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.     

Effects of asynchrony and ear of presentation on the pitch of mistuned partials in harmonic and frequency-shifted complex tones

When a partial of a periodic complex is mistuned, its change in pitch is greater than expected. Two experiments examined whether these partial-pitch shifts are related to the computation of global pitch. In experiment 1, stimuli were either harmonic or frequency-shifted (25% of F0) complexes. One partial was mistuned by +/- 4% and played with leading and lagging portions of 500 ms each, relative to the other components (1 s), in both monaural and dichotic contexts. Subjects indicated whether the mistuned partial was higher or lower in pitch when concurrent with the other components. Responses were positively correlated with the direction of mistuning in all conditions. In experiment 2, stimuli from each condition were compared with synchronous equivalents. Subjects matched a pure tone to the pitch of the mistuned partial (component 4). The results showed that partial-pitch shifts are not reduced in size by asynchrony. Similar asynchronies are known to produce a near-exclusion of a mistuned partial from the global-pitch computation. This mismatch indicates that global and partial pitch are derived from different processes. The similarity of the partial-pitch shifts observed for harmonic and frequency-shifted stimuli suggests that they arise from a grouping mechanism that is sensitive to spectral regularity.     

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.     

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.     

Effect of noise on the detectability and fundamental frequency discrimination of complex tones

Percent correct performance for discrimination of the fundamental frequency (0) of a complex tone was measured as a function of the level of a background pink noise (using fixed values of the difference in F0, deltaF0) and compared with percent correct performance for detection of the complex tone in noise, again as a function of noise level. The tone included some low, resolvable components, but not the fundamental component. The results were used to test the hypothesis that the worsening in F0 discrimination with increasing noise level was caused by the reduced detectability of the tone rather than by reduced precision of the internal representation of F0. For small values of deltaF0, the hypothesis was rejected because measured performance fell below that predicted by the hypothesis. However, this was true only for high noise levels, within 2-4.5 dB of the level required for masked threshold. The results indicate that the mechanism for extracting the F0 of a complex tone with resolved harmonics is remarkably robust. They also indicate that adding a background noise to a complex tone containing resolved harmonics is not a good means for equating its pitch salience with that of a complex tone containing only unresolved harmonics.     

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.     

Influence of fundamental frequency and source elevation on the vertical localization of complex tones and complex tone pairs

This study investigates the vertical localization of single complex tones (monads) and simultaneous complex tone pairs (dyads), especially as it is affected by their fundamental frequency and source elevation. Two complex tone timbres are considered: one consisting of five low-order harmonics, and the other of all odd harmonics (a square wave). Sound sources were at -15, 0, 15, and 30 deg from the horizontal plane at ear height. For eight subjects, this source array was in the median plane, and for a further nine subjects, it was directly to the subject's left (lateral plane). The subjects localized the angle of the auditory image(s) of one or two complex tones around the vertical plane containing the sound sources. Mean responses for the five-harmonic complex tones show a systematic effect (referred to as Pratt's effect) of fundamental frequency on vertical localization--whereby high-frequency complex tones are localized to positions higher than low-frequency complex tones for equivalent source positions. For the square wave, the sound-source position dominates localization, although some effect of fundamental frequency is evident for median plane sources.     

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.     

Effect of level on the discrimination of harmonic and frequency-shifted complex tones at high frequencies

Moore and Se?k [J. Acoust. Soc. Am. 125, 3186-3193 (2009)] measured discrimination of a harmonic complex tone and a tone in which all harmonics were shifted upwards by the same amount in Hertz. Both tones were passed through a fixed bandpass filter and a background noise was used to mask combination tones. Performance was well above chance when the fundamental frequency was 800 Hz, and all audible components were above 8000 Hz. Moore and Se?k argued that this suggested the use of temporal fine structure information at high frequencies. However, the task may have been performed using excitation-pattern cues. To test this idea, performance on a similar task was measured as a function of level. The auditory filters broaden with increasing level, so performance based on excitation-pattern cues would be expected to worsen as level increases. The results did not show such an effect, suggesting that the task was not performed using excitation-pattern cues.     

Dependence of binaural loudness summation on interaural level difference and frequency for pure tones

Most of the existing loudness models are based on the diotic listening hypothesis,though human beings always hear in dichotic listening conditions.In this situation,the arithmetic mean of loudness at both ears is usually taken as the approximate value of overall perceived loudness,unaffected by the interaural level difference(ILD).The present work investigated the overall perceived loudness for pure tones in dichotic listening conditions through a subjective experiment.Two experimental procedures and system...     

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.     

The effect of modulation rate on the detection of frequency modulation and mistuning of complex tones

Experiment 1 measured frequency modulation detection thresholds (FMTs) for harmonic complex tones as a function of modulation rate. Six complexes were used, with fundamental frequencies (F0s) of either 88 or 250 Hz, bandpass filtered into a LOW (125-625 Hz), MID (1375-1875 Hz) or HIGH (3900-5400 Hz) frequency region. The FMTs were about an order of magnitude greater for the three complexes whose harmonics were unresolved by the peripheral auditory system (F0 = 88 Hz in the MID region and both F0s in the HIGH region) than for the other three complexes, which contained some resolved harmonics. Thresholds increased with increases in FM rate above 2 Hz for all conditions. The increase was larger when the F0 was 88 Hz than when it was 250 Hz, and was also larger in the LOW than in the MID and HIGH regions. Experiment 2 measured thresholds for detecting mistuning produced by modulating the F0s of two simultaneously presented complexes out of phase by 180 degrees. The size of the resulting mistuning oscillates at a rate equal to the rate of FM applied to the two carriers. At low FM rates, thresholds were lowest when the harmonics were either resolved for both complexes or unresolved for both complexes, and highest when resolvability differed across complexes. For pairs of complexes with resolved harmonics, mistuning thresholds increased dramatically as the FM rate was increased above 2-5 Hz, in a way which could not be accounted for by the effect of modulation rate on the FMTs for the individual complexes. A third experiment, in which listeners detected constant ("static") mistuning between pairs of frequency-modulated complexes, provided evidence that this deterioration was due the harmonics in one of the two "resolved" complexes becoming unresolved at high FM rates, when analyzed over some finite time window. It is concluded that the detection of time-varying mistuning between groups of harmonics is limited by factors that are not apparent in FM detection data.     

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.     

Phase effects on the perceived elevation of complex tones

Free-field source localization experiments with 30 source locations, symmetrically distributed in azimuth, elevation, and front-back location, were performed with periodic tones having different phase relationships among their components. Although the amplitude spectra were the same for these different kinds of stimuli, the tones with certain phase relationships were successfully localized while the tones with other phases led to large elevation errors and front-back reversals, normally growing with stimulus level. The results show that it is not enough to have a smooth, broadband, long-term signal spectrum for successful sagittal-plane localization. Instead, temporal factors are important. A model calculation investigates the idea that the tonotopic details that mediate localization need to be simultaneously, or almost simultaneously, accessible in the auditory system in order to achieve normal elevation perception. A qualitative model based on lateral inhibition seems capable in principle of accounting for both the phase effects and level effects.     

Effects of frequency modulated tones and vowel formants on perioral muscle activity during isometric lip rounding

Two studies were conducted to assess the sensitivity of perioral muscles to vowel-like auditory stimuli. In one study, normal young adults produced an isometric lip rounding gesture while listening to a frequency modulated tone (FMT). The fundamental of the FMT was modulated over time in a sinusoidal fashion near the frequency ranges of the first and second formants of the vowels /u/ and /i/ (rate of modulation = 4.5 or 7 Hz). In another study, normal young adults produced an isometric lip rounding gesture while listening to synthesized vowels whose formant frequencies were modulated over time in a sinusoidal fashion to simulate repetitive changes from the vowel /u/ to /i/ (rate of modulation = 2 or 4 Hz). The FMTs and synthesized vowels were presented binaurally via headphones at 75 and 60 dB SL, respectively. Muscle activity from the orbicularis oris superior and inferior and from lip retractors was recorded with surface electromyography (EMG). Signal averaging and spectral analysis of the rectified and smoothed EMG failed to show perioral muscle responses to the auditory stimuli. Implications for auditory feedback theories of speech control are discussed.     

Effects of low cut-off frequency of optical receiver on the performance of lightwave systems using pilot tones

We investigate the effects of low cut-off frequency of optical receiver on the performance of lightwave systems. The results show that we can reduce the tone-induced power penalty by ∼0.8 dB (tone frequency = 1 MHz) using a high-pass filter in the optical receiver. In addition, our calculation shows that the power penalty can be negligible (<0.1 dB) even when the low cut-off frequency of the 10 Gb/s optical receiver is increased up to ∼10 MHz.     

Pitch of components of complex tones

Subjects made pitch matches to individual components in complex tones consisting of either the 4th to 7th or the 1st to 7th harmonics of a 200-Hz fundamental. All components were at equal levels (either 31-, 51-, or 71-dB SPL per component) and the matching pure tone was equal in level to the component being matched. Attention was drawn to the component to be matched either by giving the matching tone an initial frequency close to that of the component (standard condition) or by suppressing and then introducing the component (emergent condition). The pitch matches did not differ significantly for the two conditions, and did not change with overall level. For two subjects, matches to components in the context of the complexes were very close to matches obtained for the components presented in isolation. For a third subject, matches in context were shifted slightly upwards for the lowest component, and downwards for the highest component. A control condition showed that subjects were able accurately to match a small shift in frequency of one component in a four-tone complex. An adaptive forced-choice method described by Jesteadt [Percept. Psychophys. 28, 85-88 (1980)] was also used to estimate the pitches of the components. A very slight bias was apparent in the results, but the pitches of components in context were again found to be very close to those of components in isolation.