Overtone-based pitch selection in hermit thrush song: unexpected convergence with scale construction in human music

Abstract

Many human musical scales, including the diatonic major scale prevalent in Western music, are built partially or entirely from intervals (ratios between adjacent frequencies) corresponding to small-integer proportions drawn from the harmonic series. Scientists have long debated the extent to which principles of scale generation in human music are biologically or culturally determined. Data from animal "song" may provide new insights into this discussion. Here, by examining pitch relationships using both a simple linear regression model and a Bayesian generative model, we show that most songs of the hermit thrush (Catharus guttatus) favor simple frequency ratios derived from the harmonic (or overtone) series. Furthermore, we show that this frequency selection results not from physical constraints governing peripheral production mechanisms but from active selection at a central level. These data provide the most rigorous empirical evidence to date of a bird song that makes use of the same mathematical principles that underlie Western and many non-Western musical scales, demonstrating surprising convergence between human and animal "song cultures." Although there is no evidence that the songs of most bird species follow the overtone series, our findings add to a small but growing body of research showing that a preference for small-integer frequency ratios is not unique to humans. These findings thus have important implications for current debates about the origins of human musical systems and may call for a reevaluation of existing theories of musical consonance based on specific human vocal characteristics.

Keywords: birdsong; music; overtones.

Fig. 1.

Song of the hermit thrush (C. guttatus). One song type of a single male hermit thrush, illustrating the various elements that can be observed in songs of this species. Only “notes” (elements with stable pitch) were analyzed in this study because the other element types have no clearly defined or measurable pitch.

Fig. 2.

Frequency distribution of a hermit thrush song compared with an overtone series. (A) Notes of a hermit thrush song. (B) The same notes rearranged in ascending order to show how they correspond to overtones 3, 4, 5, and 6 of an overtone series fitted to the frequencies corresponding to these notes (the complete stacked overtone series is shown on the right).

Fig. 3.

Probability densities of frequency distributions with various degrees of jitter. Example of frequency distribution densities from which the ground truth dataset was generated. For small values of jitter (η), the densities exhibit regularly spaced, distinct peaks. Sequences of notes drawn from these densities thus display an overtone structure. For larger values of η, the peaks begin to overlap, and the overtone structure disappears.

Fig. 4.

Sensitivity analysis. Percentage of 14-note sequences classified as overtone-related (at a significance threshold α = 0.05) for the least-squares regression model (continuous line and open circles) and for the Bayesian estimator (dotted line and closed squares) for jitter values (η) ranging from 0.005 to 0.3.