either involuntarily or intentionally, from strings other than the one being played. This phenomenon enriches the sound, creating a fuller and more resonant auditory experience.
Students of stringed instruments who also have an affinity for physics are likely delighted with the subject of harmonics. They not only understand how vibrations are at the core of producing sounds, but that all things are related – including the strings of a violin, cello, bass, harp, or guitar that are not directly involved in the principal note being played in any particular instance.
Indeed, when the E-string is being played, the G-, D-, and A-strings vibrate as well, producing what are known as overtones. The effect on human ears is that a warmer, well-rounded sound is perceived. An overtone is a full octave higher than the played note. Interestingly, the listener doesn’t explicitly perceive the overtones.
There are two types of harmonics, each with distinct effects and requirements for the player:
Natural harmonics, also known as "open string" harmonics, occur due to the physics of vibrations of the played ("fundamental") string, causing a sympathetic vibration among the other strings. One need not be a physics major nor even a music theoretician to create or understand it. Natural harmonics happen naturally.
Artificial harmonics, also known as intentional or "string" harmonics, require training, practice, and skill on the part of the musician. Some musical scores specifically have harmonics written in. It involves the soft placement of a second finger on a second string as the violin bow plays the primary string.
The harmonic created by the artificial method is done so by lightly placing the third or fourth finger on the string where the harmonic node would be found (nodes are the ½, ¼, or 1/8th place on the string, where the natural overtone is otherwise produced). By placing the finger at these points, the violinist interrupts all the other overtones except this one.
This is science and math applied to music. But there remains a fine art and human physicality in producing an artificial harmonic as well: just the right amount of pressure – not too little and not too much – has to be applied.
The sheet music calling for string harmonics is identifiable by tiny diamond shapes over a note or notes (in some cases a circle above the note, along with the finger number, is the notation). In most cases, the composer is driving for a bell-like quality to the tone, which can create a better blend of tonality with flutes and piccolos (instruments that also have a bell-like sound). Because violins and violas have a shorter neck, the players of these instruments have to think with a bit more mathematical precision to produce the harmonic. Cellists and bassists have a bit more freedom because of the longer necks of those instruments.
What is the most likely instance of a stringed instrument harmonic? A sound that is two octaves and a major third above the fundamental tone – tones that are otherwise inaccessible on the instrument. Harmonics are more easily achieved on fine stringed instruments, which are generally easier to play than poorly crafted ones.
Understanding harmonics in stringed instruments bridges the gap between physics and music, offering a richer appreciation of the sounds produced. Whether naturally occurring or intentionally created, harmonics add depth and warmth to the music, making it a fascinating subject for both musicians and physicists alike.
For more detailed information on stringed instruments and their harmonics, you can refer to Yale University's Physics of Music and The Violin Site.
This article has been fact-checked and expanded to provide a comprehensive understanding of harmonics in stringed instruments, incorporating scientific principles and practical applications.
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