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Roughly speaking, the sound of a guitar note is characterized by an initial 'attack' where the pick or nail produces higher pitched overtones over the top of the fundamental note, followed by a diminution of these overtones. Consequently, the end of the note is softer than the attack. Volume swells alter the tone of the note, reducing the treble tones of the attack and allowing the softer tone that follows to sustain.
The technique is often executed using the guitar's volume knob. Beginning with the knob turned down to zero, it is increased when a note is played. The effect can also be performed by using a volume pedal. It is sometimes called "violining", because the sound is similar to a bowed violin. Allan Holdsworth pioneered the technique of the pedal swelling along with a delay unit to create a thicker sound that is more associated with the cello.
Roy Buchanan was famous for his emotive volume swells, often in combination with note bending and vibrato. Jan Akkerman used the technique with Focus, as did Phil Keaggy with Glass Harp, and Dickey Betts with The Allman Brothers Band's first few albums.