A study of vocal nonlinearities in humpback whale songs: from production mechanisms to acoustic analysis

Abstract

Although mammalian vocalizations are predominantly harmonically structured, they can exhibit an acoustic complexity with nonlinear vocal sounds, including deterministic chaos and frequency jumps. Such sounds are normative events in mammalian vocalizations, and can be directly traceable to the nonlinear nature of vocal-fold dynamics underlying typical mammalian sound production. In this study, we give qualitative descriptions and quantitative analyses of nonlinearities in the song repertoire of humpback whales from the Ste Marie channel (Madagascar) to provide more insight into the potential communication functions and underlying production mechanisms of these features. A low-dimensional biomechanical modeling of the whale’s U-fold (vocal folds homolog) is used to relate specific vocal mechanisms to nonlinear vocal features. Recordings of living humpback whales were searched for occurrences of vocal nonlinearities (instabilities). Temporal distributions of nonlinearities were assessed within sound units, and between different songs. The anatomical production sources of vocal nonlinearities and the communication context of their occurrences in recordings are discussed. Our results show that vocal nonlinearities may be a communication strategy that conveys information about the whale’s body size and physical fitness, and thus may be an important component of humpback whale songs.

The perceptual effects of manipulating nonlinear phenomena in synthetic nonverbal vocalizations

“…During regular voiced phonation, the main oscillatorsin most mammals, these are the left and right vocal foldsopen and close in synchrony and at a relatively stable rate, describing a so-called limit cycle in the phase space (Wilden et al 1998;Tokuda 2018). Phonation becomes less stable under certain conditions such as incomplete closure of the vocal folds with high pressure underneath them (subglottal pressure), or when fundamental frequency (f 0 ) approaches or crosses a formanta frequency band amplified by the resonance of the vocal tract (Herzel et al 1995;Wilden et al 1998;Riede et al 2000;Neubauer et al 2004;Cazau et al 2016;Tokuda 2018). Various acoustic irregularities can then occur, particularly if there is an underlying left-right asymmetry in the anatomical structure of oscillators (Herzel et al 1995).…”

“…Pitch jumps, or frequency jumps, are abrupt discontinuities of f 0 associated with unstable phonation and described in the vocal repertoire of many animal species (Mann et al 2006;Riede et al 2007;Tyson et al 2007;Schneider and Andersson 2011;Cazau et al 2016). In humans, unwanted frequency jumps are an embarrassment to amateur singers to be avoided when switching between vocal registers (Wilden et al 1998;Tokuda 2018), but they also occur in nonverbal vocalizations (Robb and Saxmann 1988).…”

“…However, their accurate measurement depends on being able to detect individual glottal cycles, which in practice is only feasible in sustained vowels (Goudbeek and Scherer 2010). Specialized algorithms borrowed from nonlinear dynamics have also been applied to biological sounds (Tokuda et al 2002;Tyson et al 2007;Cazau et al 2016), but these tools require advanced mathematical expertise and may not be superior to HNR at capturing perceptually relevant properties (Riede et al 2005).…”

“…Chaos is the most challenging nonlinearity to synthesize. Biomechanical two-mass models of vocal folds (Herzel et al 1995;Cazau et al 2016) and even physical models of the vocal tract (Tokuda 2018) have been used to simulate chaotic behaviour and to investigate under what conditions chaos is likely to occur. However, by definition it is difficult to control the exact behaviour of the system once it has switched to a chaotic mode, so these models are less suitable for synthesizing sounds with the desired duration, strength, and dynamics of chaos as well as preserved traces of harmonics with the appropriate f 0 contour.…”

“…Nonlinear vocal phenomena, which can be roughly defined as various irregularities in the vibration of vocal folds (Riede et al 2005), are common in the vocal repertoire of many avian (Fee et al 1998) and mammalian species, including meerkats (Townsend and Manser 2011;Karp et al 2014), whales (Tyson et al 2007;Cazau et al 2016), manatees (Mann et al 2006), deer (Reby et al 2005(Reby et al , 2016, canids (Wilden et al 1998;Riede et al 2000;Schneider and Anderson 2011), chimpanzees (Riede et al 2007), and humans (Robb and Saxman 1988;Mende et al 1990;Bachorowski et al 2001;Facchini et al 2005;Koutseff et al 2018;Raine et al 2018). Major advances have recently been made in providing mathematical (Mende et al 1990;Herzel et al 1995;Mergell and Herzel 1997;Tokuda et al 2002;Herbst et al 2013), physiological (Wilden et al 1998;Titze 2008), and acoustic (Riede et al 2000(Riede et al , 2005Fitch et al 2002) descriptions of these complex sounds, but their evolutionary significance and communicative roles are still debated (Fitch et al 2002;Riede et al 2007;Karp et al 2014).…”