Effects of carrier and phase on the pitch of long-duration vibrato tones

Previous studies on the pitch of long-duration vibrato tones, where the modulator is a symmetric function (e.g. sine or triangular wave) have shown that the pitch perceived corresponds to either the arithmetic or geometric mean fundamental frequency of the vibrato tone. In one study the pitch of a vibrato tone consisting of a square wave modulated by a triangular wave was found to be inexplicably lower than that of a sine wave modulated by a triangular wave. An investigation into the pitch of short-duration vibrato tones also revealed an effect of phase on vibrato pitch. An experiment was undertaken with the aim of exploring the effects of carrier and phase on the pitch of long-duration vibrato tones. Six musically trained participants made matches between modulated and unmodulated tones using a method of adjustment and free response paradigm. The following carriers were investigated: a sinusoid, a complex tone with 4 resolved harmonics, a complex tone with 12 harmonics and a complex tone containing harmonics 10 to 15 (all of equal amplitude). Initial phases of 0 and p radians were also explored and the carrier frequency was set to 500 Hz for all conditions. A repeated measures analysis of variance with factors carrier, phase and adjustment tone starting frequency revealed a statistically significant main effect of phase (F (1, 5) = 24.747, p < 0.005), but no significant main effect of carrier. The effect of phase was found to be in opposition with previous findings for short-duration vibrato tones and possible reasons are discussed.