Related papers: Gerberto e la misura delle canne d'organo
Gerbert of Aurillac wrote to Constantine of Fleury in 978 a letter to describe in detail the procedure to point the star nearest to the North celestial pole. This was made to align a sphere equipped with tubes to observe the celestial pole,…
This work focuses on the length correction due to radiation effect of a duct discontinuity or at the surface of a perforated plate in the linear acoustic domain and at large wavelengths. Two results are obtained from the comparison of…
According to the classical Helmholtz picture, an organ pipe while generating its eigentone has two anti-nodes at the two open ends of a cylinder, the anti-nodes being taken as boundary condition for the corresponding sound. Since 1860 it is…
We describe here a class of acoustic metamaterials with fractal Hilbert space-filling and coiled geometry with equal tortuosity for noise mitigation. Experiments are performed using a four-microphone impedance tube and benchmarked against…
The theory of p-adic fractal strings and their complex dimensions was developed by the first two authors in [17, 18, 19], particularly in the self-similar case, in parallel with its archimedean (or real) counterpart developed by the first…
Audio fingerprinting provides an identifiable representation of acoustic signals, which can be later used for identification and retrieval systems. To obtain a discriminative representation, the input audio is usually segmented into shorter…
In this paper we get an estimate of Favard length of an arbitrary neighbourhood of an arbitrary self-similar Cantor set. Consider $L$ closed disjoint discs of radius $1/L$ inside the unit disc. By using linear maps of smaller disc onto the…
Some early violins have been reduced during their history to fit imposed morphological standards, while more recent ones have been built directly to these standards. We can observe differences between reduced and unreduced instruments,…
The mathematics of musical intervals and scales has been extensively studied. Vastly simplified, our ears seem to prefer intervals whose frequency ratios have small numerator and denominator, such as 2:1 (octave), 3:2 (perfect fifth), 4:3…
This paper presents an analytical formulation for correcting the diffraction associated to the second harmonic of an acoustic wave, more compact than that usually used. This new formulation, resulting from an approximation of the correction…
The dynamics of an organ pipe's mouth region has been studied by numerical simulations. The investigations presented here were carried out by solving the compressible Navier-Stokes equations under suitable initial and boundary conditions…
We describe an arrangement for simultaneous recording of speech and geometry of vocal tract in patients undergoing surgery involving this area. Experimental design is considered from an articulatory phonetic point of view. The speech and…
We compare numerically computed resonances of the human vocal tract with formants that have been extracted from speech during vowel pronunciation. The geometry of the vocal tract has been obtained by MRI from a male subject, and the…
The collaboration of mathematics in the two musical systems of Pythagorean sounds and of equal sounds is evident and opportune for generating the elements and managing their relationships. The only essential notion for a rational…
In this paper we have defined one function that has been used to construct different fractals having fractal dimensions between 1.58 and 2. Also, we tried to calculate the amount of increment of fractal dimension in accordance with the base…
If our aesthetic preferences are affected by fractal geometry of nature, scaling regularities would be expected to appear in all art forms, including music. While a variety of statistical tools have been proposed to analyze time series in…
The relations between production and perception in 4-year-old children were examined in a study of compensation strategies for a lip-tube perturbation. Acoustic and perceptual analyses of the rounded vowel [u] produced by twelve 4-year-old…
This paper addresses alternative procedures to the ESO supplied pipeline procedures for the reduction of UVES spectra of two quasar spectra to determine the value of the fundamental constant mu = Mp/Me at early times in the universe. The…
A class of numerical quadrature rules is derived, with equally-spaced nodes, and unit weights except at a few points at each end of the series, for which "corrections" (not using any further information about the integrand) are added to the…
In this paper, we study the problem of computing the diameter of a set of $n$ points in $d$-dimensional Euclidean space for a fixed dimension $d$, and propose a new $(1+\varepsilon)$-approximation algorithm with $O(n+ 1/\varepsilon^{d-1})$…