Invariance in pitch perception

Information in speech and music is often conveyed through changes in fundamental frequency (f0), the perceptual correlate of which is known as "pitch". One challenge of extracting this information is that such sounds can also vary in their spectral content due to the filtering imposed by a vocal tract or instrument body. Pitch is envisioned as invariant to spectral shape, potentially providing a solution to this challenge, but the extent and nature of this invariance remain poorly understood. We examined the extent to which human pitch judgments are invariant to spectral differences between natural sounds. Listeners performed up/down and interval discrimination tasks with spoken vowels, instrument notes, or synthetic tones, synthesized to be either harmonic or inharmonic (lacking a well-defined f0). Listeners were worse at discriminating pitch across different vowel and instrument sounds compared to when vowels/instruments were the same, being biased by differences in the spectral centroids of the sounds being compared. However, there was no interaction between this effect and that of inharmonicity. In addition, this bias decreased when sounds were separated by short delays. This finding suggests that the representation of a sound's pitch is itself unbiased, but that pitch comparisons between sounds are influenced by changes in timbre, the effect of which weakens over time. Pitch representations thus appears to be relatively invariant to spectral shape. But relative pitch judgments are not, even when spectral shape variation is naturalistic, and when such judgments are based on representations of the f0.

Study On Energy Dissipation Mechanism of an Impact Damper System

The objective of this paper is to investigate how higher damping is achieved by energy dissipation as high-frequency vibration due to the addition of impact mass. In an impact damper system, collision between primary and impact masses cause an exchange of momentum resulting in dissipation of energy. A numerical model is developed to study the dynamic behaviour of an impact damper system using a MDOF system with Augmented Lagrangian Multiplier contact algorithm. Mathematical modelling and numerical simulations are carried out using ANSYS FEA package. Studies are carried out for various mass ratios subjecting the system to low-frequency high amplitude excitation. Time responses obtained from numerical simulations at fundamental mode when the system is excited in the vicinity of its fundamental frequency are validated by comparing with experimental results. Magnification factor evaluated from numerical simulation results is comparable with those obtained from experimental data. The transient response obtained from numerical simulations is used to study the behaviour of first three modes of the system excited in vicinity of its fundamental frequency. It is inferred that dissipation of energy is a main reason for achieving higher damping for an impact damper system in addition to being transformed to heat, sound, and/or those required to deform a body.

Research on the Approximate Calculation Method of the Fundamental Frequency and Its Characteristics on a Tensioned String Bridge

As a new type of composite bridge, the dynamic structural characteristics of a tensioned string bridge need to be deeply studied. In this paper, based on the structural characteristics of a tensioned string bridge, the Rayleigh method is used to derive formulas for calculating the frequencies of vertical, antisymmetric and lateral bending vibrations. The characteristics of the vertical and lateral bending vibration frequencies are summarized. The fundamental frequencies of the antisymmetric vertical bending and lateral bending of the tensioned string bridge are the same as that of the single-span beam under the corresponding constraint conditions. The shape and physical characteristics of the main cable have no effect on the frequency. The vertical bending symmetrical vibration frequency of the tensioned string bridge is greater than the corresponding symmetrical vibration frequency of the simply supported beam. The shape and physical characteristics of the main cable have a greater impact on the vertical bending symmetrical vibration frequency than the lateral bending frequency, and the vertical bending symmetrical vibration frequency increases with an increasing rise-to-span ratio. The tension force of the main cable has no influence on the frequency of tensioned string bridges. The first-order frequency of the tensioned string bridge is generally the vertical bending symmetrical vibration frequency. By adopting a tensioned string bridge structure, the fundamental frequency of a structure can be greatly increased, thereby increasing the overall rigidity of the structure. Finally, an engineering example is applied with the finite element parameter analysis method to study the vibration frequency characteristics of the tensioned string bridge, which verifies the correctness of the formula derived in this paper. The finite element analysis results show that the errors between the derived formula in this paper and the finite element calculation results are less than 2%, indicating that the formula derived in this paper has high calculation accuracy and can meet the calculation accuracy requirements of engineering applications.

Radial Oscillations of Quark Stars Admixed with Dark Matter

We investigated compact stars consisting of cold quark matter and fermionic dark matter treated as two admixed fluids. We computed the stellar structures and fundamental radial oscillation frequencies of different masses of the dark fermion in the cases of weak and strong self-interacting dark matter. We found that the fundamental frequency can be dramatically modified and, in some cases, stable dark strange planets and dark strangelets with very low masses and radii can be formed.

SOME PROBLEMS OF OPTIMIZATION AND CONTROL OF THE NATURAL FREQUENCIES OF AN ELASTICALLY SUPPORTED RIGID BODY

The article analytically investigates the behavior of the frequencies and modes of natural vibrations of a rigid body, based on point elastic supports, when the position of the supports changes. It is assumed that the body is in plane motion and has two degrees of freedom. A linear description of body vibrations is accepted. The problems of determining such optimal positions of elastic supports at which the fundamental frequency of the structure reaches its maximum value are considered. Two groups of problems were studied. The first group concerns a body supported by only two supports. It was found that in the absence of restrictions on the position of the supports to maximize the fundamental natural frequency, these supports should be positioned so that the basic natural vibrations of the body are translational. Simple analytical conditions are formulated that must be satisfied by the corresponding positions of the supports. In real practical situations, these positions may be unreachable due to the presence of various kinds of restrictions due to design requirements. In this paper, optimization problems are considered taking into account a number of restrictions on the position of supports, typical for practice, expressed analytically by equations and inequalities. For each of the considered types of constraints, results are obtained that determine the optimal positions of the supports and the corresponding maximum values of the main natural frequencies. The approach applied allows us to consider other types of restrictions, which are not considered in the article. In the second group of problems for a body resting on an arbitrary number of supports, the optimal position of an additional elastic support introduced in order to maximize the fundamental frequency in fixed positions and the stiffness coefficients of the remaining supports was sought. It was found that this position depends on the value of the stiffness coefficient of the introduced support. Results are obtained that qualitatively and quantitatively characterize this position and the corresponding frequencies and modes of natural oscillations, including taking into account practically established limitations. The research method uses a qualitative approach, systematically based on the well-known Rayleigh theorem on the effect of imposing constraints on the free vibrations of an elastic structure.

The Frequency Spectrum and Time Frequency Analysis of Different Violins Classification as Tools for Selecting a Good-Sounding Violin

This work evaluates four violins from three distinct manufacturers, notably Eurostring, Stentor, and Suzuki, using a scientific approach. Eurostring1 and Eurostring2 were the names given to the two Eurostring units. The purpose of this study is to identify elements in various violins that could be used as tools for selecting a pleasantsounding violin by having them classified by a professional violinist. The signal’s time varying frequency was evaluated using a frequency spectrum and a time frequency plane, and the combination of frequency spectrum and time frequency domain is utilised. PicoScope oscilloscopes and Adobe Audition version 3 were used to record the acoustic spectra in terms of time and frequency. The time frequency plane is identified, and time frequency analysis (TFA) is produced by Adobe Audition spectrograms. The sound was processed in order to generate Fast Fourier Transform analysis: Fourier spectra (using PicoScope) and spectrograms (using Adobe Audition). Fourier spectra identify the intensity of the fundamental frequency and the harmonic spectra of the overtone frequencies. The highest frequencies that can be read are up to and including the 9th overtone. All violins have a constant harmonic overtone pattern with an uneven acoustic spectrum pattern. Eurostring1 showed inconsistent signal in the string G with 6th and 7th overtone missing, whereas Eurostring2 lack of the 6th overtone. Among the string D, only Eurostring1 display an exponential decay for the overtone. All the string A except for Suzuki showed nice and significant peak of fundamental and overtone. Stentor displays up to the 5th overtone. Among the string E, Suzuki showed inconsistent harmonic peak intensity. TFA revealed that the fundamental frequency of string E for Eurostring1 was lower than the first overtone. Only Eurostring1 has an uneven decay for the overtone frequency, whereas Eurostring2 exhibits a large exponential decay for the overtone frequency.

The Dependence of Flue Pipe Airflow Parameters on the Proximity of an Obstacle to the Pipe’s Mouth

This paper describes the influence of the presence of an obstacle near the flue pipe’s mouth on the air jet, which directly affects the parameters of the sound generated by the flue pipe. Labial pipes of the most common types of mouth were tested. The method of interval calculus was used instead of invasive measuring instruments. The obtained results prove that the proximity of an obstacle affects the sound’s fundamental frequency, as the airflow speed coming out of the flue pipe’s mouth changes. The relationship between the airflow speed, the value of the Reynolds number, and the Strouhal number was also established. The thesis of the influence of the proximity of an obstacle on the fundamental frequency of the sound of a flue pipe was generalized, and formulas for calculating the untuning of the sound of the pipe were presented for various types of mouth.