Abstract
Onsets of acoustic stimuli are salient transients and are relevant in humans for the perception of music and speech. Previous studies of onset-duration discrimination and matching focused on whether onsets are perceived categorically. In this study, we address two issues. First, we revisit onset-duration matching and measure, for 79 conditions, how accurately and precisely human listeners can adjust the onset duration of a comparison stimulus to subjectively match that of a standard stimulus. Second, we explore measures for quantifying performance in this and other matching tasks. The conventional measures of accuracy and precision are defined by arithmetic descriptive statistics and the Euclidean distance function on the real numbers. We propose novel measures based on geometric descriptive statistics and the log-ratio distance function, the Euclidean distance function on the positive-real numbers. Only these properly account for the fact that the magnitude of onset durations, like the magnitudes of most physical quantities, can attain only positive real values. The conventional (arithmetic) measures possess a convexity bias that yields errors that grow with the width of the distribution of matches. This convexity bias leads to misrepresentations of the constant error and could even imply the existence of perceptual illusions where none exist. This is not so for the proposed (geometric) measures. We collected up to 68 matches from a given listener for each condition (about 34,000 matches in total) and examined inter-listener variability and the effects of onset duration, plateau duration, sound level, carrier, and restriction of the range of adjustable comparison stimuli on measures of accuracy and precision. Results obtained with the conventional measures generally agree with those reported in the literature. The variance across listeners is highly heterogeneous for the conventional measures but is homogeneous for the proposed measures. Furthermore, the proposed measures show that listeners tend to under- rather than to overestimate the onset duration of the comparison stimuli. They further reveal effects of the stimulus carrier on accuracy and precision which are missed by the conventional measures. Our results have broad implications for psychophysical studies that use arithmetic measures to quantify performance when geometric measures should instead be used.
Highlights
Onsets are salient features of the temporal envelopes of acoustic stimuli, with perceptual and behavioral relevance in a variety of species from insects to humans
To investigate empirically whether the matches of onset durations are consistent with an additive or with a multiplicative statistical model, we used the maximum-likelihood method to fit additive normal and multiplicative normal distributions to the distributions of matches obtained in Experiments 1 and 2, separately for each condition and listener (576 distributions in total, each based on between 36 and 68 matches)
Arithmetic descriptive statistics are appropriate for random variables over the additive Euclidean space R, whereas geometric descriptive statistics should be used for random variables over the multiplicative Euclidean space R>0, in which relative differences are measured with the log-ratio distance function
Summary
Onsets are salient features of the temporal envelopes of acoustic stimuli, with perceptual and behavioral relevance in a variety of species from insects to humans. The onset duration, called rise time or attack time, of sound pulses modeling songs of female grasshoppers determines whether a male turns toward the sound source (von Helversen, 1993). Phonotactic responses of female tree frogs to synthetic male mating calls depend on the onset duration of the calls (Gerhardt and Schul, 1999). Characteristics of the onset influence the timbre of music and speech sounds (e.g., McAdams et al, 1995; Lakatos, 2000; Halpern et al, 2004). Studies of general grouping principles of speech components imply that the onset of a sound’s envelope is more important than what follows (Darwin, 1981)
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