Objective estimation of the tuning features of historical carillons

The carillons of the Mafra National Palace are undergoing a restoration project. Together, the pair of carillons represent the largest surviving 18th century carillons in Europe. To guarantee the historical significance of these outstanding musical instruments, a detailed diagnosis of their current physical tuning state was achieved and results were analyzed with respect to historical, acoustical and musical concerns. In a first stage, we developed a suitable polyreference modal identification technique to infer the tuning status of bells from their modal parameters and we then systematically performed in-field modal testing experiments on a selection of historical bells of the Mafra carillons. For each carillon bell, tuning charts displaying the internal frequency relationships between its most important partials were obtained, as well as the mode shapes, decay times and beating frequencies between modal-doublets for every single musical partial of the bell. In a second part, since carillon bells also must be tuned very accurately one relative to the others in order to play in tune, the important topic of estimating the reference pitch and musical temperament of carillons was addressed by devising optimization techniques, here tentatively based on the actual modal frequencies of the bells. After presenting the modal identification procedure and optimal strategies developed for this work, the feasibility and interests of this instrumental approach are finally illustrated for the two carillons of Mafra.     

Subjective evaluation and an objective measure of a church bell sound quality

The research described in this paper attempts to give an answer to a very old question about a good sounding bell. To this end, a large number of listening tests were performed in which ten bells were compared in pairs to investigate whether bells could be evaluated by subjective sound quality. Furthermore, two new parameters that can be used for objective evaluation of bell sound quality are proposed: the nearest ideal bell deviation and the percentage of the sound energy contained in the first five partials. The ten bells were compared based on the values of the introduced objective parameters. The paper presents correlation of the subjective and the objective analysis, demonstrating applicability of a novel method for bell sound quality assessment.     

A theoretical study of the vibration and acoustics of ancient Chinese bells

In this paper, the acoustics of an ancient Chinese bell, which was made some 3000 years B.C., is studied theoretically. In ancient times, a set of the bells was used as a musical instrument. Unlike a western church bell and an ancient Indian bell, an ancient Chinese bell has two interesting acoustics. First, two tones can be heard separately as the bell is struck at two special points. The interval between the two pitches is always a minor or major third. Second, tones of the bell attenuate quickly, which is necessary for a musical instrument. So, an ancient Chinese bell is sometimes called a two-tone bell or a music bell. Although a three-dimensional model should be used to simulate the acoustics of the bell, a simplified model proposed in this paper does give some insight. Based on the lens-shaped cross section of an ancient Chinese bell, two tones of an ancient Chinese bell can be simulated by the vibration of a double-circular arch and the quick attenuation of tones can be simulated by acoustics of a cylinder with the lens-shaped cross section like a double-circular arch. Numerical results on the vibration and acoustics of the models are presented.     

Warble in carillon bells: An investigation using neutron diffraction

It is speculated that warble in carillon bells can be caused by mode splitting as a result of internal strains produced by non-uniform cooling during casting. The neutron diffraction technique makes possible the measurement of internal strain and is here applied to a in (166 mm) carillon bell with a pronounced 3 Hz warble. Internal strain variations with a 180° periodicity about the bell circumference were detected. From symmetry considerations this periodicity requires that all partials (other than m = 0) should have their doublets split. Measurements of the bell partials confirmed this splitting. The metallographic phases present in the bell metal were also determined and found to agree with expectations.     

Normal modes of the Indian elephant bell

The geometrical structure of the Indian elephant bell is presented and the requirements on its normal modes from group representation theory are described. These are in good agreement with the results of a finite-element model (FEM) for a specific 16-tine case. The spectrum consists of a sequence of families of modes lying on saturation curves, completely different from those of conventional bells. Physical explanations for the occurrence of these families are presented in terms of the tines behaving as a closed loop of coupled cantilevers with constraints from the dome. Each family is found to consist of modes in one of two specific sequences of symmetry types. Experimental measurements of the modes of this same 16-tine bell, using electronic speckle pattern interferometry (ESPI), have been made and are compared with the FEM predictions. Although the interpretation of the interferograms is difficult in all but the simpler cases, agreement in terms of frequencies is surprisingly good for the first few family sequences. The ESPI study also showed up numerous harmonics and subharmonics of true normal modes, showing the system to be rather non-linear and making comparisons with the FEM results tricky.     

Stability of water bells generated by jet impacts on a disk

Water bells appear when a cylindrical liquid jet impacts normally onto a disk of similar diameter. First observed and described experimentally by F. Savart, their stationary shape was analytically obtained by J. Boussinesq. Here we consider the stability of these bells and derive a general stability criterion showing their sensitivity both to the pressure difference across the liquid sheet and to the ejection angle from the impacting disk. In this later case, we find a critical angle of ejection above which the bell is periodically destroyed and created.     

Bell clapper impact dynamics and the voicing of a carillon

The periodic re-voicing of the bell clappers of the Australian National Carillon in Canberra provided an opportunity for the study of the acoustic effects of this operation. After prolonged playing, the impact of the pear-shaped clapper on a bell produces a significant flat area on both the clapper and the inside surface of the bell. This deformation significantly decreases the duration of the impact event and has the effect of increasing the relative amplitude of higher modes in the bell sound, making it "brighter" or even "clangy." This effect is studied by comparing the spectral envelope of the sounds of several bells before and after voicing. Theoretical analysis shows that the clapper actually strikes the bell and remains in contact with the bell surface until it is ejected by a displacement pulse that has traveled around the complete circumference of the bell. The contact time, typically about 1 ms, is therefore much longer than the effective impact time, which is only a few tenths of a millisecond. Both the impact time and the contact time are reduced by the presence of a flat on the clapper.     

Assessing tuning and damping of historical carillon bells and their changes through restoration

The 46 bells of the historical carillon in Perpignan have been restored: taking them down, sanding their oxide layer, and resuspending them. Sound and vibration recordings were made at each stage of the restoration process. The modal frequencies and decay rates have been estimated by means of the matrix pencil algorithm, a parametric signal processing method, with a variance of ≈ 0.1% for the frequencies and a few percents for the damping rates. Tuning is accurate in general, except for the highest notes. The quality factors of the vibration go through a broad minimum in the 2 kHz region. Measurements reveal minute but consistent frequency changes of the order of a few cents. On average, the bells ring 15% longer since the restoration. The measurements also show that the damping rates were more consistent along the range of the instrument after restoration.     

Scattering by cavities of arbitrary shape in an infinite plate and associated vibration problems

This paper presents a solution for the displacement of a uniform elastic thin plate with an arbitrary cavity, modelled using the biharmonic plate equation. The problem is formulated as a system of boundary integral equations by factorizing the biharmonic equation, with the unknown boundary values expanded in terms of a Fourier series. At the edge of the cavity we consider free-edge, simply-supported and clamped boundary conditions. Methods to suppress ill-conditioning which occurs at certain frequencies are discussed, and the combined boundary integral equation method is implemented to control this problem. A connection is made between the problem of an infinite plate with an arbitrary cavity and the vibration problem of an arbitrarily shaped finite plate, using the jump discontinuity present in single-layer distributions at the boundary. The first few frequencies and modes of displacement are computed for circular and elliptic cavities, which provide a check on our numerics, and results for the displacement of an infinite plate are given for four specific cavity geometries and various boundary conditions.     

VIBRATIONAL MODES OF TRUMPET BELLS

We report on an investigation of the normal modes of vibration of the bells of several modern trumpets. We describe the results of experiments using electronic speckle-pattern interferometry to visualize the modal structure and we show that the mode frequencies follow a generalized version of Chladni's law.     

The Simulation of Electrostatic Spray Painting Process with High‐Speed Rotary Bell Atomizers. Part II: External Charging

The present contribution summarizes investigations aiming to completely model the electrostatically supported spray painting process with high‐speed rotary bells by means of CFD. In this part II, so‐called external charging atomizers, where high voltage is applied to emitting electrode needles, are considered. Here, charging of the droplets takes place due to free ions produced from corona discharge at the electrodes. Part I [1] dealt with direct charging atomizers, where potential is applied directly to the rotating bell. The commercial CFD‐code Fluent has been extended to account for the electrostatic field and the space charge effect due to the ions. Here, a model for the time‐dependent and inhomogeneous field charging of the droplets was applied. Furthermore, the direct interaction between the ion current and the flow field, i.e., the so‐called ion wind, could be calculated. As input conditions, the airflow from the shaping air orifices and measured droplet sizes close to the bell edge using Fraunhofer diffraction were taken. In general, numerical and experimental results are in good agreement, confirming the applicability of the chosen physical approach. This is especially true for the final film thickness on the target and the transfer efficiency, i.e., the amount of paint solids that finally deposited on the target. In the near future the calculations must be extended to true unsteady simulations including the dynamic meshing procedure.     

Noise reduction using a quarter wave tube with different orifice geometries

It is well known that the acoustic performance of silencing elements decreases with an increase in exhaust gas flow. Tests were conducted on three orifice geometries of side-branches on an adaptive quarter-wave tube to determine which was the least compromised by the high-speed exhaust gas passing over the side-branch. The side-branch geometries that were tested were a sharp edge, a backward inclined branch, and a bell mouth. The experimental results show that the side-branch with a bell-mouth geometry resulted in the greatest noise reduction by an adaptive quarter-wave tube.     

中华和钟之双音鎛钟的声频特征和振动方式研究

本文对中华和种之中央Bo钟的声频特性和振动方式进行了研究。利用谱对其辐射声信号进行了谱分析;利用时频分析,研究了其谱结构随时间变化情况;为了了解其频率变化及音高情况,计算了其不同时刻的瞬时平均频率。同时,通过不同位置的振动信号谱分析,重建了其在不同频率下的振动方式。     

苯系物Cu_3金属配合物的结构与性质的理论研究

采用密度泛函理论的B3LYP方法,在6-311+G(d,p)基组水平上计算研究了Cu_3团簇与甲苯、二甲苯、三甲苯分子作用的各种异构体结构和频率,比较各异构体间的能量关系,得到最稳定的几何构型.通过分析Cu_3和苯系列化合物作用的结合能和前线轨道等性质,从而了解该类配合物的作用机理.     

Experimental studies on sound and vibration of a two-tone Chinese Peace Bell

In order to examine whether the characteristics of the bell are coincident with the design and make some constructive suggestions for the tuning of bell, the frequency characteristics of sound and the vibrational modes of a two-tone Chinese Peace Bell have been studied. With Welch's spectral estimate, the main partials of radiated sound of the bell have been found out. With time-frequency analysis, the changes of the spectrum with time have been shown. By conditional mean frequency (CMF) of the spectrogram of the sound, the change in the pitch of the bell has been discussed. With an accelerator, the vibration distributions on the different points of the bell have been measured. With short time spectrum analysis, the vibrational modes at different frequencies have been reconstructed.     

ClONO2异构化反应和分解反应的理论研究

用B3LYP/6 31+G(d)和MP2 (Full) /6 31+G(d)优化ClONO2 及其分解反应和异构化反应的过渡态和产物的分子结构 .在B3LYP/6 31+G(d)水平上计算了相关分子的振动频率 .ClONO2 的几何结构、振动频率和红外强度与实验测量值符合得很好 .找到了未曾报道的立体异构体 .对这一立体异构体进行了高级别理论方法CCSD(T) /6 311G(d)和QCISD(T) /6 311G(d)的几何结构优化和振动频率计算 ,表明它是一个稳定的立体异构体 .在所研究的几种反应中 ,ClONO2 分解为NO2 +ClO是最容易进行的反应 .而ClONO2 异构为立体异构体的反应是最难进行的反应 .其所需克服的过渡态的能垒为 4 81.5 2kJ/mol,而反应吸收能量为 2 99.85kJ/mol.次难进行的是ClONO2 经TS1到反应中间体M1,再经TS12而分解为ClNO +O2 的反应 .这个反应通道所需克服过渡态的能垒为 4 2 1.5 5kJ/mol,反应吸收能量为 15 7.98kJ/mol.从以上分析可知 ,和ClO +NO2 反应生成ClONO2 比较 ,ClONO2 具有较好的稳定性 .     

中华古编钟的乐钟性质研究

基于圆柱形模型中弹性驻波的理论振型,结合椭圆形柱面的刚性和曲率分布特征,对古编钟的一钟双音和短延音等声学特性作出物理分析;基于对测试编钟(加长钟枚的编钟)进行的频谱实验研究,提出钟枚除了装饰作用外,还具有滤去高频、改善音质的作用.     

Multiple scattering of HF radio waves propagating across the sea surface

A problem that is of considerable importance to the HF communications and radar communities is the calculation of the spatio-temporal modulations imposed on a radio wave as a result of propagating across a rough sea surface. We derive equations, in the form of a multiple-scattering series, describing the spatio-temporal structure of a radio wave at a point on the rough sea surface after propagation from an antenna at another point on the surface. We present calculations illustrating the sensitivity of the resultant Doppler spectra to ocean surface conditions, as described by well known parametric models. The generality of the approach means that it can easily accommodate user-specified antenna patterns, arbitrary coastline geometries, arbitrary sea-wave spectrum models, wave-field inhomogeneity and a wide range of seawater conductivities.     

Binding energies and K-edge spectra of NO chemisorbed on Ru(0001)

The electronic structures, adsorption energies and equilibrium geometries of chemisorbed NO on the Ru(0001) surface for several adsorption sites were determined using cluster models and employing the first principles, local density theory. Ground state one-electron eigenvalues and wave functions were obtained using the discrete variational method with numerical atomic bases. K-edge X-ray absorption spectra of both nitrogen and oxygen for each geometry were obtained using a scattered wave method. The effects of the surface on these spectra were studied by comparison with results from an isolated NO molecule and with the XPS and UPS experiments of Umbach et al. Both the NO and the NO-substrate vibration frequencies were calculated. Comparison between these theoretical results, recent electron energy loss spectra of Conrad et al. and early experiments of Thomas et al. suggests that NO is adsorbed only at threefold and top sites.     

Sample-Induced Resistance Estimation in Magnetic Resonance Experiments: Simulation and Comparison of Two Methods

Signal-to-noise ratio estimation in magnetic resonance experiments requires the knowledge of sample-induced resistance value, where the sample can be protein solutes, cell suspensions, plants, animals, portions of human body or saline solution phantoms. Many authors studied sample–coil interaction using homogeneous infinitely long cylinders, spheres or half-space as approximations of the sample geometry. However, in real magnetic resonance experiments, both sample shape and dimensions can be very different with respect to these models. This paper describes and compares two different methods developed by the authors for sample-induced resistance estimation, both useful for predicting the performance of radio-frequency coils strictly coupled to the sample, where the knowledge of a sample–coil interaction model permits to estimate the different noise contributors. The main goal of our research is testing the proposed algorithms and finding their limitations by comparing their performances for a simple case which uses a sample simplified geometry. The first method, based on the magnetostatic approach, employs vector potential calculation and can be easily implemented for simple coils and sample geometries. The second method uses finite-difference time-domain algorithm and permits to simulate systems with various geometries, without approximations in sample and coil geometries. Comparison with experimental data, performed on three homebuilt surface coils each of them successively tuned at three different frequencies, demonstrated the differences in accuracy of the developed methods.