Touch and temporal behavior of grand piano actions

This study investigated the temporal behavior of grand piano actions from different manufacturers under different touch conditions and dynamic levels. An experimental setup consisting of accelerometers and a calibrated microphone was used to capture key and hammer movements, as well as the sound signal. Five selected keys were played by pianists with two types of touch ("pressed touch" versus "struck touch") over the entire dynamic range. Discrete measurements were extracted from the accelerometer data for each of the over 2300 recorded tones (e.g., finger-key, hammer-string, and key bottom contact times, maximum hammer velocity). Travel times of the hammer (from finger-key to hammer-string) as a function of maximum hammer velocity varied clearly between the two types of touch, but only slightly between pianos. A travel time approximation used in earlier work [Goebl W., (2001). J. Acoust. Soc. Am. 110, 563-572] derived from a computer-controlled piano was verified. Constant temporal behavior over type of touch and low compression properties of the parts of the action (reflected in key bottom contact times) were hypothesized to be indicators for instrumental quality.     

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.     

Analysis and modeling of piano sustain-pedal effects

This paper describes the main features of the sustain-pedal effect in the piano through signal analysis and presents an algorithm for simulating the effect. The sustain pedal is found to increase the decay time of partials in the middle range of the keyboard, but this effect is not observed in the case of the bass and treble tones. The amplitude beating characteristics of piano tones are measured with and without the sustain pedal engaged, and amplitude envelopes of partial overtone decay are estimated and displayed. It is found that the usage of the sustain pedal introduces interesting distortions of the two-stage decay. The string register response was investigated by removing partials from recorded tones; it was observed that as the string register is free to vibrate, the amount of sympathetic vibrations is increased. The synthesis algorithm, which simulates the string register, is based on 12 string models that correspond to the lowest tones of the piano. The algorithm has been tested with recorded piano tones without the sustain pedal. The objective and subjective results show that the algorithm is able to approximately reproduce the main features of the sustain-pedal effect.     

Physical modelling of the piano string scale

Several stages of physics-based mathematical modelling are described for the design of the piano string scale. Strings are assumed to be perfectly flexible, and piano hammers are described by a nonlinear hysteretic model. It is also assumed that the parameters of the hammers for the whole hammer set are determined experimentally beforehand. Simulation procedures are used to systematically adjust the structure of the piano scale to its optimal value. The efficiency of the piano scale is improved by the analysis of the numerically simulated string motion and spectra of the string vibrations excited by the impact of the hammer. The set of variables to be optimized includes the linear mass density and tension of the piano strings and the position of the striking point. In addition, the problem of choosing appropriate tensions for neighbouring strings terminated on separate bass and treble bridges is considered.     

Piano hammers and their force compression characteristics: does a power law make sense?

We have studied the force characteristics of a collection of piano hammers, through studies of the acceleration of the hammer head, the force due to the compression of the hammer felt, Fh, and the associated bending of the hammer shank which occurs when a hammer strikes a rigid object. By integration of the acceleration one can estimate the compression of the felt, and thus obtain a force-compression Fh(z) relationship; our results for this function are compared with previous experiments and theoretical models. Close examination of our findings suggests that bending of the hammer shank, and also the time required for the force to be transmitted from the outer edge of the hammer to its core, play significant roles in the hammer dynamics. The data are used to estimate the quantitative impact of these effects on the derived Fh(z) relation. The implications for physical modeling of a piano tone are briefly discussed.     

Perception of dissonance by people with normal hearing and sensorineural hearing loss

The purpose of this study was to determine whether the perceived sensory dissonance of pairs of pure tones (PT dyads) or pairs of harmonic complex tones (HC dyads) is altered due to sensorineural hearing loss. Four normal-hearing (NH) and four hearing-impaired (HI) listeners judged the sensory dissonance of PT dyads geometrically centered at 500 and 2000 Hz, and of HC dyads with fundamental frequencies geometrically centered at 500 Hz. The frequency separation of the members of the dyads varied from 0 Hz to just over an octave. In addition, frequency selectivity was assessed at 500 and 2000 Hz for each listener. Maximum dissonance was perceived at frequency separations smaller than the auditory filter bandwidth for both groups of listners, but maximum dissonance for HI listeners occurred at a greater proportion of their bandwidths at 500 Hz than at 2000 Hz. Further, their auditory filter bandwidths at 500 Hz were significantly wider than those of the NH listeners. For both the PT and HC dyads, curves displaying dissonance as a function of frequency separation were more compressed for the HI listeners, possibly reflecting less contrast between their perceptions of consonance and dissonance compared with the NH listeners.     

Place specificity of multiple auditory steady-state responses

Auditory steady-state responses (ASSRs) were elicited by simultaneously presenting multiple AM (amplitude-modulated) tones with carrier frequencies of 500, 1000, 2000, and 4000 Hz and modulation frequencies of 77, 85, 93, and 102 Hz, respectively. Responses were also evoked by separately presenting single 500- or 2000-Hz AM tones. The objectives of this study were (i) to determine the cochlear place specificity of single and multiple ASSRs using high-pass noise masking and derived-band responses, and (ii) to determine if there were any differences between single- and multiple-stimulus conditions. For all carrier frequencies, derived-band ASSRs for 1-octave-wide derived bands ranging in center frequency from 0.25 to 8 kHz had maximum amplitudes within a 1/2 octave of the carrier frequency. For simultaneously presented AM tones of 500, 1000, 2000, and 4000 Hz, bandwidths for the function of derived-band ASSR amplitude by derived-band center frequency were 476, 737, 1177, and 3039 Hz, respectively. There were no significant differences when compared to bandwidths of 486 and 1371 for ASSRs to AM tones of 500 or 2000 Hz presented separately. Results indicate that ASSRs to moderately intense stimuli (60 dB SPL) reflect activation of reasonably narrow cochlear regions, regardless of presenting AM tones simultaneously or separately.     

Acoustic distortion products in humans: systematic changes in amplitudes as a function of f2/f1 ratio

The effects of primary-tone separation on the amplitude of distortion-product emissions (DPEs) at the 2f1-f2 frequency were systematically examined in ten ears of five subjects. All individuals had normal hearing and middle-ear function based upon standard clinical measures. Acoustic-distortion products were elicited at 1, 2.5, and 4 kHz by equilevel primaries at 65, 75, and 85 dB SPL, while f2/f1 ratios were varied in 0.02 increments from 1.01-1.41 (4 kHz), 1.01-1.59 (2.5 kHz), or 1.01-1.79 (1 kHz). A principal outcome reflected in the detailed structure of both average and individual ratio functions was a nonmonotonic change in DPE amplitude as the ratio of f2/f1 increased. Despite the presence of amplitude nonmonotonicities, there was clearly a region of f1 and f2 separation that generated a maximum DPE. The effects of primary-tone separation on DPE amplitudes were systematically related to DPE frequency and primary-tone level. For all three levels of stimulation, the f2/f1 ratio was inversely related to DPE frequency. Thus larger ratios reflecting a greater separation of f1 and f2 were more effective in generating DPEs at 1 kHz rather than at 4 kHz. The optimal ratio for 2.5 kHz fell at an intermediate value. Conversely, acoustic distortion-product amplitude as a function of primary-tone level was directly related to the frequency separation of the primary tones. Regardless of the frequency region of the primary tones, smaller f2/f1 ratios were superior in generating DPEs in response to 65-dB stimuli, whereas larger ratios elicited bigger DPEs with primaries at 75 and 85 dB SPL. Within any specific stimulus-parameter combination, individual variability in DPE amplitude was noted. When all stimulus conditions describing the variations in frequency and level were considered, an f2/f1 ratio of 1.22 was most effective in maximizing DPE amplitude.     

A comparison of steady-state evoked potentials to modulated tones in awake and sleeping humans.

Steady-state evoked potential responses were measured to binaural amplitude-modulated (AM) and combined amplitude- and frequency-modulated (AM/FM) tones. For awake subjects, AM/FM tones produced larger amplitude responses than did AM tones. Awake and sleeping responses to 30-dB HL AM/FM tones were compared. Response amplitudes were lower during sleep and the extent to which they differed from awake amplitudes was dependent on both carrier and modulation frequencies. Background EEG noise at the stimulus modulation frequency was also reduced during sleep and varied with modulation frequency. A detection efficiency function was used to indicate the modulation frequencies likely to be most suitable for electrical estimation of behavioral threshold. In awake subjects, for all carrier frequencies tested, detection efficiency was highest at a modulation frequency of 45 Hz. In sleeping subjects, the modulation frequency regions of highest efficiency varied with carrier frequency. For carrier frequencies of 250 Hz, 500 Hz, and 1 kHz, the highest efficiencies were found in two modulation frequency regions centered on 45 and 90 Hz. For 2 and 4 kHz, the highest efficiencies were at modulation frequencies above 70 Hz. Sleep stage affected both response amplitude and background EEG noise in a manner that depended on modulation frequency. The results of this study suggest that, for sleeping subjects, modulation frequencies above 70 Hz may be best when using steady-state potentials for hearing threshold estimation.     

Quantitative auger electron spectroscopy analysis of AgPd and NiPd alloys

The relationship between peak amplitude in derivative Auger spectra and alloy composition was investigated for AgPd and NiPd alloys. Measurements were performed on polished and sputter etched samples as well as on samples fractured in vacuo. For clean alloy surfaces and in the absence of sputtering, a linear relationship between peak amplitude of a given alloy component and atomic concentration was observed. Relative Auger peak amplitudes measured on sputter cleaned surfaces were different from those measured on fractured surfaces. Results were interpreted in terms of a simple model considering surface enrichment of the alloy component with the lower relative sputtering yield.     

Frenkel-Kontorova模型中基底势振动的影响

基于一维Frenkel-Kontorova模型, 研究了振动的基底势对系统纳米摩擦现象的影响. 分别在相邻原子间的距离与周期势场的周期比为不公度(incommensurate)、可公度(commensurate)两种情形下, 探讨了基底势振动的振幅和频率对滞回现象(hysteresis)、最大静摩擦力以及超滑现象的作用机理. 两种情形下, 固定频率, 随着振幅的增大, 滞回区域的面积以及最大静摩擦力都将减小, 对于不同的频率, 减小的趋势不同. 系统甚至产生了超滑现象. 但当频率过大时, 振幅的改变不会影响滞回区域的面积以及最大静摩擦力的大小, 此时与基底不加振动时的情形一致; 当振幅固定, 随着频率的增大, 滞回区域的面积将增大, 对于不同振幅, 增大的趋势不同. 特别地, 对于某些固定的振幅, 最大静摩擦力随着振动频率的增大先逐步减小直至出现超滑现象, 再进一步增大频率, 最大静摩擦力又转而逐步增大. 这一现象类似于共振, 表明存在最佳的振动频率促进系统内所有原子的共同运动, 使得整个系统的最大静摩擦力几乎消失. 另外, 两种情形的区别是, 对于某些固定的频率(如ω= 0.5)和不同的小振幅, 不可公度情形往往具有相同的平均终止速度, 而可公度情形则不同, 表明相同前提下后者具有更复杂的动力学行为. 关键词： Frenkel-Kontorova模型 滞回 最大静摩擦力 超润滑     

On the dynamics of the clavichord: from tangent motion to sound

An experimental study of variations in the sound of clavichord notes at different dynamic levels is described. Radiated acoustic signal, tangent velocity and two tangent-string contact signals are synchronously measured for all 51 notes of an unfretted instrument. More than ten repeated measures are recorded in order to obtain as much variation in dynamic level as possible. The tangent motion, expressed in terms of velocity, is studied in the time and frequency domains. A model of the tangent-string contact point velocity is proposed. Then, three aspects of the sounded tones are analyzed: SPL and its relationship to tangent velocity, spectral slope, and pitch variations. These results indicate a linear relationship between sound pressure level and tangent peak log velocity. Spectral slope seems almost constant independent of tangent velocity and dynamic level. Both tangent velocity and finger pressure are shown to influence the fundamental frequency. In conclusion, controlling both finger velocity and finger pressure may prove challenging for the player, and this may explain why the sound quality of the clavichord depends so much on the players ability.     

The contribution of the excitatory source to the perception of neutral vowels in stuttered speech

The vowel in part-word repetitions in stuttered speech often sounds neutralized. In the present article, measurements of the excitatory source made during such episodes of dysfluency are reported. These measurements show that, compared with fluent utterances, the glottal volume velocities are lower in amplitude and shorter in duration and that the energy occurs more towards the low-frequency end of the spectrum. In a first perceptual experiment, the effects of varying the amplitude and duration of the glottal source were assessed. The glottal volume velocity recordings of the /ae/ vowels used in the analyses were employed as driving sources for an articulatory synthesizer so that judgments about the vowel quality could be made. With dysfluent glottal sources (either as spoken or by editing a fluent source so that it was low in amplitude and brief), the vowels sounded more neutralized than with fluent glottal sources (as spoken or by editing a dysfluent source to increase its amplitude and lengthen it). In a second perceptual experiment, synthetic glottal volume velocities were used to verify these findings and to assess the influence of the low-frequency emphasis in the dysfluent speech. This experiment showed that spectral bias and duration both cause stuttered vowels to sound neutralized.     

PARTICULAR SOLITONS IN NONLINEAR LATTICE

One soliton of particle velocity and its amplitude (maximum particle velocity of one soliton) in Toda lattice is given analytically. It has also been known numerically that the maximum particle velocity (when the collision of two solitons reaches their maximum, we define V_n at this time as its maximum particle velocity) during the collision of two solitons moving in the same direction is equal to the difference between the amplitudes of two solitons if the difference is large enough; however, the maximum particle velocity is equal to the adding up of the amplitudes of two solitons moving in the opposite directions. The relationship between the maximum value of e^-(r_n)-1 and their initial amplitude of e^-(r_n)-1 is also given analytically in Toda lattice if the amplitudes of the two solitons are the same and their moving directions are opposite. Compared with the Boussinesq equation, there are differences between the Toda lattice equation and the Boussinesq equation for solitons during the collision.     

爆轰加载下弹塑性固体Richtmyer-Meshkov流动的扰动增长规律

研究了冲击波加载弹塑性材料扰动自由面的动力学演化过程,分析了高能炸药爆轰驱动时初始扰动与材料性质对扰动增长的影响.研究结果表明:初始扰动的振幅与波长之比越高,扰动越易增长,强度越高的材料扰动增长幅度越小;扰动增长被抑制时,尖钉的最大振幅与增长速度无量纲数之间存在线性近似关系,进一步理论分析表明尖钉的振幅增长因子与加载压力、初始扰动形态和材料强度有关,该理论关系作为扰动增长规律的线性近似在一定范围内适用于多种金属材料.     

Energy based simulation of a Timoshenko beam in non-forced rotation. Influence of the piano hammer shank flexibility on the sound

A nonlinear model for a vibrating Timoshenko beam in non-forced unknown rotation is derived from the virtual work principle applied to a system of beam with mass at the end. The system represents a piano hammer shank coupled to a hammer head. An energy-based numerical scheme is then provided, obtained by non-classical approaches. A major difficulty for time discretization comes from the nonlinear behavior of the kinetic energy of the system. This new numerical scheme is then coupled to a global energy-preserving numerical solution for the whole piano. The obtained numerical simulations show that the pianistic touch clearly influences the spectrum of the piano sound of equally loud isolated notes. These differences do not come from a possible shock excitation on the structure, or from a changing impact point, or a “longitudinal rubbing motion” on the string, since neither of these features is modeled in our study.     

Spectral shape discrimination by hearing-impaired and normal-hearing listeners

The ability to discriminate between sounds with different spectral shapes was evaluated for normal-hearing and hearing-impaired listeners. Listeners discriminated between a standard stimulus and a signal stimulus in which half of the standard components were decreased in level and half were increased in level. In one condition, the standard stimulus was the sum of six equal-amplitude tones (equal-SPL), and in another the standard stimulus was the sum of six tones at equal sensation levels re: audiometric thresholds for individual subjects (equal-SL). Spectral weights were estimated in conditions where the amplitudes of the individual tones were perturbed slightly on every presentation. Sensitivity was similar in all conditions for normal-hearing and hearing-impaired listeners. The presence of perturbation and equal-SL components increased thresholds for both groups, but only small differences in weighting strategy were measured between the groups depending on whether the equal-SPL or equal-SL condition was tested. The average data suggest that normal-hearing listeners may rely more on the central components of the spectrum whereas hearing-impaired listeners may have been more likely to use the edges. However, individual weighting functions were quite variable, especially for the HI listeners, perhaps reflecting difficulty in processing changes in spectral shape due to hearing loss. Differences in weighting strategy without changes in sensitivity suggest that factors other than spectral weights, such as internal noise or difficulty encoding a reference stimulus, also may dominate performance.     

Influence of primary frequencies ratio on distortion product otoacoustic emissions amplitude. I. Intersubject variability and consequences on the DPOAE-gram

Distortion product otoacoustic emissions (DPOAEs) are used widely in humans to assess cochlear function. The standard procedure consists of recording the 2f1-f2 DPOAE amplitude as a function of the f2 frequency, using a fixed f2/f1 ratio (DPOAE-gram), close to 1.20. DPOAE amplitude, as recorded in the DPOAE-gram, shows a wide range of values in normal-hearing subjects, which can impair the predictive value of the DPOAE-gram for hearing thresholds. This study is aimed at comparing intersubject variability in 2f1-f2 DPOAE amplitude according to three paradigms: a fixed f2/f1 ratio, such as the DPOAE-gram, a variable ratio DPOAE-gram (f2/f1 adapted to frequency) and an "optimum" DPOAE-gram, where the f2/f1 is adapted both to subject and frequency. The 2f1-f2 DPOAE amplitude has been investigated on 18 normally hearing subjects at ten different f2 frequencies (from 0.75 to 6 kHz), using an f2 fixed, f1 sweep paradigm, and allowed to define, for each frequency, the f2/f1 ratio giving the greatest 2f1-f2 DPOAE amplitude (or optimum ratio). Results showed a large intersubject variability of the optimum ratio, especially at frequencies below 1.5 kHz, and a significant decrease of the optimum ratio with frequency. The optimum DPOAE-gram was underestimated by up to 5.8 dB on average (up to 14.9 dB for an individual subject) by the fixed ratio DPOAE-gram, and by up to 3 dB on average (up to 10.6 dB for an individual subject) by the variable ratio DPOAE-gram. Intersubject variability was slightly but significantly reduced in the optimum DPOAE-gram versus the fixed-ratio DPOAE-gram. Lastly, correlations between tone-burst evoked otoacoustic emission (TBOAE) amplitudes and maximum DPOAE amplitudes were significantly greater than correlations between TBOAE amplitudes and fixed-ratio DPOAE amplitudes.     

A high-precision magnetoencephalographic study of human auditory steady-state responses to amplitude-modulated tones

The cerebral magnetic field of the auditory steady-state response (SSR) to sinusoidal amplitude-modulated (SAM) tones was recorded in healthy humans. The waveforms of underlying cortical source activity were calculated at multiples of the modulation frequency using the method of source space projection, which improved the signal-to-noise ratio (SNR) by a factor of 2 to 4. Since the complex amplitudes of the cortical source activity were independent of the sensor position in relation to the subject's head, a comparison of the results across experimental sessions was possible. The effect of modulation frequency on the amplitude and phase of the SSR was investigated at 30 different values between 10 and 98 Hz. At modulation frequencies between 10 and 20 Hz the SNR of harmonics near 40 Hz were predominant over the fundamental SSR. Above 30 Hz the SSR showed an almost sinusoidal waveform with an amplitude maximum at 40 Hz. The amplitude decreased with increasing modulation frequency but was significantly different from the magnetoencephalographic (MEG) background activity up to 98 Hz. Phase response at the fundamental and first harmonic decreased monotonically with increasing modulation frequency. The group delay (apparent latency) showed peaks of 72 ms at 20 Hz, 48 ms at 40 Hz, and 26 ms at 80 Hz. The effects of stimulus intensity, modulation depth, and carrier frequency on amplitude and phase of the SSR were also investigated. The SSR amplitude decreased linearly when stimulus intensity or the modulation depth were decreased in logarithmic steps. SSR amplitude decreased by a factor of 3 when carrier frequency increased from 250 to 4000 Hz. From the phase characteristics, time delays were found in the range of 0 to 6 ms for stimulus intensity, modulation depth, and carrier frequency, which were maximal at low frequencies, low intensities, or maximal modulation depth.     

Nonlinear solitary waves in nonlocal elastic solids

The possibility of new weakly nonlinear solitary waves in nonlocal elastic media is demonstrated. The properties of these waves are determined by the characteristic features of wave dispersion in the linear approximation, and their velocity and amplitude cannot exceed certain limiting values. In the case of small amplitudes and velocities close to the velocity of sound, the profile of the waves under consideration coincides with the profile of the soliton described by the Korteweg-de Vries equation. When the amplitude and velocity of the aforementioned waves reach their limiting values, the wave profile sharpens. It is concluded that the propagation of such waves in rocks and soils is possible.