Frequency discrimination of complex tones with overlapping and non-overlapping harmonics

These experiments address the following issues. (1) When two complex tones contain different harmonics, do the differences in timbre between them impair the ability to discriminate the pitches of the tones? (2) When two complex tones have only a single component in common, and that component is the most discriminable component in each tone, is the frequency discrimination of the component affected by differences in residue pitch between the two tones? (3) How good is the pitch discrimination of complex tones with no common components when each tone contains multiple harmonics, so as to avoid ambiguity of pitch? (4) Is the pitch discrimination of complex tones with common harmonics impaired by shifting the component frequencies to nonharmonic values? In all experiments, frequency difference limens (DLCs) were measured for multiple-component complex tones, using an adaptive two-interval, two-alternative, forced-choice task. Three highly trained subjects were used. The main conclusions are as follows. (1) When two tones have the first six harmonics in common, DLCs are larger when the upper harmonics are different than when the upper harmonics are in common or are absent. It appears that differences in timbre impair DLCs. (2) Discrimination of the frequency of a single common partial in two complex tones is worse when the two tones have different residue pitches than when they have the same residue pitch. (3) DLCs for complex tones with no common harmonics are generally larger than those for complex tones with common harmonics. For the former, large individual differences occur, probably because subjects are affected differently by differences in timbre. (4) DLCs for harmonic complex tones are smaller than DLCs for complex tones in which the components are mistuned from harmonic values. This can probably be attributed to the less distinct residue pitch of the inharmonic complexes, rather than to reduced discriminability of partials. Overall, the results support the idea that DLCs for complex tones with common harmonics depend on residue pitch comparisons, rather than on comparisons of the pitches of partials.     

The effect of hearing loss on the resolution of partials and fundamental frequency discrimination

The relationship between the ability to hear out partials in complex tones, discrimination of the fundamental frequency (F0) of complex tones, and frequency selectivity was examined for subjects with mild-to-moderate cochlear hearing loss. The ability to hear out partials was measured using a two-interval task. Each interval included a sinusoid followed by a complex tone; one complex contained a partial with the same frequency as the sinusoid, whereas in the other complex that partial was missing. Subjects had to indicate the interval in which the partial was present in the complex. The components in the complex were uniformly spaced on the ERB(N)-number scale. Performance was generally good for the two "edge" partials, but poorer for the inner partials. Performance for the latter improved with increasing spacing. F0 discrimination was measured for a bandpass-filtered complex tone containing low harmonics. The equivalent rectangular bandwidth (ERB) of the auditory filter was estimated using the notched-noise method for center frequencies of 0.5, 1, and 2 kHz. Significant correlations were found between the ability to hear out inner partials, F0 discrimination, and the ERB. The results support the idea that F0 discrimination of tones with low harmonics depends on the ability to resolve the harmonics.     

Range discrimination by big brown bats (Eptesicus fuscus) using altered model echoes: implications for signal processing

The sonar emissions of two big brown bats (Eptesicus fuscus) were modeled to create a "normal" echolocation signal for each bat which was then used as an artificial echo to synthesize a phantom target. The bat's task was to indicate which of two phantom targets (presented singly) was the "near" target and which the "far" target. Threshold range discrimination at a nominal target distance of 80 cm was about 0.6 cm for both bats. The normal signal was then modified to change the relative energy in each harmonic, the signal duration, the curvature of the frequency sweep, the absolute frequency, the phase of the second and third harmonics relative to the first, or the Doppler shift of the signal. To determine which modifications affected ranging performance, the altered models were used in tests of range discrimination that were interleaved on a day-to-day basis with tests using the normal model. Of the 12 modifications tested, only those changing the curvature of the frequency sweep affected performance. This result appears not to be predicted by current models of echo processing in FM bats. Eptesicus may be able to compensate for certain types of distortions of a returning echo, an ability possibly related to Doppler tolerance or to the characteristics of the natural variation in a bat's emissions.     

Perception of the low pitch of frequency-shifted complexes

When all of the components in a harmonic complex tone are shifted in frequency by delta f, the pitch of the complex shifts roughly in proportion to delta f. For tones with a small number of components, the shift is usually somewhat larger than predicted from pitch theories, which has been attributed to the influence of combination tones [Smoorenburg, J. Acoust. Soc. Am. 48, 924-941 (1970)]. Experiment 1 assessed whether combination tones influence the pitch of complex tones with more than five harmonics, by using noise to mask the combination tones. The matching stimulus was a harmonic complex. Test complexes were bandpass filtered with passbands centered on harmonic numbers 5 (resolved), 11 (intermediate), or 16 (unresolved) and fundamental frequencies (FOs) were 100, 200, or 400 Hz. For the intermediate and unresolved conditions, the matching stimuli were filtered with the same passband to minimize differences in the excitation patterns of the test and matching stimuli. For the resolved condition, the matching stimulus had a passband centered above that of the test stimulus, to avoid common partials. For resolved and intermediate conditions, pitch shifts were observed that could generally be predicted from the frequencies of the partials. The shifts were unaffected by addition of noise to mask combination tones. For the unresolved condition, no pitch shift was observed, which suggests that pitch is not based on temporal fine structure for stimuli containing only high unresolved harmonics. Experiment 2 used three-component complexes resembling those of Schouten [J. Acoust. Soc. Am. 34, 1418-1424 (1962)]. Nominal harmonic numbers were 3, 4, 5 (resolved), 8, 9, 10 (intermediate), or 13, 14, 15 (unresolved) and F0s were 50, 100, 200, or 400 Hz. Clear shifts in the matches were found for all conditions, including unresolved. For the latter, subjects may have matched the "center of gravity" of the excitation patterns of the test and matching stimuli.     

Thresholds for the detection of inharmonicity in complex tones

Thresholds were measured for the detection of inharmonicity in complex tones. Subjects were required to distinguish a complex tone whose partials were all at exact harmonic frequencies from a similar complex tone with one of the partials slightly mistuned. The mistuning which allowed 71% correct identification in a two-alternative forced-choice task was estimated for each partial in turn. In experiment I the fundamental frequency was either 100, 200, or 400 Hz, and the complex tones contained the first 12 harmonics at equal levels of 60 dB SPL per component. The stimulus duration was 410 ms. For each fundamental the thresholds were roughly constant when expressed in Hz, having a mean value of about 4 Hz (range 2.4-7.3 Hz). In experiment II the fundamental frequency was fixed at 200 Hz, and thresholds for inharmonicity were measured for stimulus durations of 50, 110, 410, and 1610 ms. For harmonics above the fifth the thresholds increased from less than 1 Hz to about 40 Hz as duration was decreased from 1610-50 ms. For the lower harmonics (up to the fourth) threshold changed much less with duration, and for the three shorter durations thresholds for each duration were roughly a constant proportion of the harmonic frequency. The results suggest that inharmonicity is detected in different ways for high and low harmonics. For low harmonics the inharmonic partial appears to "stand out" from the complex tone as a whole. For high harmonics the mistuning is detected as a kind of "beat" or "roughness," presumably reflecting a sensitivity to the changing relative phase of the mistuned harmonic relative to the other harmonics.(ABSTRACT TRUNCATED AT 250 WORDS)     

Affect cues in vocalizations of the bat, Megaderma lyra, during agonistic interactions

Some features of emotional prosody in human speech may be traced back to affect cues in mammalian vocalizations. The present study addresses the question whether affect intensity, as expressed by the intensity of behavioral displays, is encoded in vocal cues, i.e., changes in the structure of associated calls, in bats, a group evolutionarily remote from primates. A frame-by-frame video analysis of 109 dyadic agonistic interactions recorded in approach situations was performed to categorize displays into two intensity levels based on a cost-benefit estimate. M. lyra showed graded visual displays accompanied by specific calls and response calls of the second bat. A sound analysis revealed systematic changes of call sequence parameters with display level. At the high intensity level, total call duration, number of syllables within a call, and the number of calls within a sequence were increased, while intervals between call syllables were decreased for both call types. In addition, the latency of the response call was shorter, and its main syllable-type durations and fundamental frequency were increased. These systematic changes of vocal parameters with affect intensity correspond to prosodic changes in human speech, suggesting that emotion-related acoustic cues are a common feature of vocal communication in mammals.     

An account of monaural phase sensitivity

Listeners can detect phase differences between the envelopes of sounds occupying remote frequency regions, and between the fine structures of partials that interact within a single auditory filter. They are insensitive to phase differences between partials that differ sufficiently in frequency to preclude within-channel interactions. A new model is proposed that can account for all three of these findings, and which, unlike currently popular approaches, does not discard across-channel timing information. Sensitivity is predicted quantitatively by analyzing the output of a cochlear model using a spectro-temporal decomposition inspired by responses of neurons in the auditory cortex, and by computing a distance metric between the responses to two stimuli to be discriminated. Discriminations successfully modeled include phase differences between pairs of bandpass filtered harmonic complexes, and between pairs of sinusoidally amplitude modulated tones, discrimination between amplitude and frequency modulation, and discrimination of transient signals differing only in their phase spectra ("Huffman sequences").     

Evidence against an effect of grouping by spectral regularity on the perception of virtual pitch

Two experiments investigated the role of the regularity of the frequency spacing of harmonics, as a separate factor from harmonicity, on the perception of the virtual pitch of a harmonic series. The first experiment compared the shifts produced by mistuning the 3rd, 4th, and 5th harmonics in the pitch of two harmonic series: the odd-H and the all-H tones. The odd-H tone contained odd harmonics 1 to 11, plus the 4th harmonic; the all-H tone contained harmonics 1 to 12. Both tones had a fundamental frequency of 155 Hz. Pitch shifts produced by mistuning the 3rd harmonic, but not the 4th and 5th harmonics, were found to be significantly larger for the odd-H tone than for the all-H tone. This finding was consistent with the idea that grouping by spectral regularity affects pitch perception since an odd harmonic made a larger contribution than an adjacent even harmonic to the pitch of the odd-H tone. However, an alternative explanation was that the 3rd mistuned harmonic produced larger pitch shifts within the odd-H tone than the 4th mistuned harmonic because of differences in the partial masking of these harmonics by adjacent harmonics. The second experiment tested these explanations by measuring pitch shifts for a modified all-H tone in which each mistuned odd harmonic was tested in the presence of the 4th harmonic, but in the absence of its other even-numbered neighbor. The results showed that, for all mistuned harmonics, pitch shifts for the modified all-H tone were not significantly different from those for the odd-H tone. These findings suggest that the harmonic relations among frequency components, rather than the regularity of their frequency spacing, is the primary factor for the perception of the virtual pitch of complex sounds.     

Effect of duration on the frequency discrimination of individual partials in a complex tone and on the discrimination of fundamental frequency

Thresholds for the discrimination of fundamental frequency (FODLs) and frequency difference limens (FDLs) for individual partials within a complex tone (F0=250 Hz, harmonics 1-7) were measured for stimulus durations of 200, 50, and 16 ms. The FDLs increased with decreasing duration. Although the results differed across subjects, the effect of duration generally decreased as the harmonic number increased from 1 to 4, then increased as the harmonic number increased to 6, and finally decreased for the seventh harmonic. For each duration, FODLs were smaller than the smallest FDL for any individual harmonic, indicating that information is combined across harmonics in the discrimination of FO. FODLs predicted from the FDLs corresponded well with observed FODLs for the 200- and 16-ms durations but were significantly larger than observed FODLs for the 50-ms duration. A supplementary pitch-matching experiment using two subjects indicated that the contribution of the seventh harmonic to the pitch of the 16-ms complex tone was smaller than would be predicted from the FDL for that harmonic. The results are consistent with the idea that the dominant region shifts upward with decreasing duration, but that the weight assigned to individual harmonics is not always adjusted in an optimal way.     

A masking level difference due to harmonicity

The role of harmonicity in masking was studied by comparing the effect of harmonic and inharmonic maskers on the masked thresholds of noise probes using a three-alternative, forced-choice method. Harmonic maskers were created by selecting sets of partials from a harmonic series with an 88-Hz fundamental and 45 consecutive partials. Inharmonic maskers differed in that the partial frequencies were perturbed to nearby values that were not integer multiples of the fundamental frequency. Average simultaneous-masked thresholds were as much as 10 dB lower with the harmonic masker than with the inharmonic masker, and this difference was unaffected by masker level. It was reduced or eliminated when the harmonic partials were separated by more than 176 Hz, suggesting that the effect is related to the extent to which the harmonics are resolved by auditory filters. The threshold difference was not observed in a forward-masking experiment. Finally, an across-channel mechanism was implicated when the threshold difference was found between a harmonic masker flanked by harmonic bands and a harmonic masker flanked by inharmonic bands. A model developed to explain the observed difference recognizes that an auditory filter output envelope is modulated when the filter passes two or more sinusoids, and that the modulation rate depends on the differences among the input frequencies. For a harmonic masker, the frequency differences of adjacent partials are identical, and all auditory filters have the same dominant modulation rate. For an inharmonic masker, however, the frequency differences are not constant and the envelope modulation rate varies across filters. The model proposes that a lower variability facilitates detection of a probe-induced change in the variability, thus accounting for the masked threshold difference. The model was supported by significantly improved predictions of observed thresholds when the predictor variables included envelope modulation rate variance measured using simulated auditory filters.     

Does fundamental-frequency discrimination measure virtual pitch discrimination?

Studies of pitch perception often involve measuring difference limens for complex tones (DLCs) that differ in fundamental frequency (F0). These measures are thought to reflect F0 discrimination and to provide an indirect measure of subjective pitch strength. However, in many situations discrimination may be based on cues other than the pitch or the F0, such as differences in the frequencies of individual components or timbre (brightness). Here, DLCs were measured for harmonic and inharmonic tones under various conditions, including a randomized or fixed lowest harmonic number, with and without feedback. The inharmonic tones were produced by shifting the frequencies of all harmonics upwards by 6.25%, 12.5%, or 25% of F0. It was hypothesized that, if DLCs reflect residue-pitch discrimination, these frequency-shifted tones, which produced a weaker and more ambiguous pitch than would yield larger DLCs than the harmonic tones. However, if DLCs reflect comparisons of component pitches, or timbre, they should not be systematically influenced by frequency shifting. The results showed larger DLCs and more scattered pitch matches for inharmonic than for harmonic complexes, confirming that the inharmonic tones produced a less consistent pitch than the harmonic tones, and consistent with the idea that DLCs reflect F0 pitch discrimination.     

Accuracy of pitch matching for pure tones and for complex tones with overlapping or nonoverlapping harmonics.

The discrimination of the fundamental frequency (fo) of pairs of complex tones with no common harmonics is worse than the discrimination of fo for tones with all harmonics in common. These experiments were conducted to assess whether this effect is a result of pitch shifts between pairs of tones without common harmonics or whether it reflects influences of spectral differences (timbre) on the accuracy of pitch perception. In experiment 1, pitch matches were obtained between sounds drawn from the following types: (1) pure tones (P) with frequencies 100, 200, or 400 Hz; (2) a multiple-component complex tone, designated A, with harmonics 3, 4, 8, 9, 10, 14, 15, and fo = 100, 200, or 400 Hz; (3) A multiple-component complex tone, designated B, with harmonics 5, 6, 7, 11, 12, 13, 16, and with fo = 100, 200 or 400 Hz. The following matches were made; A vs A, B vs B, A vs P, B vs P and P vs P. Pitch shifts were found between the pure tones and the complex tones (A vs P and B vs P), but not between the A and B tones (A vs B). However, the variability of the A vs B matches was significantly greater than that of the A vs A or B vs B matches. Also, the variability of the A vs P and B vs P matches was greater than that for the A vs B matches. In a second experiment, frequency difference limens (DLCs) were measured for the A vs A, B vs B, and A vs B pairs of sounds. The DLCs were larger for the A vs B pair than for A vs A or B vs B. The results suggest that the poor frequency discrimination of tones with no common harmonics does not result from pitch shifts between the tones. Rather, it seems that spectral differences between tones interfere with judgements of their relative pitch.     

Frequency and intensity difference limens for harmonics within complex tones

A two-interval, two-alternative forced choice task was used to estimate frequency difference limens (DLs) for individual harmonics within complex tones, and DLs for the periodicity (i.e., number of periods per s) of the whole complexes. For complex tones with equal-amplitude harmonics, the DLs for the lowest harmonics were small (less than one percent). The DLs increased rather abruptly around the fifth to seventh harmonic. The highest harmonic in each complex was also well discriminated, and the discriminability of a single high harmonic was markedly improved by increasing its level relative to the other components. The DL for a complex tone was generally smaller than the frequency DL of its most discriminable component. The DL for a complex was found to be predictable from the DLs of the harmonics comprising the complex, using a formula derived by Goldstein [J. Acoust. Soc. Am. 54, 1496-1516 (1973)] from his optimum processor theory for the formation of the pitch of complex tones. The DL for a complex is sometimes primarily determined by high harmonics, such as the highest harmonic, or a harmonic whose level exceeds that of adjacent harmonics. We also measured intensity DLs for individual harmonics within complex tones. The intensity DLs were smallest for low harmonic numbers, and for the highest harmonic in a complex. An excitation-pattern model was used to determine whether the frequency DLs of harmonics within complex tones could be explained in terms of place mechanisms, i.e., in terms of changes in the amount of excitation at appropriate frequency places. We conclude that place mechanisms are not adequate, and that information about the frequencies of individual harmonics is probably carried in the time patterning of neural impulses.     

Discriminating between coherent and incoherent frequency modulation of complex tones

A series of experiments measured the discrimination by human listeners of frequency-modulated complex tones which differed only in the coherence of frequency modulation (FM). For the coherently modulated tones all components were modulated by the same 5-Hz sinusoid, and by the same percentage of their starting frequencies, whereas for the incoherently modulated tones the modulation of one (target) component differed from that of the rest. When the 400-ms complex was composed of consecutive harmonics of a common fundamental, performance improved monotonically with increases in modulator delay, and was nearly perfect at the longest delays. When the complex was inharmonic, performance was near chance at all modular delays, both for component frequencies between 1500 and 2500 Hz, and for component frequencies between 400 and 800 Hz. It is argued that listeners detected incoherence in harmonic complexes by detecting the resulting mistuning of the target component. This conclusion was supported by the finding that listeners were usually at least as good at detecting a fixed mistuning of the center component of a harmonic complex as they were at detecting a modulator phase delay imposed on it. A final experiment, with a stimulus duration of 1 s and slower modulation rates, showed that listeners could detect incoherence for some inharmonic complexes. However, detection was worse than for harmonic complexes and was, it is argued, based on weak harmonicity cues. The results of all experiments point to the absence of an across-frequency mechanism specific to the detection of FM incoherence.     

The perception of complex tones by a false killer whale (Pseudorca crassidens)

Complex tonal whistles are frequently produced by some odontocete species. However, no experimental evidence exists regarding the detection of complex tones or the discrimination of harmonic frequencies by a marine mammal. The objectives of this investigation were to examine the ability of a false killer whale to discriminate pure tones from complex tones and to determine the minimum intensity level of a harmonic tone required for the whale to make the discrimination. The study was conducted with a go/no-go modified staircase procedure. The different stimuli were complex tones with a fundamental frequency of 5 kHz with one to five harmonic frequencies. The results from this complex tone discrimination task demonstrated: (1) that the false killer whale was able to discriminate a 5 kHz pure tone from a complex tone with up to five harmonics, and (2) that discrimination thresholds or minimum intensity levels exist for each harmonic combination measured. These results indicate that both frequency level and harmonic content may have contributed to the false killer whale's discrimination of complex tones.     

Thresholds for hearing mistuned partials as separate tones in harmonic complexes

When a low harmonic in a harmonic complex tone is mistuned from its harmonic value by a sufficient amount it is heard as a separate tone, standing out from the complex as a whole. This experiment estimated the degree of mistuning required for this phenomenon to occur, for complex tones with 10 or 12 equal-amplitude components (60 dB SPL per component). On each trial the subject was presented with a complex tone which either had all its partials at harmonic frequencies or had one partial mistuned from its harmonic frequency. The subject had to indicate whether he heard a single complex tone with one pitch or a complex tone plus a pure tone which did not "belong" to the complex. An adaptive procedure was used to track the degree of mistuning required to achieve a d' value of 1. Threshold was determined for each ot the first six harmonics of each complex tone. In one set of conditions stimulus duration was held constant at 410 ms, and the fundamental frequency was either 100, 200, or 400 Hz. For most conditions the thresholds fell between 1% and 3% of the harmonic frequency, depending on the subject. However, thresholds tended to be greater for the first two harmonics of the 100-Hz fundamental and, for some subjects, thresholds increased for the fifth and sixth harmonics. In a second set of conditions fundamental frequency was held constant at 200 Hz, and the duration was either 50, 110, 410, or 1610 ms. Thresholds increased by a factor of 3-5 as duration was decreased from 1610 ms to 50 ms. The results are discussed in terms of a hypothetical harmonic sieve and mechanisms for the formation of perceptual streams.     

Effects of signal envelope on the pitch of short complex tones

Envelope-induced pitch shifts were measured for exponentially decaying complex tones consisting of two sinusoidal components with frequencies f1 = nf0 + 50 Hz and f2 = (n + 1) f0 + 50 Hz, where n equals 3, 4, or 5 and exponential decay rates were 0, 0.5, 1, and 2 dB/ms. Four subjects adjusted a sinusoidal comparison tone to match the virtual pitch of the (missing) fundamental and the pitches of the lower and upper partials f1 and f2. Pitch shifts for f1 are generally less, and pitch shifts for f2 always greater, than envelope-induced shifts observed in isolated sinusoidal tones of comparable frequency and envelope decay rate. Pitch-shift functions for virtual pitch are similar in magnitude and shape to average pitch-shift functions of the partials, which supports the idea that virtual pitch depends on spectral pitch.     

Pitch shift of pure and complex tones induced by masking noise

Psychoacoustic experiments were performed to measure the pitch-shift effects of pure and complex tones resulting from the addition of a masking noise to the tonal stimuli. Harmonic residue tones with either two or three harmonics and a fundamental frequency of 200 Hz were chosen as test tones. The pitch shifts of virtual and spectral pitches of the residue tones were measured as a function of the intensity of a low-pass noise with 600-Hz cutoff frequency. The SPL of this noise varied between 30 and 70 dB. In another experiment, the pitch shifts of single pure tones corresponding to the frequencies and SPLs of the harmonics of the residue tones were measured using the same masking noise. The results from five subjects for the harmonic residue tones show only a weak dependence of pitch shift on masking noise intensity. This dependence exists for both spectral and virtual pitches. In the case of single pure tones, pitch shift depends more distinctly on noise intensity. Pitch shifts of up to 5% were found in the range of noise intensity investigated. The magnitude of pitch shift shows pronounced interindividual differences, but the direction of the shift effect is always the same. In all cases pitch increases with higher masking noise levels.     

Model-based automated detection of echolocation calls using the link detector

The link detector combines a model-based spectral peak tracker with an echo filter to detect echolocation calls of bats. By processing calls in the spectrogram domain, the links detector separates calls that overlap in time, including call harmonics and echoes. The links detector was validated by using an artificial recording environment, including synthetic calls, atmospheric absorption, and echoes, which provided control of signal-to-noise ratio and an absolute ground truth. Maximum hit rate (2% false positive rate) for the links detector was 87% compared to 1.5% for a spectral peak detector. The difference in performance was due to the ability of the links detector to filter out echoes. Detection range varied across species from 13 to more than 20 m due to call bandwidth and frequency range. Global features of calls detected by the links detector were compared to those of synthetic calls. The error in all estimates increased as the range increased, and estimates of minimum frequency and frequency of most energy were more accurate compared to maximum frequency. The links detector combines local and global features to automatically detect calls within the machine learning paradigm and detects overlapping calls and call harmonics in a unified framework.     

Perceptual learning of fundamental frequency discrimination: effects of fundamental frequency, harmonic number, and component phase

Thresholds (F0DLs) were measured for discrimination of the fundamental frequency (F0) of a group of harmonics (group B) embedded in harmonics with a fixed F0. Miyazono and Moore [(2009). Acoust. Sci. & Tech. 30, 383386] found a large training effect for tones with high harmonics in group B, when the harmonics were added in cosine phase. It is shown here that this effect was due to use of a cue related to pitch pulse asynchrony (PPA). When PPA cues were disrupted by introducing a temporal offset between the envelope peaks of the harmonics in group B and the remaining harmonics, F0DLs increased markedly. Perceptual learning was examined using a training stimulus with cosine-phase harmonics, F0 = 50 Hz, and high harmonics in group B, under conditions where PPA was not useful. Learning occurred, and it transferred to other cosine-phase tones, but not to random-phase tones. A similar experiment with F0 = 100 Hz showed a learning effect which transferred to a cosine-phase tone with mainly high unresolved harmonics, but not to cosine-phase tones with low harmonics, and not to random-phase tones. The learning found here appears to be specific to tones for which F0 discrimination is based on distinct peaks in the temporal envelope.