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.     

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.     

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.     

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.     

Influence of spectral locus and F0 changes on the pitch and timbre of complex tones.

Harmonic complex tones comprising components in different spectral regions may differ considerably in timbre. While the pitch of "residue" tones of this type has been studied extensively, their timbral properties have received little attention. Discrimination of F0 for such tones is typically poorer than for complex tones with "corresponding" harmonics [A. Faulkner, J. Acoust. Soc. Am. 78, 1993-2004 (1985)]. The F0 DLs may be higher because timbre differences impair pitch discrimination. The present experiment explores effects of changes in spectral locus and F0 of harmonic complex tones on both pitch and timbre. Six normally hearing listeners indicated if the second tone of a two-tone sequence was: (1) same, (2) higher in pitch, (3) lower in pitch, (4) same in pitch but different in "something else," (5) higher in pitch and different in "something else," or (6) lower in pitch and different in "something else" than the first. ("Something else" is assumed to represent timbre.) The tones varied in spectral loci of four equal-amplitude harmonics m, m + 1, m + 2, and m + 3 (m = 1,2,3,4,5,6) and ranged in F0 from 200 to 200 +/- 2n Hz (n = 0,1,2,4,8,16,32). Results show that changes in F0 primarily affect pitch, and changes in spectral locus primarily affect timbre. However, a change in spectral locus can also influence pitch. The direction of locus change was reported as the direction of pitch change, despite no change in F0 or changes in F0 in the opposite direction for delta F0 < or = 0-2%. This implies that listeners may be attending to the "spectral pitch" of components, or to changes in a timbral attribute like "sharpness," which are construed as changes in overall pitch in the absence of strong F0 cues. For delta F0 > or = 2%, the direction of reported pitch change accord with the direction of F0 change, but the locus change continued to be reported as a timbre change. Rather than spectral-pitch matching of corresponding components, a context-dependent spectral evaluation process is thus implied in discernment of changes in pitch and timbre. Relative magnitudes of change in derived features of the spectrum such as harmonic number and F0, and absolute features such as spectral frequencies are compared. What is called "spectral pitch," contributes to the overall pitch, but also appears to be an important dimension of the multidimensional percept, timbre.     

The effect of inharmonic partials on pitch of piano tones

Piano tones have partials whose frequencies are sharp relative to harmonic values. A listening test was conducted to determine the effect of inharmonicity on pitch for piano tones in the lowest three octaves of a piano. Nine real tones from the lowest three octaves of a piano were analyzed to obtain frequencies, relative amplitudes, and decay rates of their partials. Synthetic inharmonic tones were produced from these results. Synthetic harmonic tones, each with a twelfth of a semitone increase in the fundamental, were also produced. A jury of 21 listeners matched the pitch of each synthetic inharmonic tone to one of the synthetic harmonic tones. The effect of the inharmonicity on pitch was determined from an average of the listeners' results. For the nine synthetic piano tones studied, pitch increase ranged from approximately two and a half semitones at low fundamental frequencies to an eighth of a semitone at higher fundamental frequencies.     

Perception of the missing fundamental in nonhuman primates

In preparation for neurophysiological experiments aimed at mechanisms of pitch perception, four rhesus monkeys were trained to press a button when the fundamental frequencies (missing or present) of two complex tones in a tone pair matched. Both tones were based on a five-component harmonic series. Zero to three of the lowest components could be missing in the first tone, while the second (comparison) tone contained all five harmonics. The range of fundamentals tested varied from 200 to 600 Hz. Three monkeys learned to match tones missing their fundamentals to comparison harmonic complexes with the same pitch, whereas the fourth monkey required the physical presence of the fundamental. Consideration of several cues available to the monkeys suggests that the animals could perceive the missing fundamental.     

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.     

兴奋模式下谐波复合音音高感知机制的研究

通过测量谐波复合音的基频辨别阈,探讨中等"高次谐波"的音高感知是否依赖于谐波的可分离性,以及掩蔽音对实验结果的影响。实验方法:在目标音单独存在或目标音与掩蔽音混合时,将刺激通过高、中、低三个带通滤波器以获得不同的谐波可分离度。实验刺激设计为5种基频差异和4种相位组合。五名被试均为年轻人,纯音听阈≤15 dB HL。研究结果发现:谐波复合音的基频辨别阈随着信号频段的上移而增大;目标音和掩蔽音的基频差异对基频辨别阈有显著影响;但相位影响不显著。结论:谐波的可分离性对基频辨别阈有显著影响,但中等"高次谐波"的音高感知不依赖于可分离性;混合音的大部分音高感知结果与兴奋模式的峰值大小密切相关。      

Across-frequency pitch discrimination interference between complex tones containing resolved harmonics

Pitch discrimination interference (PDI) refers to an impairment in the ability to discriminate changes in the fundamental frequency (F0) of a target harmonic complex, caused by another harmonic complex (the interferer) presented simultaneously in a remote spectral region. So far, PDI has been demonstrated for target complexes filtered into a higher spectral region than the interferer and containing no peripherally resolved harmonics in their passband. Here, it is shown that PDI also occurs when the target harmonic complex contains resolved harmonics in its passband (experiment 1). PDI was also observed when the target was filtered into a lower spectral region than that of the interferer (experiment 2), revealing that differences in relative harmonic dominance and pitch salience between the simultaneous target and the interferer, as confirmed using pitch matches (experiment 3), do not entirely explain PDI. When the target was in the higher spectral region, and the F0 separation between the target and the interferer was around 7% or 10%, dramatic PDI effects were observed despite the relatively large FO separation between the two sequential targets (14%-20%). Overall, the results suggest that PDI is more general than previously thought, and is not limited to targets consisting only of unresolved harmonics.     

The relation between the human frequency-following response and the low pitch of complex tones

The relation between the auditory brain stem potential called the frequency-following response (FFR) and the low pitch of complex tones was investigated. Eleven complex stimuli were synthesized such that frequency content varied but waveform envelope periodicity was constant. This was accomplished by repeatedly shifting the components of a harmonic complex tone upward in frequency by delta f of 20 Hz, producing a series of six-component inharmonic complex tones with constant intercomponent spacing of 200 Hz. Pitch-shift functions were derived from pitch matches for these stimuli to a comparison pure tone for each of four normal hearing adults with extensive musical training. The FFRs were recorded for the complex stimuli that were judged most divergent in pitch by each subject and for pure-tone signals that were judged equal in pitch to these complex stimuli. Spectral analyses suggested that the spectral content of the FFRs elicited by the complex stimuli did not vary consistently with component frequency or the first effect of pitch shift. Furthermore, complex and pure-tone signals judged equal in pitch did not elicit FFRs of similar spectral content.     

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.     

Hearing a mistuned harmonic in an otherwise periodic complex tone

The ability of a listener to detect a mistuned harmonic in an otherwise periodic tone is representative of the capacity to segregate auditory entities on the basis of steady-state signal cues. By use of a task in which listeners matched the pitch of a mistuned harmonic, this ability has been studied, in order to find dependences on mistuned harmonic number, fundamental frequency, signal level, and signal duration. The results considerably augment the data previously obtained from discrimination experiments and from experiments in which listeners counted apparent sources. Although previous work has emphasized the role of spectral resolution in the segregation process, the present work suggests that neural synchrony is an important consideration; our data show that listeners lose the ability to segregate mistuned harmonics at high frequencies where synchronous neural firing vanishes. The functional form of this loss is insensitive to the spacing of the harmonics. The matching experiment also permits the measurement of the pitches of mistuned harmonics. The data exhibit shifts of a form that argues against models of pitch shifts that are based entirely upon partial masking.     

频域分辨率和时域包络周期性对音乐音高分辨的影响

系统地分析与探讨频域分辨率及时域包络周期性对不同音色及频率覆盖范围的音乐音高分辨的影响。选择钢琴、小提琴、小号及单簧管四种乐器的乐音和特定的复合音作为测试音源。利用噪声调制的声码器模型调控音乐信号的频域分辨率和时域包络周期性。十位正常听力者参与了该项音高分辨测试。实验结果表明,随着频域分辨率的提高,受试者对音高分辨的准确率呈上升趋势,16个频带已可获得较好的音高分辨效果;当时域包络周期性信息增加时,未见其对音高分辨产生一致性积极影响。      

Effects of musical training and absolute pitch ability on event-related activity in response to sine tones.

The neural correlates of music perception have received relatively little scientific attention. The neural activity of listeners without musical training (N = 11), highly trained musicians (N = 14), and musicians possessing "absolute pitch" (AP) ability (N = 10) have been measured. Major differences were observed in the P3, an endogenous event-related potential (ERP), which is thought to be a neurophysiological manifestation of working memory processing. The P3 was elicited using the classical "oddball" paradigm with a sine-tone series. Subjects' musical backgrounds were evaluated with a survey questionnaire. AP ability was verified with an objective pitch identification test. The P3 amplitude, latency and wave shape were evaluated along with each subjects' performance score and musical background. The AP subjects showed a significantly smaller P3 amplitude than either the musicians or nonmusicians, which were nearly identical. The P3 latency was shortest for the AP subjects, and was longer for the nonmusicians. Performance scores were uniformly high in all three groups. It is concluded that AP subjects do indeed exhibit P3 ERPs, albeit with smaller amplitudes and shorter latencies. The differences in neural activity between the musicians and AP subjects were not due to musical training, as the AP subjects had similar musical backgrounds to the musician group. It is also concluded that persons with the AP ability may have superior auditory sensitivity at cortical levels and/or use unique neuropsychological strategies when processing tones.     

Evidence for a general template in central optimal processing for pitch of complex tones

Optimum processor theory successfully accounts for earlier pitch data by including the constraint that component tones in a complex stimulus are estimated as successive harmonics. This constraint gives the paradoxical prediction that a periodic complex tone comprising nonsuccessive harmonics cannot evoke periodicity pitch corresponding to its period. Most published data from pitch-shift experiments imply the necessity for this constraint. New periodicity pitch experiments on pitch shift and musical interval recognition were performed which prove that the theoretical constraint is not generally true. New and old data are reconciled by replacing the maximum likelihood estimation of the theory with maximum posterior probability estimation and removing the successive harmonic constraint. Periodicity pitch is estimated by optimizing the match between the aurally measured frequencies of stimulus components and a general harmonic template over some a priori expected pitch range. The new, more general, formulation reduces in many experimental situations to the successive harmonic constraint as a special case.     

Perception and cortical neural coding of harmonic fusion in ferrets

This study examined the perception and cortical representation of harmonic complex tones, from the perspective of the spectral fusion evoked by such sounds. Experiment 1 tested whether ferrets spontaneously distinguish harmonic from inharmonic tones. In baseline sessions, ferrets detected a pure tone terminating a sequence of inharmonic tones. After they reached proficiency, a small fraction of the inharmonic tones were replaced with harmonic tones. Some of the animals confused the harmonic tones with the pure tones at twice the false-alarm rate. Experiment 2 sought correlates of harmonic fusion in single neurons of primary auditory cortex and anterior auditory field, by comparing responses to harmonic tones with those to inharmonic tones in the awake alert ferret. The effects of spectro-temporal filtering were accounted for by using the measured spectrotemporal receptive field to predict responses and by seeking correlates of fusion in the predictability of responses. Only 12% of units sampled distinguished harmonic tones from inharmonic tones, a small percentage that is consistent with the relatively weak ability of the ferrets to spontaneously discriminate harmonic tones from inharmonic tones in Experiment 1.     

Influence of peripheral resolvability on the perceptual segregation of harmonic complex tones differing in fundamental frequency

Two experiments investigated the influence of resolvability on the perceptual organization of sequential harmonic complexes differing in fundamental frequency (F0). Using a constant-stimuli method, streaming scores for ABA-... sequences of harmonic complexes were measured as a function of the F0 difference between the A and B tones. In the first experiment, streaming scores were measured for harmonic complexes having two different nominal F0s (88 and 250 Hz) and filtered in three frequency regions (a LOW, a MID, and a HIGH region with corner frequencies of 125-625 Hz, 1375-1875 Hz, and 3900-5400 Hz, respectively). Some streaming was observed in the HIGH region (in which the harmonics were always unresolved) but streaming scores remained generally lower than in the LOW and MID regions. The second experiment verified that the streaming observed in the HIGH region was not due to the use of distortion products. Overall, the results indicated that although streaming can occur in the absence of spectral cues, the degree of resolvability of the harmonics has a significant influence.     

Octave illusion elicited by overlapping narrowband noises

The octave or Deutsch illusion occurs when two tones, separated by about one octave, are presented simultaneously but alternating between ears, such that when the low tone is presented to the left ear the high tone is presented to the right ear and vice versa. Most subjects hear a single tone that alternates both between ears and in pitch; i.e., they hear a low pitched tone in one ear alternating with a high pitched tone in the other ear. The present study examined whether the illusion can be elicited by aperiodic signals consisting of low-frequency band-pass filtered noises with overlapping spectra. The amount of spectral overlap was held constant, but the high- and low-frequency content of the signals was systematically varied. The majority of subjects perceived an auditory illusion in terms of a dominant ear for pitch and lateralization by frequency, as proposed by Deutsch [(1975a) Sci. Am. 233, 92-104]. Furthermore, the salience of the illusion increased as the high frequency of the content in the signal increased. Since no harmonics were present in the stimuli, it is highly unlikely that this illusion is perceived on the basis of binaural diplacusis or harmonic binaural fusion.