Condor 85:259-26 I Q The Cooper Ornithological Souety 1983

(carrier ).The side bands will be separatedfrom COMMENTARY the carrier frequency and, if there are several, from each other by the frequency of repetition rate, or modulating frequency. Hence, if the carrier frequency can be evenly ON SONOGRAMS, , divided by the modulatingfrequency, the sonographicpat- AND ASSUMPTIONS tern will resemble a of a tone with a equivalent to the modulating fre- The ability of sonogramsto present acoustic data in a quency. The carrier frequency usually appears as an em- format that is easily comprehended,compared, and print- phasized harmonic. Becausethe modulating frequency is ed has made them an important tool in studies of avian usually much lower than the carrier frequency, the ap- behavior and systematics.The 10 volumes of The Condor parent “fundamental frequency” is low, the “harmonic from 1972-198 1 contained 51 papers, involving 75% of spectrum” is composed of closely spaced bands, and, if all issues,that used sonographicdata and two papers dis- the carrier is high, the “lower harmonics” are usually ab- cussingthe presentationand use of such data. This com- sent. The exact sonographicpattern depends both on the ment follows in the latter series by indicating some pos- nature of the modulation and the setting of the spectro- sible pitfalls in the interpretation of sonograms. graph; the problem is acute with narrow band-pass filter Birds can utter a wide variety of phonations, but these settings.Appropriate soundsfor producing such patterns can be divided into two categoriesdepending on how the appear to be common in avian phonations (Davis 1964, soundis produced.The most common kind of avian pho- Watkins 1967, Marler 1969). nation is a simple tone, or whistle, in which all the energy Third, a freely oscillating,edge-clamped membrane, such at any given instant is concentratedin a single frequency. as a syringealmembrane, behaves quite differently from Sonogramsof unmodulated, simple tones show a single a freely oscillating,end-clamped string.A wave propagates horizontal band. The production of a whistled does in one dimension along the length of the string. If, as is not depend on the oscillation of a membrane or any other probable, the wave encountersan impedance mismatch mechanical element of the syrinx (Gaunt et al. 1982). A at the end of the string, some of it will reflect back in the second kind of sound is that in which, at any moment, opposite phase, so that it seems to have changed to the energy is distributed into more than one frequency. The opposite side of the string. If the vibration is repeated, generationof many of these soundsis supposedto involve succeedingwaves will interact with the reflected waves to either mechanical oscillatorsor coupled resonators.I am form a series of standing waves, the number of which is concernedhere with multi-frequency soundsin which the equivalent to the number of harmonics. In a membrane, energyis distributedinto distinct, discreetfrequencies, i.e., however, the wave radiates as a series of arcs from the not broad-band noises.Davis (1964) included suchsounds point of stimulation. Hence, it propagatesand is reflected among those he called “complex tones.” However, I find in two dimensions,deforming a surfacerather than a line. it useful to restrict “complex tones” to those soundsthat The resultinginteraction is far more complex than in the are produced by a single generator. A sonogram of an one-dimensional string, and the resulting are unmodulated, complex tone contains a series of parallel not normally harmonic. Rather, they will occurat varying bands. Such are popularly termed “harmonic fractional (partial) multiples of the fundamental (Rossing tones,” and the distribution of frequenciesis called a “har- 1982). Such partial overtones account for the character- monic spectrum.” In a true harmonic tone, such as is istic, pitchlesssounds of many drums. Tunable drums with producedby most stringedand wind instruments,the higher distinct pitch, suchas kettledrums,represent special classes (overtones) are integer multiples of the fun- of membrane instruments in which various factors force damental frequency (or first harmonic). This simple re- the partial frequencies closer to harmonic values of an lationship is familiar to many researchers,but some in- apparentlymissing fundamental. Casey (198 1) showedthat vestigators assume that all multi-frequency sounds are partials will be generated by membranes of a variety of harmonic tones. Therein lies a set of problems because(1) shapessubjected to various degreesof damping. Hence. it not all multi-banded figureson sonogramsrepresent com- is unlikely that a freely oscillating syringealmembrane of plex tones, (2) not all complex tones are composed of any shape, even if constrained like the head of a kettle- harmonics as here defined, and (3) the mechanism(s) drum, will producea classicharmonic spectrum.Yet some wherebya syrinx generatescomplex tonesis (are) not clear- birds, e.g., Phainopepla (Phainopepla nitens; Leger and ly understood. Carroll 1981) and Whimbrel (Numeniusphaeopus; Skeel First, an apparent harmonic may be an artifact. Sound 1978) do seem to utter soundswith true harmonic spectra. spectrographswill produce spuriousharmonics if the sig- This suggeststhat something is faulty, or at least lacking, nal is introduced at too high a gain (Davis 1964, Gree- in our present understandingof syringealmechanics. newalt 1968:9). This type of error is usually overcome Problems in the interpretation of complex tones may with experience, but that experience should not be as- be exacerbatedby improper use of a sonogram. For in- sumed in reviewers, editors, or readers. stance,the analysisof an harmonic spectrum depends on Multi-frequency soundsmay also be the product of the a rather precise determination of frequencies,but many two-voice phenomenon. If both sidesof the syrinx should sound spectrographs,including the commonly used Kay produce complex tones with slightly different fundamen- Elemetrics“Sona-Graph,” do not measurefrequency well, tals, very puzzling patterns may result (S. Nowicki, pers. especiallywhen used with a wide-band filter. The trigger comm.). The two-voice phenomenon is surelyresponsible frequency is generally assumedto lie at the center of the for instances in which frequency bands cross over each inscribed band, but that may not be so (Davis 1964) and other, diverge with falling frequencies,or converge with even if it does, the center must be estimated with some rising frequencies. (Overtones, whether partial or har- degreeof error. Further, the width of the band varies with monic, must diverge with rising frequenciesand converge the gain setting of the spectrograph.Even when using a with falling ones.) In a confusion of the conceptsof two- narrow-band pass filter, e.g., 40 Hz, for high resolution, voices and harmonics, Anderson (1978) described “pe- one should expect a production error of up to ?20 Hz. culiar harmonic bands” exhibiting several of the cri- To this must be addedthe investigator’sinterpolation error. teria for two voices, that may be an example of “dual Calibration marks are, at best, at 500 Hz, more usually control of sound production.” 1,000 Hz intervals, and intervening values must be inter- Second, if a tone is sufficientlymodulated in either fre- polated. On a sonogram with a frequency range of 80- quency or amplitude, then its sonogram will show side 8,000 Hz, which is common in avian studies, each mil- bands to both sidesof and parallel to the tone’s frequency limeter on the ordinate represents70 Hz. Hence, a mistake

12591 260 COMMENTARY of 10 Hz will result from an interpolation error of only Hand’s data probably did conform to that pattern. Her 0.14 mm! Figure 8 suggeststhat the Long Call of some gulls is com- For most behavioral or systematicinvestigations, failure posed of harmonics. The third, and in my view most se- to recognizethese problems is oflittle import, but for those rious flaw, is failure to state explicitly that at least some of us interested in syringeal function, such errors can be of her data are not easily fitted to the expected pattern. serious.The reason for this is that we have yet to devise On such discrepanciesscientific theories can hang or fall, a technique to observe a functioning syrinx in vivo. True, and failure to recognizeor proclaim them only preserves syringealstructures are well-known, but most of our no- the present paradigm. tions of how those structureswork are based on extrap- Even when performed with great care, acousticanalyses olations from the sounds they produce. Hence, misana- may not lead to unambiguoussolutions. In developing his lyzed sonogramsconstitute noise in our data base.Let me ideas of how a syrinx might produce harmonic sounds, provide an example. Greenewalt(1968, Chap. 10) consideredthe fact that many I have chosen this example for several reasons. First, birds produce soundsin which the apparent fundamental the faults in acousticanalysis are irrelevant to the author’s and severallower harmonicsare missing.He hypothesized main interest. Thus, the paper is typical of many papers that these were suppressedby proximity of the vibrating that useacoustic data but are not concernedprimarily with membrane to the opposite trachea-bronchialwall. As one acousticanalysis. Second, the author recognizesthe lim- example, he presenteda detailed analysisof the Scold call itations of sonogramsand has taken more pains than most of a Black-cappedChickadee (Parus atricapillus).A son- to insure the accuracyof her frequency estimates. Third, ogram, a “harmonic spectrum,” a chart of instantaneous and this is most unusual,she hasprovided sufficientdetails frequencies(taken from a period counter), and a table of of her methods and sufficient numerical data that I was measured“harmonic” frequencieswere included as data. able to confirm a problem rather than simply suspectit. The sonogram shows five parallel bands between 2,900 Finally, the author informs me that she was specifically and 4,000 Hz. Greenewalt interpreted these as the 7th- trying to avoid any acoustic implications, in which case 11th harmonics of a fundamental of 4 15 Hz with the dark- her failure to do so provides a splendid example of how er, ninth harmonic (3,739 Hz) “dominant.” Frequencies insidiously a hidden assumption can force us to seek a of the harmonics were determined by isolating each by preconceivedpattern where it does not exist. filtration and determining the time interval for 100 suc- In a paper on the vocalizations of gulls, Hand (198 1: cessiveperiods with a period counter. This techniquepro- 290) stated: vides far more precision than any estimate from a sono- gram. The mean harmonic band intervals were estimated On the basis of the sonogramalone, we might entertain [author’s italics] by placing a grid calibrated in 50-Hz three hypothesesfor the nature of this sound: (1) a fun- intervals over the sound figuresat the highest point. damental frequency of about 3,320 Hz (Greenewalt’s 8th Frequenciesof visible harmonics at this point were harmonic) with four overtones and a weak undertone (as estimated to the nearest 10 Hz and compared to val- sometimes occurs for kettledrums), (2) a strongly modu- ues on a numbers table, these values being integral lated tone, or (3) Greenewalt’s explanation of the higher multiples of possibleintervals. For example, a chok- harmonics of a suppressedfundamental. His other data ing sound had visible bands at the following Hz: 180, allow us to extend the analysis. The table of frequencies 320,450, and 650. The value from the numbers table clearly shows that the bands occur at regular intervals. producing the best fit to the observed bands corre- That fact alone dismissesthe first hypothesis,because par- spondsto a harmonic interval of 160 Hz. A calculated tial overtonesdo not occurat regularintervals. Moreover, mean interband interval for this call would be 156.6 the predicted partials of either a round or oval membrane, Hz, which closelyfits the 160 Hz estimate determined with fundamentalsof 3,320 Hz would be higher than the by my method. observed freouencies(Casey 1981). Both the oscillogram and instantaneousfrequency chart show strong modula- I am not sure what “closely” means in the context of a tions of both amplitude and frequency. The mean mod- supposedlyprecise mathematical relationship, but will as- ulating frequencyis given as 4 17 Hz; the interval between sume it means “within an acceptable margin of error.” bands can be calculatedto rangefrom 4 14 to 420 Hz. The Hand mentioned an error of +7 Hz. This value was cal- amplitude modulation is sufficient that I would consider culated as the variation between the estimated value of the sound a series of pulses. Greenewalt rejected the in- the supposed fundamental frequency and its frequency terpretation of a pulsed tone on the basis that a coupled calculatedfrom the mean interband interval for a sample tracheal resonance was not present. However, a pulsed of calls (Hand, pers. comm.). With this error, 156 Hz is a tone need not coupleto a resonatorto producea harmonic good approximation of 160 Hz, and we cannot quarrel spectrum (Watkins 1967). with 320 Hz for the secondharmonic of 160 Hz, but none Both of these analysesassume that the sound is gener- of the other values are close. Still, even with an error ated by a singlesource. However, S. Nowicki (pers.comm.) of &20 Hz, the values of 180 and 659 Hz for the funda- has data suggestingthat a chickadee’s “dee” contains an mental and third harmonic are only marginal, and 450 Hz effect of the two-voice phenomenon. Each side appearsto is significantly different from the expected 480 Hz of the produce a different complex tone. How the interaction of third harmonic. None of the higher frequenciesis within these producesthe sonogramand wave form analyzed by 30 Hz of the expected harmonic values of Hand’s lowest Greenewalt requires further study. If Nowicki is correct, estimatedfrequency of 180 Hz, if that were consideredthe then an already perplexing situation has become more so. fundamental. Consider also that the mean interband in- Further, the alternatives to Greenewalt’s hypothesis still terval is an averageof 130, 140, and 200(!) Hz. Whatever beg the question of how harmonics are formed in those this series may represent, it is not a simple, harmonic avian phonationsin which they are certainly present.Until series. recently, most investigatorsof syringealfunction evidently Hand’s treatment suffersfrom three flaws. The first, use assumedthat harmonic oscillation was a natural mode for of the inappropriate term “harmonic,” is trivial because membranes.As that is not so, then many avian phonations it fits a tradition that has not previously been challenged. constitute a puzzle-the key to which may lie in anyone’s The secondis choice of an analytic procedure that infers data. a certain kind of result, for the use of a numbers table In summary, a sonogram can be an extremely useful assumesthat the observed frequenciesshould be distrib- tool for investigations of behavior and systematics.It is uted in a pattern of integer multiples. Ironically, some of not a good tool for detailed acousticanalysis. Investigators COMMENTARY 261 in behavior and systematicsshould be aware of the weak- membranes in avian syrinx. M.Sc. thesis, Ohio State nessesof the technique,even thoughthose weaknesses will Univ., Columbus. seldom directly affect their own work. On a more general DAVIS,L. I. 1964. Biologicalacoustics and the use of the level, we should all remember that apparently aberrant sound spectrograph.Southwest. Nat. 9:118-145. data may representa reality rather than an expressionof GAUNT,A. S., S. L.L. GAUNT, AND R. M. CASEY. 1982. some error in the system. That which is puzzling to us Syringealmechanics reassessed: evidence from Strep- may be exactlythe information someoneelse seeks. Hence, topelia. Auk 991474-494. drawing attention to such situations may be a service. GREENEWALT,C. H. 1968. Bird song: and phys- Finally, we should constantly remind ourselvesthat all of iology. Smithsonian Inst. Press, Washington, DC. our theories are underlain by sets of assumptions,some HAND, J. L. 1981. A comparison of vocalizations of not at all obvious. A periodic review of the assumptions Western Gulls (Lams occidentalisoccidentalis and L. in one’s field, and oftheir likely effectson one’s procedures, o. livens).Condor 83:289-301. will amost always be profitable. LEGER,D. W., AND L. F. CARROLL.198 1. Mobbing calls I am extremely grateful to Judith Latta Hand for com- of Phainopepla. Condor 83:377-380. ments on an earlier draft, and for her willingnessto let her MARLER,P. 1969. Tonal quality of bird sounds, p. 5- work be usedin this way. StephenNowicki very graciously 18. In R. A. Hinde [ed.], Bird vocalizations. Cam- gave permission to use some of his unpublished ideas. bridge Univ. Press,New York. Lincoln Fairchild provided valuable discussionsand com- ROSSING, T. D. 1982. The science of sound. Addison- mented on the draft, which was also critiqued by Richard Wesley, Reading, MA. M. Caseyand SandraL. L. Gaunt. Reviewers EugeneMor- SKEEL, M. A. 1978. Vocalizations of the Whimbrel on ton and William Barklow also provided valuable com- its breeding grounds.Condor 80: 194-202. ments. This work was supported by grant number DEB- WATKINS, W. A. 1967. The harmonic interval: fact or 79 11774 from the National ScienceFoundation. artifact in spectralanalysis of pulse trains, p. 15-4 1. In W. N. Tavolga [ed.], Marine bioacoustics.Vol. 2. LITERATURE CITED Pergamon Press, New York. ANDERSON,W. L. 1978. Vocalizations of Scaled Quail. ABBOT S. GAUNT, Department of Zoology, The Ohio Condor 80:49-63. State University, 1735 Neil Avenue, Columbus, Ohio CASEY,R. M. 1981. Theoretical analysis of tympanic 43210.

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