Related papers: The Auditory Tuning of a Keyboard

We give a new analysis of a tuning problem in music theory, pertaining specifically to the approximation of harmonics on a two-dimensional keyboard. We formulate the question as a linear programming problem on families of constraints and…

The human sense of hearing perceives a combination of sounds 'in tune' if the corresponding harmonic spectra are correlated, meaning that the neuronal excitation pattern in the inner ear exhibits some kind of order. Based on this…

The aim is to explore new opportunities of the pitch organization of the musical scale. Specifically, a numerical comparison of the different musical temperaments among themselves in the degree of approximation of the Pythagorean scale is…

The tuning curve of the cochlea measures how large an input is required to elicit a given output level as a function of the frequency. It is a fundamental object of auditory theory, for it summarizes how to infer what a sound was on the…

Mathematical steps are developed to obtain optimised well tempered model "temperaments", based on a musical Well Temperament definition by H. Kelletat, that is derived from A. Werckmeister. This supports objective mathematical ranking of…

It has been asserted previously by the author that optimal control theory can be a valuable framework for theoretical studies about the shape that a wind instrument should have in order to satisfy some optimization criterion, inside a…

We present a dynamical model describing a predictable human behavior like the tuning process between singers. The purpose, inspired in physiological and behavioral grounds of human beings, is sensitive to all Fourier spectrum of each sound…

The dichotic method of hearing sound adapts in the region of musical harmony. The algorithm of the separation of the being dissonant voices into several separate groups is proposed. For an increase in the pleasantness of chords the…

The tone hole geometry of a clarinet is optimized numerically. The instrument is modeled as a network of one dimensional transmission line elements. For each (non-fork) fingering, we first calculate the resonance frequencies of the input…

The auditory and vestibular systems exhibit remarkable sensitivity of detection, responding to deflections on the order of Angstroms, even in the presence of biological noise. Further, these complex systems exhibit high temporal acuity and…

We present a formal language for assigning pitches to strings for fingered multi-string instruments, particularly the six-string guitar. Given the instrument's tuning (the strings' open pitches) and the compass of the fingers of the hand…

In classical music and in any genre of contemporary music, the tonal elements or notes used for playing are the same. The numerous possibilities of chords for a given instance in a piece make the playing, in general, very intricate, and…

The sigmoidal tuning curve that maximizes the mutual information for a Poisson neuron, or population of Poisson neurons, is obtained. The optimal tuning curve is found to have a discrete structure that results in a quantization of the input…

Designing and optimizing ion optical systems is often a complex and difficult task, which requires the use of computational tools to iterate and converge towards the desired characteristics and performances of the system. Very often these…

The sensory-triggered activity of a neuron is typically characterized in terms of a tuning curve, which describes the neuron's average response as a function of a parameter that characterizes a physical stimulus. What determines the shapes…

Western music is predominantly based on the equal temperament with a constant semitone frequency ratio of $2^{1/12}$. Although this temperament has been in use since the 19th century and in spite of its high degree of symmetry, various…

This work reviews the human auditory system, elucidating some of the specialized mechanisms and non-linear pathways along the chain of events between physical sound and its perception. Customary relationships between frequency, time, and…

Quantum annealing is a method to solve optimization problems that leverages quantum tunneling in a coupled qubit system. We present a detailed study of the coherence of a tunable capacitively-shunted flux qubit, designed for coherent…

We investigate a dynamically adapting tuning scheme for microtonal tuning of musical instruments, allowing the performer to play music in just intonation in any key. Unlike other methods, which are based on a procedural analysis of the…

A number of auditory models have been developed using diverging approaches, either physiological or perceptual, but they share comparable stages of signal processing, as they are inspired by the same constitutive parts of the auditory…