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.     

Dissimilarity and the Classification of Female Singing Voices: A Preliminary Study

Traditionally, timbre has been defined as that perceptual attribute that differentiates two sounds when pitch and loudness are equal and thus is a measure of dissimilarity. By such a definition, each voice possesses a set of timbres, and the identity of any voice or voice category across different pitch-loudness-vowel combinations must be due to an abstraction of the pattern of timbre transformation. Using stimuli produced across the singing range by singers from different voice categories, this study sought to examine how timbre and pitch interact in the perception of dissimilarity. This study also investigated whether listener experience affects the perception of timbre as a function of pitch. The resulting multidimensional scaling (MDS) representations showed that for all stimuli and listeners, dimension 1 correlated with pitch, whereas dimension 2 correlated with spectral centroid and separated vocal stimuli into the categories mezzo-soprano and soprano. Dimension 3 appeared highly idiosyncratic depending on the nature of the stimuli and on the experience of the listener. Inexperienced listeners appeared to rely more heavily on pitch in making dissimilarity judgments than did experienced listeners. The resulting MDS representations of dissimilarity across pitch provide a glimpse of the timbre transformation of voice categories across pitch.     

Dissimilarity and the Classification of Male Singing Voices

Traditionally, timbre has been defined as that perceptual attribute that differentiates two sounds when pitch and loudness are equal, and thus is a measure of dissimilarity. By such a definition, each voice possesses a set of timbres, and the ability to identify any voice or voice category across different pitch-loudness-vowel combinations must be due to an ability to "link" these timbres by abstracting the "timbre transformation," the manner in which timbre subtly changes across pitch and loudness for a specific voice or voice category. Using stimuli produced across the singing range by singers from different voice categories, this study sought to examine how timbre and pitch interact in the perception of dissimilarity in male singing voices. This study also investigated whether or not listener experience affects the perception of timbre as a function of pitch. The resulting multidimensional scaling (MDS) representations showed that for all stimuli and listeners, dimension 1 correlated with pitch, while dimension 2 correlated with spectral centroid and separated vocal stimuli into the categories baritone and tenor. Dimension 3 appeared highly idiosyncratic depending on the nature of the stimuli and on the experience of the listener. Inexperienced listeners appeared to rely more heavily on pitch in making dissimilarity judgments than did experienced listeners. The resulting MDS representations of dissimilarity across pitch provide a glimpse of the timbre transformation of voice categories across pitch.     

The effect of fundamental frequency on the brightness dimension of timbre

The dependency of the brightness dimension of timbre on fundamental frequency (FO) was examined experimentally. Subjects compared the timbres of 24 synthetic stimuli, produced by the combination of six values of spectral centroid to obtain different values of expected brightness, and four FO's, ranging over 18 semitones. Subjects were instructed to ignore pitch differences. Dissimilarity scores were analyzed by both ANOVA and multidimensional scaling (MDS). Results show that timbres can be compared between stimuli with different FO's over the range tested, and that differences in FO affect timbre dissimilarity in two ways. First, dissimilarity scores reveal a term proportional to FO difference that shows up in the MDS solution as a dimension correlated with FO and orthogonal to other timbre dimensions. Second, FO affects systematically the timbre dimension (brightness) correlated with spectral centroid. Interestingly, both terms covaried with differences in FO rather than chroma or consonance. The first term probably corresponds to pitch. The second can be eliminated if the formula for spectral centroid is modified by introducing a corrective factor dependent on FO.     

Some insight into the acoustics of the didjeridu

The Australian didjeridu is a unique and interesting instrument. Despite the fact that the bore shape is almost random in nature and varies considerably across different instruments, the didjeridu timbre is readily recognizable. This is also true despite the fact that the player can manipulate the timbre more than in most wind instruments, by changing the shape of his vocal tract. In this study we examine the didjeridu spectrum in detail, in order to determine the characteristics that are similar across different instruments, those that are constant for a given instrument, and those that are readily influenced by the player. To this end we recorded and analyzed the sounds of eight instruments of different quality, all of them played across a range of timbres. Examining the resultant spectra, along with the resonance frequencies of these instruments, leads to a number of interesting conclusions. One of these is that the random nature of the instrument bore is actually conducive to creating its typical timbre. We also give a preliminary explanation of the differences between good and poor instruments.     

Application of free sorting tasks to sound quality experiments

In many studies devoted to the sound quality of industrial products, a perceptual space is determined through dissimilarity judgements on pairs of stimuli. A drawback of this procedure is that it can be very time consuming if the number of stimuli is large. An alternative procedure consists in a free sorting of sounds: averaging individual results provides a set of data which are considered as indicators of dissimilarities and analyzed using a multi-dimensional scaling method. The validity of this alternative can be discussed, as the psychological processes involved in the two procedures are different.This study compared these two approaches in a particular case (door closure sounds). In this specific case, it was observed that dissimilarities obtained from the two procedures can be different, the more so as sounds are dissimilar and these differences can lead to slightly different perceptual spaces. Nevertheless, a free sorting experiment is a reliable way of reducing the number of stimuli in a large set of sounds. It allows selecting some representative sounds and narrowing the set of sounds while keeping in the subset most of the timbre features. This provides a useful preliminary step to a paired-comparison experiment.     

DCMDS-RV: density-concentrated multi-dimensional scaling for relation visualization

Journal of Visualization - This paper proposes a novel unsupervised multi-dimensional scaling (MDS) method to visualize high-dimensional data and their relations in a low-dimensional (e.g., 2D)...     

How do clarinet players adjust the resonances of their vocal tracts for different playing effects?

In a simple model, the reed of the clarinet is mechanically loaded by the series combination of the acoustical impedances of the instrument itself and of the player's airway. Here we measure the complex impedance spectrum of players' airways using an impedance head adapted to fit inside a clarinet mouthpiece. A direct current shunt with high acoustical resistance allows players to blow normally, so the players can simulate the tract condition under playing conditions. The reproducibility of the results suggest that the players' "muscle memory" is reliable for this task. Most players use a single, highly stable vocal tract configuration over most of the playing range, except for the altissimo register. However, this "normal" configuration varies substantially among musicians. All musicians change the configuration, often drastically for "special effects" such as glissandi and slurs: the tongue is lowered and the impedance magnitude reduced when the player intends to lower the pitch or to slur downwards, and vice versa.     

Perceptual organization of complex-tone sequences: a tradeoff between pitch and timbre?

Sequences of rapidly occurring sounds that differ from each other are often perceptually segregated into "streams" within which the range of differences is smaller [Bregman and Campbell, J. Exp. Psychol. 89, 244-249 (1971)]. Early research on streaming implied it to be pitch dominated, but Wessel [Comput. Music J. 3, 45-52 (1979)] demonstrated that timbre differences could also bring about segregation. In the present study, pitch and timbre attributes were put in competition in four-tone sequences of the form: T2P1-TmP1-T2Pn-TmPn, with the first pair assigned pitch P1 but different timbres T2 and Tm, and the second pair pitch Pn, and similarly contrasted timbres. Six listeners were asked to indicate whether perceived grouping of 49 such sequences was based on pitch proximity, timbre similarity, or ambiguous percepts not dominated by either cue. Results confirm that timbre can segregate sequences and imply that timbre and pitch compete in perceptually organizing complex sequences. Because timbre differences were provided by varying the locus of four equal-amplitude harmonics, and pitch differences were provided by varying their relative spacing, it is suggested that the tradeoffs observed may actually arise due to differences in perceived salience of "spectral pitch" and "virtual pitch" [Terhardt, J. Acoust. Soc. Am. 55, 1061-1069 (1974)] dependent on relative changes in spectral locus and spectral spacing over time.     

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.     

Acoustical analysis and model-based sound synthesis of the kantele

The five-string Finnish kantele is a traditional folk music instrument that has unique structural features, resulting in a sound of bright and reverberant timbre. This article presents an analysis of the sound generation principles in the kantele, based on measurements and analytical formulation. The most characteristic features of the unique timbre are caused by the bridgeless string termination around a tuning pin at one end and the knotted termination around a supporting bar at the other end. These result in prominent second-order nonlinearity and strong beating of harmonics, respectively. A computational model of the instrument is also formulated and the algorithm is made efficient for real-time synthesis to simulate these features of the instrument timbre.     

笙的簧片物理参数与音色相关性的初步研究

为了改善笙的声音品质,本文研究了笙的簧片物理尺度与笙的音色之间的相关性。在提出笙的物理模型并验证其有效性的基础上,固定音高,改变簧舌的厚度、长度以及缝隙宽度,合成一组笙的声样本。通过对偶比较法以及多维尺度法分析笙的音色空间,根据簧舌参数及音色特征量解释该音色空间的物理意义,并从发声原理比较簧舌参数对音色的作用。结果表明,音高一定时,簧舌宽度对音色的作用可忽略,厚度(及长度)和缝隙宽度对音色的作用相似,但影响方式不同。改变簧舌物理参数所形成的二维音色空间与声音的对数起振时间、频谱丰富性以及频谱不规则度有关。起振特征与频谱丰富性特征存在共变关系,通过改变这两个特征,能够改变音色的明亮度和柔软度。     

Formant-frequency matching between sounds with different bandwidths and on different fundamental frequencies

The two experiments described here use a formant-matching task to investigate what abstract representations of sound are available to listeners. The first experiment examines how veridically and reliably listeners can adjust the formant frequency of a single-formant sound to match the timbre of a target single-formant sound that has a different bandwidth and either the same or a different fundamental frequency (F0). Comparison with previous results [Dissard and Darwin, J. Acoust. Soc. Am. 106, 960-969 (2000)] shows that (i) for sounds on the same F0, introducing a difference in bandwidth increases the variability of matches regardless of whether the harmonics close to the formant are resolved or unresolved; (ii) for sounds on different F0's, introducing a difference in bandwidth only increases variability for sounds that have unresolved harmonics close to the formant. The second experiment shows that match variability for sounds differing in F0, but with the same bandwidth and with resolved harmonics near the formant peak, is not influenced by the harmonic spacing or by the alignment of harmonics with the formant peak. Overall, these results indicate that match variability increases when the match cannot be made on the basis of the excitation pattern, but match variability does not appear to depend on whether ideal matching performance requires simply interpolation of a spectral envelope or also the extraction of the envelope's peak frequency.     

Influence of the Number of Loudspeakers on the Timbre in Horizontal and Mixed-Order Ambisoncis Reproduction

Ambisonics is a series of flexible spatial sound reproduction systems based on spatial harmonics decomposition of sound field. Traditional horizontal and spatial Ambisonics reconstruct horizontal and spatial sound field with certain order of spatial harmonics, respectively. Both the Shannon-Nyquist spatial sampling frequency limit for accurately reconstructing sound field and the complexity of system increase with the increasing order of Ambisonics. Based on the fact that the horizontal localization resolution of human hearing is higher than vertical resolution, mixed-order Ambisonics (MOA) reconstructs horizontal sound field with higher order spatial harmonics, while reconstructs vertical sound field with lower order spatial harmonics, and thereby reaches a compromise between the perceptual performance and the complexity of system. For a given order horizontal Ambisoncis or MOA reproduction, the number of horizontal loudspeakers is flexible, providing that it exceeds some low limit. By using Moore’s revised loudness model, the present work analyzes the influence of the number of horizontal loudspeakers on timbre both in horizontal Ambisonics and MOA reproduction. The binaural loudness level spectra (BLLS) of Ambisoncis reproduction are calculated and then compared with those of target sound field. The results indicate that below the Shannon-Nyquist limit of spatial sampling, increasing the number of horizontal loudspeakers influence little on BLLS then timbre. Above the limit, however, the BLLS for Ambisoncis reproduction deviate from those of target sound field. The extent of deviation depends on both the direction of target sound field and the number of loudspeakers. Increasing the number of horizontal loudspeakers may increase the change of BLLS then timbre in some cases, but reduce the change in some other cases. For MOA, the influence of the number of horizontal loudspeakers on BLLS and timbre reduces when virtual source departs from horizontal plane to the high or low elevation. The subjective evaluation experiment also validates the analysis.     

The use of multidimensional perceptual models in the selection of sonar echo features

The development of an accurate and efficient sonar-target classification system depends upon the identification of a set of signal features which may be used to discriminate important classes of signals. Feature selection can be facilitated through the identification of perceptual features used by human listeners in discriminating relevant sonar echoes. This study was conducted to establish a more reliable means of identifying perceptual features in terms of physical signal parameters as an initial step toward the development of an automatic sonar-target classification system. The results of an experiment involving eight subjects and six sonar echoes are presented. A model of the perceptual structure of these echoes was derived from subject similarity judgments using a multidimensional scaling (MDS) technique. It was found that three perceptual features accounted for the similarity judgments made by the human listeners. Echoes modified along candidate physical dimensions were employed to aid in the identification of perceptual dimensions in terms of physical signal parameters. The three perceptual features could be associated with signal parameters involving the amplitude envelope of the echoes.     

基于音色单元分布的音乐结构分析

音乐的结构是音乐作品表达作者思想的一种重要形式,也是听众理解音乐作品内涵的有效途径。本文研究了基于音乐特征的音色单元建模方法,研究了在Fisher准则下,根据局部范围音色单元的分布,采用非监督聚类方法分析音乐的结构。实验结果证明了基于离散余弦变换的音色特征,用音色单元分布聚类算法进行音乐结构分析的有效性。      

An exact solution to the multi-dimensional line transfer equation

The theory of generalized analytic functions is used to obtain an exact closed form analytical solution to a transfer problem for spectral line radiation in a multi-dimensional atmosphere. The multi-dimensional full-space and half-space Green's functions so obtained are quite general and may be used, along with the corresponding orthogonality relationships, to obtain solutions to any general multi-dimensional radiative transfer problem involving model two-level atoms. An application of the method using perturbation techniques is illustrated.     

Multidimensional Scaling of Breathy Voice Quality: Individual Differences in Perception

Experiments on disordered voice quality with multidimensional scaling (MDS) have resulted in solutions with low R-square and have failed to show consistent dimensions across different listeners. These findings have been suggested to indicate large individual differences in the perception of voice quality. However, these inconsistencies may originate from several factors, including random stimulus selection, instructions that encourage listeners to respond to global difference in pairs of voices, and noisy perceptual data. This experiment used MDS techniques to study individual differences in perception of breathiness. The voices in the experiment were selected to have a relatively wide variation in breathiness but only minimal variation in roughness, strain, and fundamental frequency. Additionally, listeners were instructed specifically to rate similarities in breathiness rather than judging global differences in voices, and several judgments from each listener were averaged to minimize noise in the data. It was hypothesized that these modifications would result in an MDS solution that accounted for greater variance in perceptual data than previously shown. Results show that averaging multiple responses from each listener increased the R-square from 45% to approximately 75%. The poor R-square and large individual differences in voice quality perception observed in past research may have partly resulted from the experimental procedures in previous studies. These findings suggest that individual differences in the perception of voice quality are not as large as previously thought, and a model of voice quality perception for an "average" listener may be a good representation for the general population.     

Analysis of car door closing sound quality

The perception of the noise coming from a car’s door closure has been analyzed, the focus being put on the image of the quality of the car that the listener can have in mind while hearing the sound. Different experiments have been realized: a free sorting experiment for reducing the number of stimuli without any loss of generality, paired comparisons with similarity and preference ratings and, finally, free verbalizations analysis. The results have agreed on the importance of two timbre parameters, the frequency balance of the sound and its cleanness (only one temporal event should be audible). In particular, even if loudness had appeared as the most important sound feature in previously published studies, it did not in this one; the reason is probably that previous studies had focused on annoyance creating by sounds.In a more general way, this study has proved the stability of the perceptual space derived from two different methods: a multi-dimensional analysis of similarity ratings and the analysis of free verbalizations.     

Astronomical speckle imaging

The many methods suggested and (some of them) tried out experimentally and/or observationally for imaging celestial objects through the Earth's atmosphere are reviewed. Their theoretical and physical bases are examined. Most attention is paid to Labeyrie's speckle interferometry and its several extensions devised during the past decade-astrophysical results obtained with the aid of these techniques are listed. Other forms of optical interferometry are discussed, as are related techniques in radio astronomy and ultrasonics.