Effects of Twisting and Surface Finish on the Mechanical Properties of Natural Gut Harp Strings.

Natural gut harp strings are made from twisted bundles of gut strips, which are dried, ground, and varnished. The effects of varying the twist angle and surface finishing on the mechanical properties of gut harp strings have been explored. Strings were tested over a range of twist angles from 23.5∘ to 58.3∘, and with all four combinations of ground or unground and varnished or unvarnished surface finishing. The principal effects of varying the degree of twisting were that the breaking strength and tensile Young's modulus both fell as the twist angle was increased. String makers must therefore make a compromise between sound quality and string strength and durability. Leaving the string unvarnished dramatically increased the sensitivity to changes in humidity, which, in turn, affected the thermal tuning sensitivity and creep behaviour. Grinding the string surface prior to varnishing had no significant effect on the behaviour, but did make some difference to the thermal tuning sensitivity if the string was left unvarnished. Increasing the humidity frequently triggered episodes of additional string creep. There appeared to be a threshold effect, with the additional creep triggered when the string linear density exceeded its previous maximum. When the string was not creeping, there appeared to be a strong coupling mechanism between changes in the linear density and complementary changes in the string tension, such that there was almost no net effect on the string frequency. This behaviour was independent of the twist angle and the surface finishing, suggesting that whatever the coupling mechanism was, it was not dependent on the twisted structure of the string.

A necessary condition for double-decay envelopes in stringed instruments.

Measurements of body vibration characteristics of five different stringed musical instruments have been used to address the question of whether and when they might be expected to produce transient response featuring a "double decay" sound profile. The phenomenon has been well documented and studied in the context of the piano but has not been systematically studied for other instruments. The results show considerable variation among instruments. The piano is indeed predicted to show double decays over most of its range. In the tested guitar, by contrast, double decays are likely to be confined to a few notes near strong body resonances. Other instruments fall between these extremes. The lute and the mandolin, both normally strung with double strings, should both exhibit double decays over much of their playing range, especially towards the higher end. The banjo is single-strung but is also predicted to show strong double decays, especially for higher notes in its range.

Playability of the wolf note of bowed string instruments.

Playability is an important aspect of the evaluation of bowed string instruments. The well-known "wolf note" of a cello is a particularly obvious playability issue, and it has been suggested that susceptibility to wolfiness might be deduced directly from a measurement of the Schelleng minimum bow force for the playing of a steady note. This prediction is explored by comparing physical measurements with the experience of players after making controlled mechanical changes to a cello. Experienced luthiers and musicians made subjective judgements of changes in the severity of the wolf note, under blinded conditions. The results strongly suggest a direct and intimate link between the measurable acoustical parameter and perceptual discrimination. This simple acoustical measurement can help instrument makers to identify problem notes, and to assess the effectiveness of different possible interventions.

Comparison of Mechanical Properties of Natural Gut and Synthetic Polymer Harp Strings.

The long-term mechanical behaviour of a number of fluorocarbon and gut harp strings has been examined, and the results compared with a previous study of rectified nylon strings. The stretching behaviour of the three materials was studied via different measures of the Young's modulus; with test time scales on the order of weeks, minutes, and milliseconds. The strings were subjected to cyclic variations in temperature, enabling various aspects of their thermal behaviour to be investigated. The effects of humidity changes on gut strings were also examined. The behaviour of the fluorocarbon strings was found to be similar in many ways to that of the nylon strings, despite their different chemical formulation and significantly higher density. In particular, the faster measures of Young's modulus were found to show an almost identical strong variation with the applied stress; while the thermal behaviour of both materials was largely determined by the balance between opposing effects associated with thermal contraction and thermal variations in the Young's modulus. The gut strings showed some similarities of behaviour to the synthetic materials, but also major differences. All three measures of the Young's modulus remained constant as the applied stress was increased. The gut strings were far more sensitive to changes in humidity than the synthetic materials, although some of the results, especially the thermal tuning sensitivity of the strings when held at constant length, displayed remarkable stability under changing humidity. The observed behaviour suggests very strongly that there is significant coupling between humidity-related changes in the linear density of a gut string and complementary changes in its tension.

Effect of back wood choice on the perceived quality of steel-string acoustic guitars.

Some of the most prized woods used for the backs and sides of acoustic guitars are expensive, rare, and from unsustainable sources. It is unclear to what extent back woods contribute to the sound and playability qualities of acoustic guitars. Six steel-string acoustic guitars were built for this study to the same design and material specifications except for the back/side plates which were made of woods varying widely in availability and price (Brazilian rosewood, Indian rosewood, mahogany, maple, sapele, and walnut). Bridge-admittance measurements revealed small differences between the modal properties of the guitars which could be largely attributed to residual manufacturing variability rather than to the back/side plates. Overall sound quality ratings, given by 52 guitarists in a dimly lit room while wearing welder's goggles to prevent visual identification, were very similar between the six guitars. The results of a blinded ABX discrimination test, performed by another subset of 31 guitarists, indicate that guitarists could not easily distinguish the guitars by their sound or feel. Overall, the results suggest that the species of wood used for the back and sides of a steel-string acoustic guitar has only a marginal impact on its body mode properties and perceived sound.

Mechanical Properties of Nylon Harp Strings.

Monofilament nylon strings with a range of diameters, commercially marketed as harp strings, have been tested to establish their long-term mechanical properties. Once a string had settled into a desired stress state, the Young's modulus was measured by a variety of methods that probe different time-scales. The modulus was found to be a strong function of testing frequency and also a strong function of stress. Strings were also subjected to cyclical variations of temperature, allowing various thermal properties to be measured: the coefficient of linear thermal expansion and the thermal sensitivities of tuning, Young's modulus and density. The results revealed that the particular strings tested are divided into two groups with very different properties: stress-strain behaviour differing by a factor of two and some parametric sensitivities even having the opposite sign. Within each group, correlation studies allowed simple functional fits to be found to the key properties, which have the potential to be used in automated tuning systems for harp strings.

Motion of the cello bridge.

This paper presents an experimental investigation of the motion of the bridge of a cello, in the frequency range up to 2 kHz. Vibration measurements were carried out on three different cellos, and the results used to determine the position of the Instantaneous Centre of rotation of the bridge, treated as a rigid body. The assumption of rigid body rotation is shown to give a good approximation up to at least 1 kHz. The instantaneous centre moves from the sound-post side of the bridge at the lowest frequencies towards the bass-bar side at higher frequencies, remaining close to the surface of the top plate of the instrument. The trajectory as a function of frequency sheds light on the response of the cello in response to excitation by bowing the different strings. The correlation between the motion at the four string notches and directly measured transfer functions at these four notches is examined and verified for some important low-frequency body resonances.

Are there reliable constitutive laws for dynamic friction?

Structural vibration controlled by interfacial friction is widespread, ranging from friction dampers in gas turbines to the motion of violin strings. To predict, control or prevent such vibration, a constitutive description of frictional interactions is inevitably required. A variety of friction models are discussed to assess their scope and validity, in the light of constraints provided by different experimental observations. Three contrasting case studies are used to illustrate how predicted behaviour can be extremely sensitive to the choice of frictional constitutive model, and to explore possible experimental paths to discriminate between and calibrate dynamic friction models over the full parameter range needed for real applications.

Reliability of the input admittance of bowed-string instruments measured by the hammer method.

The input admittance at the bridge, measured by hammer testing, is often regarded as the most useful and convenient measurement of the vibrational behavior of a bowed string instrument. However, this method has been questioned, due especially to differences between human bowing and hammer impact. The goal of the research presented here is to investigate the reliability and accuracy of this classic hammer method. Experimental studies were carried out on cellos, with three different driving conditions and three different boundary conditions. Results suggest that there is nothing fundamentally different about the hammer method, compared to other kinds of excitation. The third series of experiments offers an opportunity to explore the difference between the input admittance measuring from one bridge corner to another and that of single strings. The classic measurement is found to give a reasonable approximation to that of all four strings. Some possible differences between the hammer method and normal bowing and implications of the acoustical results are also discussed.

The acoustics of the violin: a review.

To understand the design and function of the violin requires investigation of a range of scientific questions. This paper presents a review: the relevant physics covers the nonlinear vibration of a bowed string, the vibration of the instrument body, and the consequent sound radiation. Questions of discrimination and preference by listeners and players require additional studies using the techniques of experimental psychology, and these are also touched on in the paper. To address the concerns of players and makers of instruments requires study of the interaction of all these factors, coming together in the concept of 'playability' of an instrument.

Observation of locked phase dynamics and enhanced frequency stability in synchronized micromechanical oscillators.

Even though synchronization in autonomous systems has been observed for over three centuries, reports of systematic experimental studies on synchronized oscillators are limited. Here, we report on observations of internal synchronization in coupled silicon micromechanical oscillators associated with a reduction in the relative phase random walk that is modulated by the magnitude of the reactive coupling force between the oscillators. Additionally, for the first time, a significant improvement in the frequency stability of synchronized micromechanical oscillators is reported. The concept presented here is scalable and could be suitably engineered to establish the basis for a new class of highly precise miniaturized clocks and frequency references.

Modeling nonlinearities in MEMS oscillators.

We present a mathematical model of a microelectromechanical system (MEMS) oscillator that integrates the nonlinearities of the MEMS resonator and the oscillator circuitry in a single numerical modeling environment. This is achieved by transforming the conventional nonlinear mechanical model into the electrical domain while simultaneously considering the prominent nonlinearities of the resonator. The proposed nonlinear electrical model is validated by comparing the simulated amplitude-frequency response with measurements on an open-loop electrically addressed flexural silicon MEMS resonator driven to large motional amplitudes. Next, the essential nonlinearities in the oscillator circuit are investigated and a mathematical model of a MEMS oscillator is proposed that integrates the nonlinearities of the resonator. The concept is illustrated for MEMS transimpedance-amplifier- based square-wave and sine-wave oscillators. Closed-form expressions of steady-state output power and output frequency are derived for both oscillator models and compared with experimental and simulation results, with a good match in the predicted trends in all three cases.

Exploring violin sound quality: investigating English timbre descriptors and correlating resynthesized acoustical modifications with perceptual properties.

Performers often discuss the sound quality of a violin or the sound obtained by particular playing techniques, calling upon a diverse vocabulary. This study explores the verbal descriptions, made by performers, of the distinctive timbres of different violins. Sixty-one common descriptors were collected and then arranged by violinists on a map, so that words with similar meanings lay close together, and those with different meanings lay far apart. The results of multidimensional scaling demonstrated consistent use among violinists of many words, and highlighted which words are used for similar purposes. These terms and their relations were then used to investigate the perceptual effect of acoustical modifications of violin sounds produced by roving of the levels in five one-octave wide bands, 190-380, 380-760, 760-1520, 1520-3040, and 3040-6080 Hz. Pairs of sounds were presented, and each participant was asked to indicate which of the sounds was more bright, clear, harsh, nasal, or good (in separate runs for each descriptor). Increased brightness and clarity were associated with moderately increased levels in bands 4 and 5, whereas increased harshness was associated with a strongly increased level in band 4. Judgments differed across participants for the qualities nasal and good.

Perceptual studies of violin body damping and vibrato.

This work explored how the perception of violin notes is influenced by the magnitude of the applied vibrato and by the level of damping of the violin resonance modes. Damping influences the "peakiness" of the frequency response, and vibrato interacts with this peakiness by producing fluctuations in spectral content as well as in frequency and amplitude. Initially, it was shown that thresholds for detecting a change in vibrato amplitude were independent of body damping, and thresholds for detecting a change in body damping were independent of vibrato amplitude. A study of perceptual similarity using triadic comparison showed that vibrato amplitude and damping were largely perceived as independent dimensions. A series of listening tests was conducted employing synthesized, recorded, or live performance to probe perceptual responses in terms of "liveliness" and preference. The results do not support the conclusion that liveliness results from the combination of the use of vibrato and a "peaky" violin response. Judgments based on listening to single notes showed inconsistent patterns for liveliness, while preferences were highest for damping that was slightly less than for a reference (real) violin. In contrast, judgments by players based on many notes showed preference for damping close to the reference value.

Perceptual thresholds for detecting modifications applied to the acoustical properties of a violin.

This study is the first step in the psychoacoustic exploration of perceptual differences between the sounds of different violins. A method was used which enabled the same performance to be replayed on different "virtual violins," so that the relationships between acoustical characteristics of violins and perceived qualities could be explored. Recordings of real performances were made using a bridge-mounted force transducer, giving an accurate representation of the signal from the violin string. These were then played through filters corresponding to the admittance curves of different violins. Initially, limits of listener performance in detecting changes in acoustical characteristics were characterized. These consisted of shifts in frequency or increases in amplitude of single modes or frequency bands that have been proposed previously to be significant in the perception of violin sound quality. Thresholds were significantly lower for musically trained than for nontrained subjects but were not significantly affected by the violin used as a baseline. Thresholds for the musicians typically ranged from 3 to 6 dB for amplitude changes and 1.5%-20% for frequency changes. Interpretation of the results using excitation patterns showed that thresholds for the best subjects were quite well predicted by a multichannel model based on optimal processing.