trilled. In very high positions, where the trilled distance is less than the width of the finger, a vibrato trill may be the only option for trill effects. Harmonics Lightly touching the string with a fingertip at a harmonic node, but without fully pressing the string, and then plucking or bowing the string, creates harmonics. Instead of the normal tone, a higher pitched note sounds. Each node is at an integer division of the string, for example half-way or one-third along the length of the string. A responsive instrument will sound numerous possible harmonic nodes along the length of the string. Harmonics are marked in music either with a little circle above the note that determines the pitch of the harmonic, or by diamond-shaped note heads. There are two types of harmonics: natural harmonics and artificial harmonics (also known as false harmonics). Natural harmonics are played on an open string. The pitch of the open string when it is plucked or bowed is called the fundamental frequency. Harmonics are also called overtones or partials. They occur at whole-number multiples of the fundamental, which is called the first harmonic. The second harmonic is the first overtone (the octave above the open string), the third harmonic is the second overtone, and so on. The second harmonic is in the middle of the string and sounds an octave higher than the string's pitch. The third harmonic breaks the string into thirds and sounds an octave and a fifth above the fundamental, and the fourth harmonic breaks the string into quarters sounding two octaves above the first. The sound of the second harmonic is the clearest of them all, because it is a common node with all the succeeding even-numbered harmonics (4th, 6th, etc.). The third and succeeding odd-numbered harmonics are harder to play because they break the string into an odd number of vibrating parts and do not share as many nodes with other harmonics. Artificial harmonics are more difficult to produce than natural harmonics, as they involve both stopping the string and playing a harmonic on the stopped note. Using the octave frame (the normal distance between the first and fourth fingers in any given position) with the fourth finger just touching the string a fourth higher than the stopped note produces the fourth harmonic, two octaves above the stopped note. Finger placement and pressure, as well as bow speed, pressure, and