Two-voice complexity from a single side of the syrinx in northern mockingbird Mimus polyglottos vocalizations

Abstract

The diverse vocal signals of songbirds are produced by highly coordinated motor patterns of syringeal and respiratory muscles. These muscles control separate sound generators on the right and left side of the duplex vocal organ, the syrinx. Whereas most song is under active neural control, there has been a growing interest in a different class of nonlinear vocalizations consisting of frequency jumps, subharmonics, biphonation and deterministic chaos that are also present in the vocal repertoires of many vertebrates, including many birds. These nonlinear phenomena may not require active neural control, depending instead on the intrinsic nonlinear dynamics of the oscillators housed within each side of the syrinx. This study investigates the occurrence of these phenomena in the vocalizations of intact northern mockingbirds Mimus polyglottos. By monitoring respiratory pressure and airflow on each side of the syrinx, we provide the first analysis of the contribution made by each side of the syrinx to the production of nonlinear phenomena and are able to reliably discriminate two-voice vocalizations from potentially similar appearing, unilaterally produced, nonlinear events. We present the first evidence of syringeal lateralization of nonlinear dynamics during bilaterally produced chaotic calls. The occurrence of unilateral nonlinear events was not consistently correlated with fluctuations in air sac pressure or the rate of syringeal airflow. Our data support previous hypotheses for mechanical and acoustic coupling between the two sides of the syrinx. These results help lay a foundation upon which to understand the communicative functions of nonlinear phenomena.

Figure 1

Synthesized examples illustrating 4 types of biphonation and two-voice phenomena observed in mockingbird songs. The spectrogram (top) and spectrum (bottom) in box (A) illustrate the spectral properties typical of both “type A” biphonation and two-voice phenomena, consisting of two independent f₀s. “Type B” biphonation (B) consists of a fundamental frequency and sidebands. In this synthesized example, f₀ is a 1 kHz tone. The second frequency is a 250 Hz modulation frequency, m₀, which appears spectrographically as sound energy 250 Hz above and below f₀. (C) A synthesized example of “dual biphonation” similar to the type observed in mockingbird vocalizations. Each side of the syrinx produces “type B” biphonation simultaneously. In this example, two unrelated fundamental frequencies (f₀ and g₀), originate from opposite sides of the syrinx. The two “voices” are each modulated by an unrelated, lower modulating frequency (250 Hz, m₀). (D) A synthesized example of “dual biphonation” similar to panel C, but in this case m₀ is also frequency modulated, resulting in sidebands that are not parallel to f₀ or g₀. BP, biphonation 2VC, two-voice phenomena; SB, sidebands; 2SB, dual biphonation (two f₀s, each with sidebands).

Figure 2

Spectral properties typical of three types of nonlinear phenomena; frequency jumps, subharmonics and deterministic chaos. (A) A 3500 Hz tone with two 250 Hz frequency jumps. A power spectrum (a) taken at arrow a shows a single peak of sound energy corresponding to f₀. (B) A 3750 Hz tone, with a series of bifurcations, the first from a single f₀ to a 1/2 f₀ subharmonic regime, then an abrupt transition to deterministic chaos, and then to a 1/3 f₀ subharmonic regime. Comparing spectra and b illustrates the increase in spectral complexity resulting from the addition of subharmonic values and their harmonics (b, Box B). (C) A 10 ms section of deterministic chaos (in this case, a low-dimensional noise, generated using a Rossler attractor equation). The aperiodicity of the sound waveform (V) and the sound energy fairly evenly distributed across the entire spectrum (spectrogram C, and power spectrum, c) are indicators used to identify potential chaos in mockingbird songs. Abbreviations the same as those in Tables 1 and 2; FJ, frequency jump; SH, subharmonics; CH, deterministic chaos; 1 f₀, single frequency sounds; V, amplitude of sound waveform.

Figure 3

Examples of frequency jumps and subharmonics in mockingbird song (bird m123). (A) Frequency jumps occurred with airflow through only the right (arrow a) or left (arrow c) side of the syrinx. Arrow b indicates a shift from a ½ f₀ to ¼ f₀ subharmonic regime. Arrow c indicates a shift between a 1/3 f₀ and ½ f₀ subharmonic regime. (B) Expanded views of the sound waveform at each arrow in spectrogram (A), showing the abrupt changes in oscillation patterns at bifurcation points. (C) Power spectrum taken at arrow b, showing spectral peaks at f₀ and its harmonics (2 f₀, 3f₀, etc), as wel as at fractional integer values corresponding with a ¼ f₀ subharmonic, and its harmonics. F _L and F_R, rate of airflow through left and right bronchus, respectively. Airflow associated with positive pressure is expiratory, and that associated with negative pressure is inspiratory. P, pressure in the cranial thoracic air sac; V, oscillogram of vocalization (sound waveform). Horizontal lines indicate ambient pressure or zero air flow.

Figure 4

Normalized rates of bronchial airflow 25 ms before to 5 ms after a frequency jump (A) or the onset of subharmonics (B). Bifurcations occurred at time 0. Slopes of linear regressions over thre different 5 ms periods were measured (25-20 ms before, 5-0 ms before, and 0-5 ms after bifurcation points, indicated by vertical lines). Rates of bronchial airflow (A) show greater variance in their slope 0-5 ms before and 0-5 ms after a frequency jump than at an earlier point in the syllable, where no NLP were observed (failed Levene’s test of equal variances below the 5% level, P<0.05. Variance at 25-20 ms prior to bifurcation, σ² = 0.8; 5-0 ms prior, σ² = 7.7; 0-5 ms after, σ² = 7.2). Airflow was normalized to percent of maximum flow rate during syllable. Grey lines = upward jump in frequency; black lines - downward jump. (B) Rate of bronchial airflow 25-20 ms prior, 5-0 ms prior and 0-5 ms after onset of subharmonics did not show significant differences in slope (passed Levene’s test for equal variances wel above the 5% level, P = 0.21).

Figure 5

Unilaterally-produced subharmonics and deterministic chaos (mockingbird m152). (A) Arrows indicate abrupt transitions from a harmonic vocalization to a chaotic sound. The chaotic region is followed by a period of subharmonics (arrow b) after which the vocalization returns to a periodic state. (B) A 25 ms segment of the sound waveform showing the abrupt transition from periodic to aperiodic oscillation. (C) Power spectrum taken at arrow b (spectrogram, A). Spectral peaks show sound energy at f₀ and associated harmonics (2 f₀, 3f₀, etc) as well as at 0.5 f₀ and related harmonics (1.5 f₀, 2.5f₀, 3.5f₀, etc.) Abbreviations as in Fig 3.

Figure 6

Biphonation in mockingbird song. (A) Two independent frequencies produced by a single side of the syrinx. Arrows a and b indicate biphonic sounds concurrent with airflow through only the left side of the syrinx. At arrow a, sound energy is present at 990 Hz (f₀) and 1505 Hz (g₀), and their harmonics, 2 f₀ (1980 Hz) and 2 g₀ (3010 Hz). (B) An expanded view of the sound waveform at arrow a (spectrogram, A), showing a change from the biphonation event to a single f₀ tone. (C) Power spectrum taken at arrow b, in spectrogram (A), showing the two fundamental frequencies (f₀, and g₀), as wel as sound energy at various linear combinations of the two fundamentals. Abbreviations as in Fig 3.

Figure 7

Unilateral biphonation and “dual biphonation” in mockingbird song. (A) Spectrogram of two syllables produced in sequence by mockingbird m108. The first syllable in the pair (a) is an example of unilateral biphonation. This syllable is produced with the left side only, but two independent frequencies are present, the fundamental frequency (f₀) at ∼1800 Hz, and a lower, modulating frequency (m₀) visible as sidebands ∼115 Hz above and below f₀. The bird adds phonation from the right side of the syrinx in second syllable (b), and a second fundamental (g₀) appears, also with sidebands 115 Hz above and below, indicating that g₀ is also modulated by m₀. This is a two-voice syllable in which each voice is biphonic. (B) Expanded view of the sound waveform at arrows a and b in spectrogram (A), showing the AM pattern on the waveforms at a rate of ∼115 Hz (period of one modulation cycle ∼11.5 ms) both during unilateral flow (a) and bilateral flow (b). In addition to the 115 Hz modulation pattern, the two-voiced sound exhibits a second pattern in the waveform which is likely the result of beating between f₀ and g₀. A beat frequency is equal to the difference between f₀ and g₀, in this example, the second modulation rate in b is approximately equal to 550, which corresponds with the difference frequency between g₀ and f₀ (2695 - 2135 Hz). (C) Power spectra taken at arrows a and b in panel (A). Sound was filtered with a digital 800 Hz Hanning shape high pass filter. Peaks labeled correspond with fundamental frequencies as well as the sidebands resulting from the interaction of modulating frequency (m₀) with the carrier (f₀) in a, and with the two carrier frequencies (f₀ and g₀) in b. Abbreviations as in Fig 3.

Figure 8

(A) Dual biphonation (two-voice phenomenon with biphonation in both voices) The sound at the arrow consists of two fundamental frequencies (f₀ and g₀), both simultaneously modulated by a third frequency (m₀). Although f₀ and g₀ are modulated in opposite patterns in the frequency domain (one downsweeping and the other upsweeping in frequency), m₀, or the rate of amplitude modulation frequency is the same (approx 250 Hz) for both, as evidenced by evenly spaced sidebands the same distance from both f₀ and g₀. (B) An expanded view of the sound waveform showing the pattern of amplitude modulation. (C) Power spectrum taken at arrow a in spectrogram (A). Abbreviations as in Fig 3.

Figure 9

Unequal contribution of right and left sides to bilaterally-produced chaos. Chaotic sounds often contained harmonic windows, or brief moments of periodic oscillation, such as that seen around arrow b. Mockingbird “loud hew” calls (A) were always produced with flow through both sides of the syrinx for the entire duration of the call. In most cases (56 of 67 calls) one side alone appeared to contribute the majority of the aperiodicity in the call, while the contribution of the other side is more pure-tonal. (B) The difference in aperiodic behavior of the two sides is shown by examination of sound recorded inside the right and left bronchi and cranial thoracic air sac (obtained by high-pas filtering and amplifying thermistor and pressure transducer outputs). (C) 20 ms segment of the sound waveform, at the time indicated by arrow a in the spectrogram, illustrating the aperiodic nature of the oscillation. (D) Power spectrum of the sound taken at arrow a in the spectrogram (A). Additionally, the air flow in the right side (F _R) shows an aperiodic, rapid modulation, which not present in the flow on the left (F _L). Other abbreviations as in Fig 3.