Audibility of Initial Pitch Glides in String Instrument Sounds Hanna J¨ arvel¨ ainen, Vesa V¨ alim¨ aki Laboratory of Acoustics and Audio Signal Processing, Helsinki University of Technology email: hanna.jarvelainen@hut.fi Abstract Listening experiments were made to measure the detection thresholds for initial pitch glides in string instrument sounds, where a rapid decline of pitch is caused by tension modu- lation during the attack. Realistic sounding synthetic tones were generated by additive synthesis. The frequency decay of the glide was defined through the overall decay rate of am- plitude, simulating the behavior of real instruments. It was found that on the ERB frequency scale, the thresholds re- mained roughly constant at approximately 0.1 ERB with vary- ing fundamental frequency. Thus, any pitch glide weaker than the given threshold remains inaudible for most listeners and could be left unimplemented in digital sound synthesis. 1 Introduction High-quality sound synthesis is possible with the modern synthesis methods, such as physical modeling (Smith 1998) and sinusoidal modeling (Serra and Smith 1990). However, implementing all details of the sound is computationally costly. It would be desirable to leave such features, whose effects are not perceived by the listener, unimplemented. A rapid descent of pitch during the attack is character- istic to many plucked and struck string instruments in forte playing. It can be detected for instance in the clavichord (V¨ alim¨ aki et al. 2000), the guitar (Tolonen et al. 2000), and the kantele – a traditional Finnish string instrument (V¨ alim¨ aki et al. 1999). The primary cause of the pitch descent is the varying string tension as a consequence of finite string dis- placement after plucking or striking the string (Legge and Fletcher 1984). In the clavichord, the effect is boosted by the mechanical aftertouch. The string tension can be directly controlled by the player through key pressure. Fig. 1 shows a fundamental frequency estimate obtained from a recorded electric guitar tone by the autocorrelation method (Tolonen et al. 2000). The estimate decreases exponentially with time from 499 to 496 Hz, giving a glide extent of approximately 3 Hz. The tension modulation can be implemented in physical modeling, for instance, by a special filter structure with signal- dependent fractional delay elements (Tolonen et al. 2000), (V¨ alim¨ aki et al. 1998), but ignoring it would bring remark- able computational savings. The detection and discrimination of frequency glides has been previously studied from a more theoretical viewpoint. Still the underlying mechanism remains unclear. It was sug- gested by Madden and Fire (1997) that the detection is based on changes in the low-frequency side of the excitation pattern. Moore and Sek (1998) argued that at least both sides of the excitation pattern should be compared, and that for low cen- ter frequencies the time-related cues, such as phase locking could have an effect as well. The studies agree that the detec- tion and discrimination of glides is little affected by duration, center frequency, or direction (up or down). However, the previous results are of little help for the synthesis of instru- ment tones, since the range of center frequencies was from 0.5 to 6.0 kHz and the shape of the glide as a function of time was unnatural to real instruments. The objective of this study is to set perceptually motivated guidelines for the need to implement the initial pitch glide in string instrument synthesis. The test tones were synthesized and the pitch glides were defined in a way typical of string instruments. The results of two listening experiments are re- ported. 0 0.2 0.4 0.6 0.8 1 -1 0 1 Level 0 0.2 0.4 0.6 0.8 1 496 497 498 499 F0 (Hz) Time (s) Figure 1: Waveform of a single tone played on the electric guitar (top) and its short-time fundamental frequency esti- mate, which shows a typical descent (bottom).