What Is a Harmonic? Touching a String Lightly to Silence Everything Except One Note

A stretched string fixed at both ends can vibrate in several patterns simultaneously. The simplest has the whole string moving as one, with the ends stationary and the centre moving furthest, and that pattern produces the lowest note. The string can also vibrate in two halves moving in opposite directions, with a stationary point at the centre, producing a note an octave higher. It can divide into three, four and further parts, each producing a higher note in a fixed mathematical series. In ordinary playing all of these occur together, and the mixture of their strengths is what gives the instrument its characteristic sound while the lowest one determines the pitch heard. Touching the string at a point that is stationary in one pattern and moving in the others suppresses all but the one.

Several techniques exploit the same physics differently:

• •Natural harmonics, produced by touching the open string at a fraction of its length, giving notes fixed by the tuning
• •Artificial harmonics, where one finger stops the string firmly to set a new length and another touches lightly at a fraction of that, which makes any note available
• •Touching at a half gives the octave, at a third gives an octave and a fifth, at a quarter gives two octaves, and so on up the series
• •Harp harmonics, produced by touching the centre of a string and plucking with the same hand
• •Pinch harmonics on electric guitar, where the thumb touches the string immediately after the pick
• •Wind instruments producing the same series by overblowing, which is the same physics in an air column

The available notes follow a fixed mathematical pattern rather than the scale, which is the source of both their usefulness and their limitation. Dividing the string into whole-number parts produces frequencies that are whole-number multiples of the lowest, and the intervals that result narrow as the series ascends, giving an octave, then a fifth, then a fourth, then progressively smaller steps. Some of those notes correspond closely to notes of the usual scale and some do not, with the seventh member noticeably flat compared to the equivalent scale note and the eleventh sitting between two scale notes, which is why the higher members are used sparingly. Brass instruments before valves could play only these notes, which is why early horn and trumpet parts sit high in the range, since the notes are closer together there.

The same series underlies a great deal that is not obviously connected to strings. A bugle plays only these notes, which is why bugle calls use a restricted set of pitches and why they sound the way they do. Overtone singing, practised in several Central Asian traditions, produces two audible pitches at once by shaping the vocal tract to amplify one member of the series over a sustained low note. Wind chimes and tubular bells produce them. The quality of any instrument's tone is determined by the relative strength of these components, which is what a spectrum analyser displays and what distinguishes a clarinet from an oboe playing the same note. And the tuning systems used in music are attempts to reconcile the simple whole-number ratios this series produces with the requirement that an instrument play in several keys, which is a problem with no exact solution.

The resulting tone is distinctive because of what has been removed. An ordinary note contains the whole mixture of vibration patterns, and a harmonic contains essentially one, which produces a pure flute-like sound with none of the richness that the mixture supplies. It is also quieter, since less of the string's energy is involved, and it decays differently. Composers use the effect for its otherworldly quality, for delicacy and for the abrupt change in colour it produces against ordinary playing. In orchestral writing a passage of string harmonics is immediately recognisable and is used constantly in film scoring for the same associations. Guitarists use them melodically and as an ornament. And the technique is a standard demonstration in teaching acoustics, since the relationship between where the finger goes and what note results is directly audible.

A string vibrates in several patterns at once, and touching it at a point stationary in one of them suppresses the rest and leaves that one sounding. Dividing at a half, a third or a quarter gives an octave, an octave and a fifth, and two octaves. The available notes follow a fixed series rather than the scale, and the tone is pure because the usual mixture has been removed.