The perception of octave pitch affinity and harmonic fusion have a common origin

Highlights

• The detection of deviations from an octave interval is generally asymmetric.

• Octave compressions are generally better detected than octave stretchings.

• This is true for simultaneous (harmonic) as well as sequential (melodic) octaves.

• In these two conditions, the magnitude of the asymmetry is listener-dependent.

• The listener-specific asymmetries found in the two conditions are correlated.

Abstract

Musicians say that the pitches of tones with a frequency ratio of 2:1 (one octave) have a distinctive affinity, even if the tones do not have common spectral components. It has been suggested, however, that this affinity judgment has no biological basis and originates instead from an acculturation process ‒ the learning of musical rules unrelated to auditory physiology. We measured, in young amateur musicians, the perceptual detectability of octave mistunings for tones presented alternately (melodic condition) or simultaneously (harmonic condition). In the melodic condition, mistuning was detectable only by means of explicit pitch comparisons. In the harmonic condition, listeners could use a different and more efficient perceptual cue: in the absence of mistuning, the tones fused into a single sound percept; mistunings decreased fusion. Performance was globally better in the harmonic condition, in line with the hypothesis that listeners used a fusion cue in this condition; this hypothesis was also supported by results showing that an illusory simultaneity of the tones was much less advantageous than a real simultaneity. In the two conditions, mistuning detection was generally better for octave compressions than for octave stretchings. This asymmetry varied across listeners, but crucially the listener-specific asymmetries observed in the two conditions were highly correlated. Thus, the perception of the melodic octave appeared to be closely linked to the phenomenon of harmonic fusion. As harmonic fusion is thought to be determined by biological factors rather than factors related to musical culture or training, we argue that octave pitch affinity also has, at least in part, a biological basis.

Introduction

Humans enjoy melody, "the essential basis of music" in the words of Helmholtz (1863/1954). A melody is a sequence of periodic sounds with specific frequency ratios, forming musical intervals that are perceived as pitch relations. The precision with which these intervals are perceived is of course limited; it depends on the listener's musical training, the intervals themselves, and other factors (Burns and Ward, 1978; Rakowski, 1990; Perlman and Krumhansl, 1996; McDermott et al., 2010; McClaskey, 2017; Graves and Oxenham, 2017). However, in the Western world at least, even people with no substantial musical education readily detect an error of only one semitone (corresponding to a frequency change of about 6%) in the production of one note of a familiar melody (Dowling and Fujitani, 1971; Trainor and Trehub, 1994).

Throughout the human auditory system, up to the cortical level, frequency is represented tonotopically, along unidimensional neural maps (Romani et al., 1982; Talavage et al., 2004). A straightforward hypothesis, therefore, is that the representation of a melodic interval in the auditory system is simply a distance between neural excitations along an axis representing pitch as a logarithmic function of frequency. This would suggest that there is no "physiologically special" melodic interval (apart from the unison). Psychophysical results in line with this hypothesis were obtained by Kallman (1982, experiment 1), who required ordinary Western students to rate the similarity of successive pure tones as a function of their frequency ratio. The ratings smoothly decreased as the frequency ratio varied in small logarithmic steps from 1:1 to about 5:1. Remarkably, no local peak was observed for the simple frequency ratio 2:1, i.e., one octave, even though in the Western musical system two notes forming an octave interval bear the same name and are treated as equivalent sounds (Krumhansl and Shepard, 1979). Analogous findings were reported by Hoeschele et al. (2012, experiment 1).

However, at odds with these results, a number of other experiments have suggested that for a substantial proportion of human listeners, two tones forming a small-integer frequency ratio have a distinctive affinity (or similarity) in pitch. Ratios such as 3:2, 4:3, or 5:4 have been used in some of these experiments (Cohen et al., 1987; Schellenberg and Trehub, 1994, 1996), but the ratio most often used was 2:1, one octave. The demonstrations of octave pitch affinity (OPA) have been based on a variety of methodologies (Deutsch, 1973; Idson and Massaro, 1978; Kallman and Massaro, 1979; Massaro et al., 1980; Demany and Armand, 1984; Hoeschele et al., 2012; Borra et al., 2013; Jacoby et al., 2019).¹ In the eight studies that we just cited, OPA was observed using pure-tone stimuli. This is an important detail since the peripheral auditory system behaves as a spectrum analyzer (Schnupp et al., 2012). Ordinary periodic sounds are instead complex tones, and thus consist of a sum of harmonics with frequencies equal to integer multiples of a given fundamental frequency. Consequently, two complex tones one octave apart typically have common spectral components. In addition, the pitch of certain complex tones is subject to octave ambiguities (Terhardt et al., 1982, 1986), which could explain the perception of an affinity between such tones when their fundamental frequencies are one octave apart (Regev et al., 2019). The phenomenon of OPA is more intriguing when it is observed for sounds with no common spectral component and an unambiguous pitch, such as pure tones.

The origin of OPA, for sounds such as pure tones, is the subject of a basic controversy. On one side of the debate, it is contended that OPA is essentially the consequence of an acculturation process (Burns and Ward, 1982; Sergeant, 1983; Jacoby et al., 2019). According to this culturalist hypothesis, Western listeners exhibit OPA because they have learned, consciously or unconsciously, a musical grammar in which tones one octave apart are functionally equivalent. Arbitrary musical grammars can be learned quite rapidly, by mere passive exposure to sound sequences constructed from these grammars (Loui et al., 2010; Rohrmeier et al., 2011). The musical rule of octave equivalence is certainly not arbitrary, because this rule is culturally widespread (Dowling and Harwood, 1986; Brown and Jordania, 2011). However, its main origin might be unrelated to the perception of pitch relations (Burns and Ward, 1982; McPherson et al., 2020). The rule might originate from the mere fact that the sum of two complex tones one octave apart is a single complex tone, with the same period as one of the two added tones. The culturalist explanation of OPA is consistent with the fact that, within the Western adult population, sensitivity to OPA appears to be stronger in musicians than in non-musicians (Allen, 1967; Demany and Armand, 1984; Jacoby et al., 2019), although this could of course be due to an influence of sensitivity to OPA on the willingness to become a musician. Jacoby et al. (2019) suggested in addition that the Tsimane', an Amazonian population living in isolation from Western culture, are completely insensitive to OPA. Western children tested by Sergeant (1983) showed a similar insensitivity and this led the author to assert that OPA was a "concept" rather than a percept. In line with such a view, Regev et al. (2019) found that musically educated listeners who were able to identify an octave interval as such did not manifest a sensitivity to OPA when their brain response to pitch changes was assessed via the "mismatch negativity" evoked potential.

On the other side of the debate, it is contended that OPA originates from physiological processes that are essentially independent of the cultural environment. The experimental evidence supporting this general hypothesis is currently very limited. Sensitivity to OPA has been found in two studies on non-human animals (Blackwell and Schlosberg, 1943; Wright et al., 2000); but the stimuli used by Wright et al. were spectrally rich periodic sounds. Using instead pure tones, Demany and Armand (1984) obtained results suggesting that OPA exists, and is even strong, in 3-month-old human infants. Another argument was put forth by Terhardt (1971, 1974, 1987). In his view, OPA originates from a learning process, but not from musical acculturation: what is learned is the harmonic structure of natural periodic sounds, such as human vocalizations. Due to this learning process, the pitch interval corresponding to a subjectively perfect melodic octave is the pitch interval of harmonics with a frequency ratio of 2:1 in natural periodic sounds. A well-established fact is that when musically educated listeners are requested to set two successive pure tones exactly one octave apart by adjusting their frequency ratio, the obtained ratio is generally slightly larger than 2:1 (Ward, 1954; Ohgushi, 1983; Demany and Semal, 1990; Hartmann, 1993; Rosner, 1999). Terhardt argued that this apparent anomaly ‒ often called the "octave enlargement" effect ‒ can be explained by small repulsive interactions between the representations of simultaneous pure tones in the periphery of the auditory system. He found confirmation of this hypothesis in precise measurements of the pitch of individual spectral components of complex tones. However, Peters et al. (1983) and Hartmann and Doty (1996) failed to replicate Terhardt's observations: they found that the pitch of a complex tone component is not significantly affected by the other components. Their work thus cast serious doubts on the validity of Terhardt's ideas about OPA.

Here, we report new evidence that OPA has a natural basis. More precisely, our study indicates that even for musically educated Western listeners, the pitch interval defining a subjectively perfect melodic octave is largely determined by universal auditory processes rather than by cultural factors. Our essential finding is that the perception of OPA is closely linked to the auditory phenomenon of harmonic fusion. A periodic complex tone is normally heard as a single sound, with a single pitch (related to the fundamental frequency). Yet, it is initially represented in the auditory system as a set of harmonics that, in isolation, evoke different pitches. Their subsequent fusion involves a detection of small-integer frequency ratios ("harmonicity"). When, for example, a 800-Hz harmonic is mistuned by 5% in a complex tone with a 400-Hz fundamental frequency, adult Western listeners perceive two sounds rather than one: the mistuned harmonic is heard as a pure tone standing out of a complex tone (Moore et al., 1986; Hartmann et al., 1990). Harmonic fusion is thought to be helpful in everyday life because real-world acoustic scenes often include simultaneous periodic sounds, produced by separate sources and differing in fundamental frequency; the perceptual segregation of such sounds requires a grouping of their respective spectral components (Bregman, 1990; de Cheveigné, 1997; Kidd et al., 2003; Carlyon and Gockel, 2008; Micheyl and Oxenham, 2010; Popham et al., 2018). Harmonic fusion is apparently operative in newborn infants (Bendixen et al., 2015), in Amazonian listeners isolated from Western culture (McDermott et al., 2016; McPherson et al., 2020), and in at least some non-human mammals (Tomlinson and Schwarz, 1988; Kalluri et al., 2008; Song et al., 2016). Moreover, neural correlates of this perceptual phenomenon have been found in the auditory cortex of monkeys (Fishman and Steinschneider, 2010; Fishman et al., 2014; Feng and Wang, 2017). Thus, harmonic fusion clearly has a natural basis. This should also be the case for OPA if OPA is closely linked to harmonic fusion.

In all but three of the past studies concerning OPA and harmonic fusion, these two phenomena have been investigated in isolation. Interestingly, a similar asymmetry was observed in both cases. First, the "octave enlargement" effect mentioned above suggests that OPA is generally stronger slightly above the physical octave (2:1) than slightly below it. Second, when the listeners' task was to detect small octave mistunings in stimuli consisting of simultaneous pure tones, performance was found to be generally poorer when the octave was stretched than when it was compressed, thus suggesting that harmonic fusion is more tolerant to stretchings than to compressions (Demany et al., 1991; Borchert et al., 2011; Bonnard et al., 2013, 2017). From this resemblance, one could suspect the existence of a link between OPA and harmonic fusion. However, the three studies in which the two phenomena were examined jointly, in the same listeners, did not provide evidence for such a link (Demany and Semal, 1990; Bonnard et al., 2013, 2016). In the present study, OPA and harmonic fusion were again investigated in the same listeners, but with a new methodology. We provide evidence that the two phenomena are linked by showing that the perception of OPA by a given listener is highly correlated with the perception of harmonic fusion by the same listener.