String harmonic

Playing a string harmonic (a flageolet) is a string instrument technique that uses the nodes of natural harmonics of a musical string to isolate overtones. Playing string harmonics produces high pitched tones, often compared in timbre to a whistle or flute. Overtones can be isolated "by lightly touching the string with the finger instead of pressing it down" against the fingerboard (without stopping). For some instruments this is a fundamental technique, such as the Chinese guqin, where it is known as fan yin (泛音, lit. "floating sound"), and the Vietnamese đàn bầu.

When a string is plucked or bowed normally, the ear hears the fundamental frequency most prominently, but the overall sound is also colored by the presence of various overtones (frequencies greater than the fundamental frequency). The fundamental frequency and its overtones are perceived by the listener as a single note; however, different combinations of overtones give rise to noticeably different overall tones (see timbre). A harmonic overtone has evenly spaced nodes along the string, where the string does not move from its resting position.

The nodes of natural harmonics are located at the following points along the string:

Above, the length fraction is the point, with respect to the length of the whole string, the string is lightly touched. It is expressed as a fraction ⁠n/m⁠, where m is the mode (2 through 16 are given above), and n the node number. The node number for a given mode can be any integer from 1 to m − 1. However, certain nodes of higher harmonics are coincident with nodes of lower harmonics, and the lower sounds overpower the higher ones. For example, mode number 4 can be fingered at nodes 1 and 3; it will occur at node 2 but will not be heard over the stronger first harmonic. Ineffective nodes to finger are not listed above.

The fret number, which shows the position of the node in terms of half tones (or frets on a fretted instrument) then is given by:

With s equal to the twelfth root of two, notated s because it's the first letter of the word "semitone".

When a string is only lightly pressed by one finger (that is, isolating overtones of the open string), the resulting harmonics are called natural harmonics. However, when a string is held down on the neck in addition to being lightly pressed on a node, the resulting harmonics are called artificial harmonics. In this case, as the total length of the string is shortened, the fundamental frequency is raised, and the positions of the nodes shift accordingly (that is, by the same number of frets), thereby raising the frequency of the overtone by the same interval as the fundamental frequency.

Artificial harmonics are produced by stopping the string with the first or second finger, and thus making an artificial 'nut,' and then slightly pressing the node with the fourth finger. By this means harmonics in perfect intonation can be produced in all scales.