Gabriel Weinreich

Coupled piano strings

The admittance of the piano bridge has a crucial effect on piano tone by coupling together the strings belonging to one note into a single dynamical system. In this paper, we first develop theoretical expressions that show how the rate of energy transmission to the bridge as a function of time (including the phenomena of beats and ’’aftersound’’) depends on bridge admittance, hammr irregularities, and the exact state in which the piano is tuned. We then present experimental data showing the effects of mutual string coupling on beats and aftersound, as well as the great importance of the two polarizations of the string motion. The function of the una corda pedal in controlling the aftersound is explained, and the stylistic possibilities of a split damper are pointed out. The way in which an excellent tuner can use fine tuning of the unisons to make the aftersound more uniform is discussed.

Method for measuring acoustic radiation fields

An acoustic field which varies sinusoidally in time is completely determined by the complex values of its pressure on two concentric spheres. We have developed an experimental procedure which carries out such a measurement. If the source of sound is located inside the inner sphere, we experimentally obtain an expansion in spherical waves whose outgoing and incoming (that is, reflected) components are independently determined. This paper describes both the apparatus and the underlying theory, and presents illustrative results on the wave reflected from the wall of an anechoic chamber.

Directional tone color

Above about 1 kHz, the angular radiation pattern of a violin begins to vary rapidly not only with direction but also with frequency, typically changing drastically from one semitone to the next. In an enclosed space, this characteristic, which we have named “directional tone color,” can sometimes produce the illusion that each note played by a solo violin comes from a different direction, endowing fast passages with a special flashing brilliance. It also has important consequences for the perception of vibrato, for the difference in sound between a solo violin and an orchestral section playing in unison, for the problem of reproducing violin sounds through a loudspeaker, and possibly for the mysterious quality called “projection.” This paper introduces the theoretical basis of directional tone color, presents data to support its existence, and discusses the various ways in which it can be musically important.

Sound hole sum rule and the dipole moment of the violin

It is shown both theoretically and experimentally that at long enough wavelengths the radiation pattern of a violin, or of any similar instrument with a sound hole in its shell, becomes that of a dipole. The transition from this region to the one in which the monopole dominates is traced in detail. The experimental method used to measure the ‘‘radiativities’’ of the violin, that is, the amplitudes of the various multipole moments developed per unit force applied to the bridge by the vibrating string, utilizes an extension of the reciprocity principle in which the multipole fields play the role of generalized coordinates. Absolute measurements of the radiativity are obtained, and their phases and amplitudes explained in terms of the mechanical motions of the violin shell and the enclosed air.

Music and Technology in the Twentieth Century

Contents:Introduction Keyboards, Crankshafts and Communication Electronic Instruments It all Began with a Broken Organ The Social Contruction of the Early My Soul is in the Machine Music and the City Monin On A Servile Imitation From Polka to Punk The Orgins of the 45 rpm Record at RCA Victor Tape Recording and Music Making Musicians and the Sounf Revolution Aesthetics out of Exigency The Social Reconstruction of a Reverse Salient in Electrical Guitar Technology Sound Sampling New Technology Musical Education and the New Media

Three-dimensional mechanical admittance: Theory and new measurement method applied to the violin bridge

The mechanical admittance (or mobility) measures the generalized velocities of a system under generalized forces, whereas the impedance measures the forces when velocities are imposed. It is shown that generally, and in cases of practical interest, the experimental determination of the impedance and that of the admittance must comply with different requirements. Therefore, one description cannot be derived from the other unless the degrees of freedom of the system which are not measured are properly dealt with. Some of the experimental methods presented in the literature are discussed along these lines. A new method is proposed for measuring locally the mobility matrix: it is based on comparison with a known mechanical impedance and requires no force measurements. A realization is presented in the case of the bridge of a violin and a quarter-size cello. Theoretical requirements are found to be met between ∼450–1500 Hz for the violin and ∼250–2000 Hz for the cello. Limitations of the method are found to be...

Elementary stability considerations for bowed‐string motion

Using the approach first pioneered by Raman, the Helmholtz motion of a bowed string is discussed as a special case of “two‐velocity motions,” in which a given point (at which the bow is located) alternates, in the course of a cycle, between two constant velocities. The fact that the bow typically presents a negative resistance to the string during the “slipping” part of the cycle is adduced as a reason for the “duty cycle,” that is, the fraction of the period that corresponds to slipping, to try to become as short as possible. It is shown that, for a string without dissipation or stiffness, this duty cycle can be arbitrarily low for general bow positions; data obtained with the “digital bow” illustrate this behavior. It is shown theoretically, and confirmed with computer simulations, that instabilities arising from the negative slipping resistance cannot be eliminated by assigning a finite positive value to the sticking resistance. The apparent stability of Helmholtz motion observed in real playing situat...

Klopsteg Memorial Lecture (August, 1992): What science knows about violins—and what it does not know

This is the edited text of the Klopsteg Lecture delivered to the Summer Meeting of the AAPT on August 13, 1992. It sketches the current state of knowledge about the violin—at least as seen by the author—in two parts, Physics of the Bowed String and The Violin as a Radiator of Sound, punctuated by a number of ‘‘meditations’’ about the nature of scientific knowledge.

Acoustical spectroscopy of violins

The normal modes of the violin system are investigated by studying its response to external excitation by an incident sinusoidal sound wave of variable frequency. Appropriate transducers are used to sense the vibration of wood, air, and strings. The data are analyzed by computer to yield information on the complex eigenfrequencies and eigenfunctions of the various normal modes. Methods of minimizing errors due to resonances outside the frequency window are discussed. Some representative results are shown.

Sound radiation from boxes with tone holes.

The normal modes of a hollow box with one or more sound holes, such as forms the radiating element of a typical string instrument, are combinations of ‘‘wood modes’’ and ‘‘air modes.’’ Wood modes have an average frequency spacing independent of frequency, whereas the average spacing of air modes is inversely proportional to frequency for frequencies low enough to make the ‘‘thin’’ dimension of the box smaller than half a wavelength, becoming inversely proportional to the square of the frequency for frequencies above that. As a result, the density of modes of, say, a violin, is generally dominated by wood modes at low frequencies and by air modes at high frequencies. The interplay of the two types of modes has radical consequences for the directivity of string instruments, in that the directional pattern can change drastically within very small musical intervals, perhaps accounting for the special ‘‘flashing brilliance’’ that such instruments exhibit. This talk will outline the theory of these effects and ...