Noncommutative geometry and fundamental interactions: the first ten years

This is the full text of a survey talk for nonspecialists, delivered at the 66th Annual Meeting of the German Physical Society in Leipzig, March 2002. We have not taken pains to suppress the colloquial style. References are given only insofar as they help to underline the points made; this is not a full‐blooded survey. The connection between noncommutative field theory and string theory is mentioned, but deemphasized. Contributions to noncommutative geometry made in Germany are emphasized.     

Vocal fundamental frequency measures as a reflection of tumor response to chemotherapy in patients with advanced laryngeal cancer

The fundamental frequency (F₀) characteristics of 19 male patients with advanced laryngeal cancer, treated with cisplatin-based chemotherapy as part of a Larynx Preservation Protocol (LPP), were measured before each of three cycles of chemotherapy received before definitive radiotherapy (RT). In these select patients, for whom chemotherapy resulted in 50% decrease in the tumor bulk, it was found that mean F₀ was essentially unaffected by the disease and did not change over the course of chemotherapy, although the cycle of their treatment could be differentiated by both speaking F₀ variability (pitch sigma) and F₀ perturbation (fitter). Although these measures failed to distinguish between those patients showing a complete response (CR) (no measurable disease) versus a partial (PR) (residual) tumor response at the primary disease site, the significant changes observed in both groups indicate that frequency variation measures could prove valuable in the documentation of tumor response to nonsurgical therapeutic intervention if the voice is directly affected. Additional assessment of 15 age- and disease-matched patients who showed minimal or no primary response to the chemotherapy showed no significant change in any of the frequency measures after one chemotherapy cycle, suggesting that vocal improvement seen in the successful chemotherapy patients was not due to postbiopsy healing or other systemic influence unassociated with tumor reduction.     

Speaking fundamental frequency characteristics as a function of age and professional singing

The purposes of this project were to discover (1) if the speaking fundamental frequency (SFF) levels of professional singers differ significantly from those of nonsingers and (2) if the age-related SFF patterns are similar for these two classes of individuals. Sixty professional singers and 94 nonsingers were recorded reading the first paragraph of the “Rainbow Passage;” both males and females were included. Three paired groups (young, middle, and old age) were studied; they were selected on the basis of health and age. The professional singer groups were further divided by a binary voice classification system, specifically that of soprano/alto for women and tenor/baritone for men. It was found that the sopranos and tenors exhibited significantly higher SFF levels then did the age-matched nonsingers, whereas the altos and baritones did not differ significantly from the controls. Relationships within the performer groups were mixed. For example, there appeared to be a systemic trend for the sopranos and tenors to exhibit higher SFF levels than the altos and baritones. Finally, although the nonsinger SFF levels varied significantly as a function of age, those for the professional singers did not.     

Vocalization and breathing during the first year of life

Vocalization and breathing were studied in 40 healthy infants, including five boys and five girls each at ages 5 weeks, 2.5 months, 6.5 months, and 12 months. Breathing was monitored through the use of a variable inductance plethysmograph that enabled estimates of the volume changes of the rib cage, abdomen, and lung, as well as estimates of selected temporal features of the breathing cycle. Four vocalization types were studied intensively. These included cries, whimpers, grunts, and syllable utterances. Breathing behavior was highly variable across the four vocalization types, demonstrating the degrees of freedom of performance available to the infant to accomplish the aeromechanical drive required. Such behavior was influenced by body length, body position, and age, but not by vocalization type and sex. The protocol established is a useful tool for observing the natural course of the emergence of vocalization and breathing during the first year of life.     

Vocal loudness and frequency capabilities of the voice

A phonetogram is a graph showing the sound pressure level (SPL) of softest and loudest phonation over the entire fundamental frequency range of a voice. A physiological interpretation of a phonetogram is facilitated if the SPL is measured with a flat frequency curve and if the vowel /a/ is used. It was found that in soft phonation, the SPL is mainly dependent on the amplitude of the fundamental, while in loud phonation, the SPL is mainly determined by overtones. The short-term SPL variation, i.e., the level variation within a tone, was about 5 dB in soft phonation and close to 2 dB in loud phonation. For two normal voices the long-term SPL variation, calculated as the mean standard deviation of SPL for day-to-day variation, was found to be between 2.4 and 3.4 dB in soft and loud phonation. Speakers who raise their loudness of phonation also tend to raise their mean voice fundamental frequency. Measures obtained from speaking at various voice levels were combined so that typical pathways could be introduced into the phonetogram. The average slope of these pathways was 0.3–0.5 st/dB for healthy subjects. Averaged phonetograms for male singers and male nonsingers did not differ significantly, but averaged phonetograms for female singers and female nonsingers did, in that the upper contour was higher for the female singers. Averaged phonetograms for female patients with non-organic dysphonia showed significantly lower SPL values in loudest phonation as compared to healthy female subjects, while no corresponding difference was seen for males in this regard. With respect to the SPL values for softest phonation, male dysphonic patients showed significantly higher SPL values than healthy male subjects, while no corresponding difference was seen in female subjects. The subglottal pressure mirrored these phonetogram differences between healthy and pathological voices. The averaged phonetograms of female patients after voice therapy showed an increased similarity with those of normal voices. For the male patients the averaged phonetogram did not change significantly after therapy.     

Bound formula for determining the fundamental frequency

The extent of interference with various activities was studied among populations in areas exposed to noise from aircraft, road traffic, trains and tramways. When areas with differences in the extent of general annoyance were compared, similar differences in the extent of the various activity interferences were found, except for those due to vibrations. As an example of the differences in the activity interference pattern, it was found that road traffic noise interfered significantly less with speech than train noise, whereas both noise types caused roughly the same interference with rest/sleep. The results suggest that uniform weighted annoyance scores incorporating various kinds of activity interference are not valid for all types of environmental noises. Interference due to vibrations probably has to be treated separately from that due to noise.     

Measuring the rate of change of voice fundamental frequency in fluent speech during mental depression

A method of measuring the rate of change of fundamental frequency has been developed in an effort to find acoustic voice parameters that could be useful in psychiatric research. A minicomputer program was used to extract seven parameters from the fundamental frequency contour of tape-recorded speech samples: (1) the average rate of change of the fundamental frequency and (2) its standard deviation, (3) the absolute rate of fundamental frequency change, (4) the total reading time, (5) the percent pause time of the total reading time, (6) the mean, and (7) the standard deviation of the fundamental frequency distribution. The method is demonstrated on (a) a material consisting of synthetic speech and (b) voice recordings of depressed patients who were examined during depression and after improvement.     

The perception of fundamental frequency declination

A series of experiments was carried out to investigate how fundamental frequency declination is perceived by speakers of English. Using linear predictor coded speech, nonsense sentences were constructed in which fundamental frequency on the last stressed syllable had been systematically varied. Listeners were asked to judge which stressed syllable was higher in pitch. Their judgments were found to reflect normalization for expected declination; in general, when two stressed syllables sounded equal in pitch, the second was actually lower. The pattern of normalization reflected certain major features of production patterns: A greater correction for declination was made for wide pitch range stimuli than for narrow pitch range stimuli. The slope of expected declination was less for longer stimuli than for shorter ones. Lastly, amplitude was found to have a significant effect on judgments, suggesting that the amplitude downdrift which normally accompanies fundamental frequency declination may have an important role in the perception of phrasing.     

Nonconscious control of fundamental voice frequency

The aim of this paper is to answer the question whether "perception-action" dissociation, which is well documented in vision, may also be found in auditory information processing. Trained singers were asked to produce vowel sounds into a microphone. The sound that each singer produced was fed back to their ears via headphones. Two seconds after the sound production had begun, the auditory feedback was shifted in pitch by a certain degree (9, 19, 50, or 99 cents in either direction). In every set of sounds, instances without any pitch shifts also appeared. After each trial, participants reported whether they were aware of a pitch change or not. It was found that even though the participants were unaware of subtle pitch changes, the fundamental frequency of their vowel production was found to shift slightly in the opposite direction to the pitch shift. These results show that auditory information is processed by two separate systems: one for perception and one for action. They also show that the function of the auditory control system differs from the visual control system. The latter is used to control bodily movements while the function of the former is a nonconscious, instant control of vocalization.     

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.     

Vocalization and breathing during the second and third years of life

Vocalization and breathing were studied in 40 healthy young children,including 5 boys and 5 girls at each, of ages of 18, 24, 30, and 36 months. A variable inductance plethysmograph was used to obtain estimates of volume changes of the rib cage, abdomen, and lung, as well as estimates of selected temporal features of the breathing cycle. Results indicated that breathing behavior was influenced by height and age, but not by vocalization type or sex. Such behavior was found to be highly variable, demonstrating that these young children had multiple degrees of freedom of performance available to accomplish the aeromechanical drive required.     

Better place-coding of the fundamental frequency in cochlear implants

In current cochlear implant systems, the fundamental frequency F0 of a complex sound is encoded by temporal fluctuations in the envelope of the electrical signals presented on the electrodes. In normal hearing, the lower harmonics of a complex sound are resolved, in contrast with a cochlear implant system. In the present study, it is investigated whether "place-coding" of the first harmonic improves the ability of an implantee to discriminate complex sounds with different fundamental frequencies. Therefore, a new filter bank was constructed, for which the first harmonic is always resolved in two adjacent filters, and the balance between both filter outputs is directly related to the frequency of the first harmonic. The new filter bank was compared with a filter bank that is typically used in clinical processors, both with and without the presence of temporal cues in the stimuli. Four users of the LAURA cochlear implant participated in a pitch discrimination task to determine detection thresholds for F0 differences. The results show that these thresholds decrease noticeably for the new filter bank, if no temporal cues are present in the stimuli. If temporal cues are included, the differences between the results for both filter banks become smaller, but a clear advantage is still observed for the new filter bank. This demonstrates the feasibility of using place-coding for the fundamental frequency.     

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.     

Limits to the role of a common fundamental frequency in the fusion of two sounds with different spatial cues

Two experiments establish constraints on the ability of a common fundamental frequency (F0) to perceptually fuse low-pass filtered and complementary high-pass filtered speech presented to different ears. In experiment 1 the filter cut-off is set at 1 kHz. When the filters are sharp, giving little overlap in frequency between the two sounds, listeners report hearing two sounds even when the sounds at the two ears are on the same F0. Shallower filters give more fusion. In experiment 2, the filters' cut-off frequency is varied together with their slope. Fusion becomes more frequent when the signals at the two ears share low-frequency components. This constraint mirrors the natural filtering by head-shadow of sound sources presented to one side. The mechanisms underlying perceptual fusion may thus be similar to those underlying auditory localization.     

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.     

Effects of fundamental frequency and vocal-tract length changes on attention to one of two simultaneous talkers

Three experiments used the Coordinated Response Measure task to examine the roles that differences in F0 and differences in vocal-tract length have on the ability to attend to one of two simultaneous speech signals. The first experiment asked how increases in the natural F0 difference between two sentences (originally spoken by the same talker) affected listeners' ability to attend to one of the sentences. The second experiment used differences in vocal-tract length, and the third used both F0 and vocal-tract length differences. Differences in F0 greater than 2 semitones produced systematic improvements in performance. Differences in vocal-tract length produced systematic improvements in performance when the ratio of lengths was 1.08 or greater, particularly when the shorter vocal tract belonged to the target talker. Neither of these manipulations produced improvements in performance as great as those produced by a different-sex talker. Systematic changes in both F0 and vocal-tract length that simulated an incremental shift in gender produced substantially larger improvements in performance than did differences in F0 or vocal-tract length alone. In general, shifting one of two utterances spoken by a female voice towards a male voice produces a greater improvement in performance than shifting male towards female. The increase in performance varied with the intonation patterns of individual talkers, being smallest for those talkers who showed most variability in their intonation patterns between different utterances.