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.     

Pitch matches between unresolved complex tones differing by a single interpulse interval

The experiment compared the pitches of complex tones consisting of unresolved harmonics. The fundamental frequency (F0) of the tones was 250 Hz and the harmonics were bandpass filtered between 5500 and 7500 Hz. Two 20-ms complex-tone bursts were presented, separated by a brief gap. The gap was an integer number of periods of the waveform: 0, 4, or 8 ms. The envelope phase of the second tone burst was shifted, such that the interpulse interval (IPI) across the gap was reduced or increased by 0.25 or 0.75 periods (1 or 3 ms). A "no shift" control was also included, where the IPI was held at an integer number of periods. Pitch matches were obtained by varying the F0 of a comparison tone with the same temporal parameters as the standard but without the shift. Relative to the no-shift control, the variations in IPI produced substantial pitch shifts when there was no gap between the bursts, but little effect was seen for gaps of 4 or 8 ms. However, for some conditions with the same IPI in the shifted interval, an increase in the IPI of the comparison interval from 4 to 8 ms (gap increased from 0 to 4 ms) changed the pitch match. The presence of a pitch shift suggests that the pitch mechanism is integrating information across the two tone bursts. It is argued that the results are consistent with a pitch mechanism employing a long integration time for continuous stimuli that is reset in response to temporal discontinuities. For a 250-Hz F0, an 8-ms IPI may be sufficient for resetting. Pitch models based on a spectral analysis of the simulated neural spike train, on an autocorrelation of the spike train, and on the mean rate of pitch pulses, all failed to account for the observed pitch matches.     

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.     

Perception of intonation in Mandarin Chinese

There is a tendency across languages to use a rising pitch contour to convey question intonation and a falling pitch contour to convey a statement. In a lexical tone language such as Mandarin Chinese, rising and falling pitch contours are also used to differentiate lexical meaning. How, then, does the multiplexing of the F(0) channel affect the perception of question and statement intonation in a lexical tone language? This study investigated the effects of lexical tones and focus on the perception of intonation in Mandarin Chinese. The results show that lexical tones and focus impact the perception of sentence intonation. Question intonation was easier for native speakers to identify on a sentence with a final falling tone and more difficult to identify on a sentence with a final rising tone, suggesting that tone identification intervenes in the mapping of F(0) contours to intonational categories and that tone and intonation interact at the phonological level. In contrast, there is no evidence that the interaction between focus and intonation goes beyond the psychoacoustic level. The results provide insights that will be useful for further research on tone and intonation interactions in both acoustic modeling studies and neurobiological studies.     

Louder sounds can produce less forward masking: effects of component phase in complex tones

The influence of the degree of envelope modulation and periodicity on the loudness and effectiveness of sounds as forward maskers was investigated. In the first experiment, listeners matched the loudness of complex tones and noise. The tones had a fundamental frequency (F0) of 62.5 or 250 Hz and were filtered into a frequency range from the 10th harmonic to 5000 Hz. The Gaussian noise was filtered in the same way. The components of the complex tones were added either in cosine phase (CPH), giving a large crest factor, or in random phase (RPH), giving a smaller crest factor. For each F0, subjects matched the loudness between all possible stimulus pairs. Six different levels of the fixed stimulus were used, ranging from about 30 dB SPL to about 80 dB SPL in 10-dB steps. Results showed that, at a given overall level, the CPH and the RPH tones were louder than the noise, and that the CPH tone was louder than the RPH tone. The difference in loudness was larger at medium than at low levels and was only slightly reduced by the addition of a noise intended to mask combination tones. The differences in loudness were slightly smaller for the higher than for the lower F0. In the second experiment, the stimuli with the lower F0s were used as forward maskers of a 20-ms sinusoid, presented at various frequencies within the spectral range of the maskers. Results showed that the CPH tone was the least effective forward masker, even though it was the loudest. The differences in effectiveness as forward maskers depended on masker level and signal frequency; in order to produce equal masking, the level of the CPH tone had to be up to 35 dB above that of the RPH tone and the noise. The implications of these results for models of loudness are discussed and a model is presented based on neural activity patterns in the auditory nerve; this predicts the general pattern of loudness matches. It is suggested that the effects observed in the experiments may have been influenced by two factors: cochlear compression and suppression.     

Across-frequency interference effects in fundamental frequency discrimination: questioning evidence for two pitch mechanisms

Carlyon and Shackleton [J. Acoust. Soc. Am. 95, 3541-3554 (1994)] presented an influential study supporting the existence of two pitch mechanisms, one for complex tones containing resolved and one for complex tones containing only unresolved components. The current experiments provide an alternative explanation for their finding, namely the existence of across-frequency interference in fundamental frequency (F0) discrimination. Sensitivity (d') was measured for F0 discrimination between two sequentially presented 400 ms complex (target) tones containing only unresolved components. In experiment 1, the target was filtered between 1375 and 15,000 Hz, had a nominal F0 of 88 Hz, and was presented either alone or with an additional complex tone ("interferer"). The interferer was filtered between 125-625 Hz, and its F0 varied between 88 and 114.4 Hz across blocks. Sensitivity was significantly reduced in the presence of the interferer, and this effect decreased as its F0 was moved progressively further from that of the target. Experiment 2 showed that increasing the level of a synchronously gated lowpass noise that spectrally overlapped with the interferer reduced this "pitch discrimination interference (PDI)". In experiment 3A, the target was filtered between 3900 and 5400 Hz and had an F0 of either 88 or 250 Hz. It was presented either alone or with an interferer, filtered between 1375 and 1875 Hz with an F0 corresponding to the nominal target F0. PDI was larger in the presence of the resolved (250 Hz F0) than in the presence of the unresolved (88 Hz F0) interferer, presumably because the pitch of the former was more salient than that of the latter. Experiments 4A and 4B showed that PDI was reduced but not eliminated when the interferer was gated on 200 ms before and off 200 ms after the target, and that some PDI was observed with a continuous interferer. The current findings provide an alternative interpretation of a study supposedly providing strong evidence for the existence of two pitch mechanisms.     

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.     

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.     

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.     

The speed of pitch resolution in a musical context.

In five experiments, we investigated the speed of pitch resolution in a musical context. In experiments 1-3, listeners were presented an incomplete scale (doh, re, mi, fa, sol, la, ti) and then a probe tone. Listeners were instructed to make a rapid key-press response to probe tones that were relatively proximal in pitch to the last note of the scale (valid trials), and to ignore other probe tones (invalid trials). Reaction times were slower if the pitch of the probe tone was dissonant with the expected pitch (i.e., the completion of the scale, or doh) or if the probe tone was nondiatonic to the key implied by the scale. In experiments 4 and 5, listeners were presented a two-octave incomplete arpeggio, and then a probe tone. In this case, listeners were asked to make a rapid key-press response to probe tones that were relatively distant in pitch from the last note of the arpeggio. Under these conditions, registral direction and pitch proximity were the dominant influences on reaction time. Results are discussed in view of research on auditory attention and models of musical pitch.     

Virtual pitch integration for asynchronous harmonics

This experiment examined the generation of virtual pitch for harmonically related tones that do not overlap in time. The interval between successive tones was systematically varied in order to gauge the integration period for virtual pitch. A pitch discrimination task was employed, and both harmonic and nonharmonic tone series were tested. The results confirmed that a virtual pitch can be generated by a series of brief, harmonically related tones that are separated in time. Robust virtual pitch information can be derived for intervals between successive 40-ms tones of up to about 45 ms, consistent with a minimum estimate of integration period of about 210 ms. Beyond intertone intervals of 45 ms, performance becomes more variable and approaches an upper limit where discrimination of tone sequences can be undertaken on the basis of the individual frequency components. The individual differences observed in this experiment suggest that the ability to derive a salient virtual pitch varies across listeners.     

Constrained tone transformation technique for separation and combination of Mandarin tone and intonation

This paper addresses a classical but important problem: The coupling of lexical tones and sentence intonation in tonal languages, such as Chinese, focusing particularly on voice fundamental frequency (F1) contours of speech. It is important because it forms the basis of speech synthesis technology and prosody analysis. We provide a solution to the problem with a constrained tone transformation technique based on structural modeling of the F1 contours. This consists of transforming target values in pairs from norms to variants. These targets are intended to sparsely specify the prosodic contributions to the F1 contours, while the alignment of target pairs between norms and variants is based on underlying lexical tone structures. When the norms take the citation forms of lexical tones, the technique makes it possible to separate sentence intonation from observed F0 contours. When the norms take normative F0 contours, it is possible to measure intonation variations from the norms to the variants, both having identical lexical tone structures. This paper explains the underlying scientific and linguistic principles and presents an algorithm that was implemented on computers. The method's capability of separating and combining tone and intonation is evaluated through analysis and re-synthesis of several hundred observed F0 contours.     

Learning to perceive pitch differences

This paper reports two experiments concerning the stimulus specificity of pitch discrimination learning. In experiment 1, listeners were initially trained, during ten sessions (about 11,000 trials), to discriminate a monaural pure tone of 3000 Hz from ipsilateral pure tones with slightly different frequencies. The resulting perceptual learning (improvement in discrimination thresholds) appeared to be frequency-specific since, in subsequent sessions, new learning was observed when the 3000-Hz standard tone was replaced by a standard tone of 1200 Hz, or 6500 Hz. By contrast, a subsequent presentation of the initial tones to the contralateral ear showed that the initial learning was not, or was only weakly, ear-specific. In experiment 2, training in pitch discrimination was initially provided using complex tones that consisted of harmonics 3-7 of a missing fundamental (near 100 Hz for some listeners, 500 Hz for others). Subsequently, the standard complex was replaced by a standard pure tone with a frequency which could be either equal to the standard complex's missing fundamental or remote from it. In the former case, the two standard stimuli were matched in pitch. However, this perceptual relationship did not appear to favor the transfer of learning. Therefore, the results indicated that pitch discrimination learning is, at least to some extent, timbre-specific, and cannot be viewed as a reduction of an internal noise which would affect directly the output of a neural device extracting pitch from both pure tones and complex tones including low-rank harmonics.     

Perceptual components of pitch: spatial representation using a multidimensional scaling technique

Paired comparison experiments were carried out on the pitch of 18 computer-generated complex tones synthesized by slight modification of the frequency structure of Shepard's endless scale sounds. The results were analyzed by a multidimensional scaling technique, and simple helixes were obtained in which two components of pitch (tone height and tone chroma) were represented. Some individual differences in perception of pitch were observed according to the weight that the subject gives to each component.     

Effects of signal envelope on the pitch of short sinusoidal tones

The pitch of short sinusoidal tones with exponentially rising or decaying envelopes is judged higher than the pitch of a gated tone of the same frequency, duration, and energy. The upward pitch shift depends on the rise or decay rate, the intensity, and the frequency. The effect, which requires a nonlinearity in the auditory system, cannot be adequately explained by existing models of hearing. Control experiments on pitch matching for short tones of varying duration and varying intensity are described. These suggest that envelope-induced pitch effects are linked to changes in average intensity, so that they are essentially the same as intensity-induced pitch changes. A model based on these considerations is proposed.     

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 dependency of timbre on fundamental frequency

The dependency of the timbre of musical sounds on their fundamental frequency (F0) was examined in three experiments. In experiment I subjects compared the timbres of stimuli produced by a set of 12 musical instruments with equal F0, duration, and loudness. There were three sessions, each at a different F0. In experiment II the same stimuli were rearranged in pairs, each with the same difference in F0, and subjects had to ignore the constant difference in pitch. In experiment III, instruments were paired both with and without an F0 difference within the same session, and subjects had to ignore the variable differences in pitch. Experiment I yielded dissimilarity matrices that were similar at different F0's, suggesting that instruments kept their relative positions within timbre space. Experiment II found that subjects were able to ignore the salient pitch difference while rating timbre dissimilarity. Dissimilarity matrices were symmetrical, suggesting further that the absolute displacement of the set of instruments within timbre space was small. Experiment III extended this result to the case where the pitch difference varied from trial to trial. Multidimensional scaling (MDS) of dissimilarity scores produced solutions (timbre spaces) that varied little across conditions and experiments. MDS solutions were used to test the validity of signal-based predictors of timbre, and in particular their stability as a function of F0. Taken together, the results suggest that timbre differences are perceived independently from differences of pitch, at least for F0 differences smaller than an octave. Timbre differences can be measured between stimuli with different F0's.     

Dead regions and pitch perception

The perception of pitch for pure tones with frequencies falling inside low- or high-frequency dead regions (DRs) was examined. Subjects adjusted a variable-frequency tone to match the pitch of a fixed tone. Matches within one ear were often erratic for tones falling in a DR, indicating unclear pitch percepts. Matches across ears of subjects with asymmetric hearing loss, and octave matches within ears, indicated that tones falling within a DR were perceived with an unclear pitch and/or a pitch different from "normal" whenever the tones fell more than 0.5 octave within a low- or high-frequency DR. One unilaterally impaired subject, with only a small surviving region between 3 and 4 kHz, matched a fixed 0.5-kHz tone in his impaired ear with, on average, a 3.75-kHz tone in his better ear. When asked to match the 0.5-kHz tone with an amplitude-modulated tone, he adjusted the carrier and modulation frequencies to about 3.8 and 0.5 kHz, respectively, suggesting that some temporal information was still available. Overall, the results indicate that the pitch of low-frequency tones is not conveyed solely by a temporal code. Possibly, there needs to be a correspondence between place and temporal information for a normal pitch to be perceived.     

Perception of musical and lexical tones by Taiwanese-speaking musicians

This study explored the relationship between music and speech by examining absolute pitch and lexical tone perception. Taiwanese-speaking musicians were asked to identify musical tones without a reference pitch and multispeaker Taiwanese level tones without acoustic cues typically present for speaker normalization. The results showed that a high percentage of the participants (65% with an exact match required and 81% with one-semitone errors allowed) possessed absolute pitch, as measured by the musical tone identification task. A negative correlation was found between occurrence of absolute pitch and age of onset of musical training, suggesting that the acquisition of absolute pitch resembles the acquisition of speech. The participants were able to identify multispeaker Taiwanese level tones with above-chance accuracy, even though the acoustic cues typically present for speaker normalization were not available in the stimuli. No correlations were found between the performance in musical tone identification and the performance in Taiwanese tone identification. Potential reasons for the lack of association between the two tasks are discussed.