Generating Quadratic Difference Tone Spectra for Auditory Distortion Synthesis

Quadratic difference tones are one of a family of perceptual phenomena that arise from the neuromechanics of the auditory system in response to particular properties of physical sound. Long deployed as ’ghost tones’ by improvisers, computer musicians and sound artists, in this paper we address the problem of creating quadratic difference tone spectra, where a QDT fundamental and harmonic overtone series is specified and the necessary acoustic components needed to evoke it are synthesised. A numerical algorithm for solving target distributions of amplitudes for the synthesis of quadratic distortion tone spectra is proposed. The algorithm aims to find a solution for a target distribution of amplitudes that matches the desired spectrum as closely as possible. The experiments were conducted using different parameter settings and target distributions. The results show that the algorithm is effective in solving the problem in the majority of cases, with at least 99% of the cases being solvable in real-time. The article also discusses the convergence of the algorithm and its potential mathematical properties. Additionally, audio examples implemented in Max are provided to demonstrate the synthesis of different quadratic distortion tone spectra using this approach

Generating Quadratic Difference Tone Spectra for Auditory Distortion Synthesis

Quadratic difference tones are one of a family of perceptual phenomena that arise from the neuromechanics of the auditory system in response to particular properties of physical sound. Long deployed as ’ghost tones’ by improvisers, computer musicians and sound artists, in this paper we address the problem of creating quadratic difference tone spectra, where a QDT fundamental and harmonic overtone series is specified and the necessary acoustic components needed to evoke it are synthesised. A numerical algorithm for solving target distributions of amplitudes for the synthesis of quadratic distortion tone spectra is proposed. The algorithm aims to find a solution for a target distribution of amplitudes that matches the desired spectrum as closely as possible. The experiments were conducted using different parameter settings and target distributions. The results show that the algorithm is effective in solving the problem in the majority of cases, with at least 99% of the cases being solvable in real-time. The article also discusses the convergence of the algorithm and its potential mathematical properties. Additionally, audio examples implemented in Max are provided to demonstrate the synthesis of different quadratic distortion tone spectra using this approach

Audiográficos: implementación y evaluación de un programa informático para el aprendizaje de la interpretación y representación matemática de coordenadas a través de la música y el sonido.

En este artículo se presenta el diseño, desarrollo y evaluación de una solución modular informática denominada AudioGráficos, parte de un proyecto de mayor alcance denominado Picalab: MMSI (Laboratorio Virtual para el Programa de Innovación en Ciencias y Arte). Este programa proporciona actividades que relacionan las matemáticas con la música y el sonido. Su objetivo es el de favorecer los procesos de aprendizaje de representación matemática a través de actividades en las que el alumnado tiene que realizar gráficos de ejes de coordenadas que describen la variación de la frecuencia del sonido en el tiempo (patrones de altura). AudioGráficos ha sido diseñado para su uso en los niveles tercero cuarto y quinto de Ed. Primaria en el sistema educativo de Chile. Para la realización del programa, se siguió una metodología en tres etapas; 1) generación de metáforas significativas que vinculan la representación de coordenadas y el sonido; 2) desarrollo de un prototipo funcional con una guía didáctica, sometido a proceso de evaluación de usabilidad; 3) evaluación del programa por parte de profesores y alumnos (esta última mostrada en este artículo). Los resultados de valoración del alumnado (N=67) en 3 centros prioritarios chilenos muestran una excelente recepción del programa. Las dimensiones de evaluación ¿aprendizaje matemático, aprendizaje musical, global, técnica- han mostrado altas puntuaciones. Asimismo, muestra un excelente balance emocional positivo: el alumnado sintió más emociones positivas que negativas en el trabajo con el programa. Esto constituye un indicador de validación respecto a las dimensiones de evaluación reseñadas

Audiográficos: implementación y evaluación de un programa informático para el aprendizaje de la interpretación y representación matemática de coordenadas a través de la música y el sonido

En este artículo se presenta el diseño, desarrollo y evaluación de una solución modular informática denominada AudioGráficos, parte de un proyecto de mayor alcance denominado Picalab: MMSI (Laboratorio Virtual para el Programa de Innovación en Ciencias y Arte). Este programa proporciona actividades que relacionan las matemáticas con la música y el sonido. Su objetivo es el de favorecer los procesos de aprendizaje de representación matemática a través de actividades en las que el alumnado tiene que realizar gráficos de ejes de coordenadas que describen la variación de la frecuencia del sonido en el tiempo (patrones de altura). AudioGráficos ha sido diseñado para su uso en los niveles tercero cuarto y quinto de Ed. Primaria en el sistema educativo de Chile. Para la realización del programa, se siguió una metodología en tres etapas; 1) generación de metáforas significativas que vinculan la representación de coordenadas y el sonido; 2) desarrollo de un prototipo funcional con una guía didáctica, sometido a proceso de evaluación de usabilidad; 3) evaluación del programa por parte de profesores y alumnos (esta última mostrada en este artículo). Los resultados de valoración del alumnado (N=67) en 3 centros prioritarios chilenos muestran una excelente recepción del programa. Las dimensiones de evaluación –aprendizaje matemático, aprendizaje musical, global, técnica- han mostrado altas puntuaciones. Asimismo, muestra un excelente balance emocional positivo: el alumnado sintió más emociones positivas que negativas en el trabajo con el programa. Esto constituye un indicador de validación respecto a las dimensiones de evaluación reseñada

Sound Synthesis with Auditory Distortion Products

This article describes methods of sound synthesis based on auditory distortion products, often called combination tones. In 1856, Helmholtz was the first to identify sum and difference tones as products of auditory distortion. Today this phenomenon is well studied in the context of otoacoustic emissions, and the “distortion” is understood as a product of what is termed the cochlear amplifier. These tones have had a rich history in the music of improvisers and drone artists. Until now, the use of distortion tones in technological music has largely been rudimentary and dependent on very high amplitudes in order for the distortion products to be heard by audiences. Discussed here are synthesis methods to render these tones more easily audible and lend them the dynamic properties of traditional acoustic sound, thus making auditory distortion a practical domain for sound synthesis. An adaptation of single-sideband synthesis is particularly effective for capturing the dynamic properties of audio inputs in real time. Also presented is an analytic solution for matching up to four harmonics of a target spectrum. Most interestingly, the spatial imagery produced by these techniques is very distinctive, and over loudspeakers the normal assumptions of spatial hearing do not apply. Audio examples are provided that illustrate the discussion

Application of Response Surface Methodologies to Optimize High-Added Value Products Developments: Cosmetic Formulations as an Example

In recent years, green and advanced extraction technologies have gained great interest to revalue several food by-products. This by-product revaluation is currently allowing the development of high value-added products, such as functional foods, nutraceuticals, or cosmeceuticals. Among the high valued-added products, cosmeceuticals are innovative cosmetic formulations which have incorporated bioactive natural ingredients providing multiple benefits on skin health. In this context, the extraction techniques are an important step during the elaboration of cosmetic ingredients since they represent the beginning of the formulation process and have a great influence on the quality of the final product. Indeed, these technologies are claimed as efficient methods to retrieve bioactive compounds from natural sources in terms of resource utilization, environmental impact, and costs. This review offers a summary of the most-used green and advanced methodologies to obtain cosmetic ingredients with the maximum performance of these extraction techniques. Response surface methodologies may be applied to enhance the optimization processes, providing a simple way to understand the extraction process as well as to reach the optimum conditions to increase the extraction efficiency. The combination of both assumes an economic improvement to attain high value products that may be applied to develop functional ingredients for cosmetics purposes