Harmonic series (music)

Summary

A harmonic series (also overtone series) is the sequence of harmonics, musical tones, or pure tones whose frequency is an integer multiple of a fundamental frequency. Pitched musical instruments are often based on an acoustic resonator such as a string or a column of air, which oscillates at numerous modes simultaneously. At the frequencies of each vibrating mode, waves travel in both directions along the string or air column, reinforcing and canceling each other to form standing waves. Interaction with the surrounding air causes audible sound waves, which travel away from the instrument. Because of the typical spacing of the resonances, these frequencies are mostly limited to integer multiples, or harmonics, of the lowest frequency, and such multiples form the harmonic series. The musical pitch of a note is usually perceived as the lowest partial present (the fundamental frequency), which may be the one created by vibration over the full length of the string or air column, or a hi

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Abstract Based on binaural signals, i.e. the signals observed at the two ears, a listener can localize and recognize different sound sources and then focus on one of these. For decades, researchers have tried to invent a machine that can do the same under similar conditions. Despite all the efforts, the human auditory system is, by far, superior to any machine that has been devised. The topic of this thesis is computational techniques for the localization and separation of sources in binaural signals. In order to give an overview of different areas of research that have considered the problems of source localization and separation, we start with a review of existing techniques. This provides the background for the techniques that we propose subsequently. Binaural Localization The most important cues for localization of sound sources in binaural signals are the level and time differences between the ears. We propose a technique for the joint evaluation of these cues where noisy level difference estimates are combined with less noisy but ambiguous time difference estimates in order to provide accurate azimuth estimates. The proposed technique enables the localization of sources and the tracking of these in dynamic scenes. Head model Based on a study of the level and time differences as function of azimuth angle for different heads, we propose a generic model that is parametrized by the distance between the ears only. This enables the use of the binaural localization technique mentioned above for a listener whose head related transfer functions have not been measured. Binaural separation For the separation of sources we propose a method based on spatial windowing in the azimuth parameter space. Separation of overlapping partials Finally, we propose a technique for the separation of overlapping partials in mixtures of harmonic instruments. The technique is based on the similarity of temporal envelopes between the different partials of a harmonic note.

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Camille Sophie Brès, Jianqi Hu, Edgars Nitiss, Anton Stroganov

Quasi-phase-matching has long been a widely used approach in nonlinear photonics, enabling efficient parametric frequency conversions such as second-harmonic generation. However, in silicon photonics the task remains challenging, as materials best suited for photonic integration lack second-order susceptibility (χ(2)), and means for achieving momentum conservation are limited. Here we present optically reconfigurable quasi-phase-matching in large-radius silicon nitride microresonators, resulting in up to 12.5-mW on-chip second-harmonic generated power and a conversion efficiency of 47.6% W−1. Most importantly, we show that such all-optical poling can occur unconstrained from intermodal phase-matching, leading to broadly tunable second-harmonic generation. We confirm the phenomenon by two-photon imaging of the inscribed χ(2) grating structures within the microresonators as well as by in situ tracking of both the pump and second-harmonic mode resonances during all-optical poling. These results unambiguously establish that the photogalvanic effect, responsible for all-optical poling, can overcome phase mismatch constraints, even in resonant systems.

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