With a bow force greater than the Schelleng maximum and careful control, it will be demonstrated that it is possible to produce sounds on a violin of definite pitch ranging from approximately a musical third to a twelfth or more below the normal pitch. The lowered pitch is in agreement with the fundamental frequency of the observed harmonic series. The fundamental itself is very weak if the sounds are produced on the open G string. Mari Kimura has utilized the effect in performances [New York Times, 21 April 1994, p. B3, and Strings, Sept./Oct. 1994, 60–66]. These anomalous low frequencies (ALF) occur when the bow force is great enough to prevent the Helmholtz kink from triggering the normal release of the string from the bow hair. As a result of pronounced bow-nut and bow-bridge reflections there is at the bow a very complex string waveform, some portion of which regularly triggers the slipping of the string. ALF can also be produced on a bowed string mounted on a steel beam, where the motion is detected optically. Computer simulation is used to show how a string can be forced to vibrate at frequencies lower than the natural fundamental frequency of the string.
For bowing forces greater than the Schelling maximum [J. Shelling, J. Acoust. Soc. Am. 53, 26–41 (1973)] there are various periodic motions possible with periods much longer than any natural period of the string [M. E. McIntyre, R. T. Schumacher, and J. Woodhouse, J. Acoust. Soc. Am. 74, 1325–1345 (1983)]. Aperiodic motion with a corresponding raucous sound are, however, much more readily produced with a large bowing force. If care is exercised by the player, a repetitive waveform with a nonraucous sound for very large bowing forces can be maintained for as long as several seconds. The resulting pitch that is heard is in agreement with the fundamental frequency of the harmonic series obtained with a frequency analyzer. This is not the small flattening effect with moderately high bowing force analyzed by McIntyre et al. but is a large effect producing pitches typically ranging from a musical 6th to a musical 12th below the normal pitch. Systematic patterns of the measured frequencies as a function of normal string frequencies have been observed and possible interpretations will be presented.
With a bow force grater than the %helieng maximum and careful bow control, it is possible on a violin to produce sounds of definite pitch ranging from approximately a musid tilrd to as much as two @ves below the nornud pitch. These anomalous low fiquencies occur when the bow force is great enough to prevent the Helmholtz tink from trigering the normal rel=e of the string from the bow hair, and the release is tri~ered later by another part of the mmplex waveform. Some musid appli~tions of the effeet are discussed.
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