Forum for Science, Industry and Business

Sponsored by:     3M 
Search our Site:

 

Mathematical model for the vibrato

18.08.2004


As her PhD defended at the Public University of Navarre, telecommunications engineer Ixone Arroabarren has analysed the vibrato, one of the most important tools of classical singers.



The study applies both to the teaching of singing in music as well as to the medical treatment of voice pathologies. It has put forward a mathematical model for the production of the voice that can be used both in the medical study/detection of pathologies of the vocal chords and speech as well as the teaching of the art of singing. This PhD has been developed within the framework of the research project awarded by CEIN as the best Project for the Transference of Research Result.

Amongst these differences, the engineer points out, that the vibrato is an exclusively musical characteristic which is of great use to the classical singer because, on the one hand, it enables the unmasking of possible off-key notes and, on the other, it makes sure the listener does not have the sensation that they are listening to the same sound. Furthermore, the theme itself has been of great interest to many researchers in areas such as physiology and musicology.


From an acoustic perspective, the vibrato in classical singing can be defined as a regular fluctuation in the fundamental frequency of the pitch or signal, the timbre and/or the volume of a single note. Nevertheless, the origin of these variations and their relation with mechanisms of voice production are still enigmatic.

Ixone Arroabarren’s thesis studies this theme in depth with aim of carrying out a complete characterisation of the vibrato in the art of classical singing, starting from the measuring and the performance of its most relevant acoustic characteristics, and ending with an analysis of its origin and relation to the mechanisms of voice production. In brief, what we are doing is to relate what we perceive acoustically what is generated physiologically. In this way, we offer an explanation of the collateral effects which we knew were there but the exact origin of which was unknown.

To carry out this study a number of Signal Processing tools have been used - “the most suitable in each case, given that the overall study of the vibrato has implicitly involved the resolution of very different problems, from calculating the instantaneous frequency of non-stationary signals to estimating the source by means of Inverse Filtering.

As an end result of the researcher’s study, she puts forward a mathematical model of voice production that can be used both for the study and medical treatment of vocal chord and speech pathologies as well as for learning the art of singing.

This model of vibrato production has permitted relating the most important acoustic characteristics - fundamental frequency, timbre and volume, with the most relevant elements in voice production at the level of acoustics, glottal source and response of the vocal tract. In this way we have demonstrated that the features of both elements do not show substantial changes during vibrato, only the fundamental frequency of the glottal excitation varying.

All this enables two models of signal production of the vibrato to be put forward. A Non-Interactive Model of Vibrato Production, has enabled relating the most important acoustic characteristics – variations in fundamental frequency, timbre and volume, with and Response of Vocal Tract elements in voice production. With this it has been shown that variations in fundamental frequency generated in the Glottal Source are the cause of the variations in timbre and volume, dependant on both elements of voice production.

Besides, there is an Interactive Model of Vibrato Production, which enables us to state that the variations in amplitude and frequency of the harmonics of the acoustic signal can be used to obtain more information about the mechanisms of voice production. Moreover, this model admits the inclusion of additional effects, such as synchronic variations of the Response of the Vocal Tract, which may be related to similar effects identified by other authors through physiological studies.

Garazi Andonegi | alfa
Further information:
http://www.elhuyar.com

More articles from Physics and Astronomy:

nachricht Shape matters when light meets atom
05.12.2016 | Centre for Quantum Technologies at the National University of Singapore

nachricht Climate cycles may explain how running water carved Mars' surface features
02.12.2016 | Penn State

All articles from Physics and Astronomy >>>

The most recent press releases about innovation >>>

Die letzten 5 Focus-News des innovations-reports im Überblick:

Im Focus: Shape matters when light meets atom

Mapping the interaction of a single atom with a single photon may inform design of quantum devices

Have you ever wondered how you see the world? Vision is about photons of light, which are packets of energy, interacting with the atoms or molecules in what...

Im Focus: Novel silicon etching technique crafts 3-D gradient refractive index micro-optics

A multi-institutional research collaboration has created a novel approach for fabricating three-dimensional micro-optics through the shape-defined formation of porous silicon (PSi), with broad impacts in integrated optoelectronics, imaging, and photovoltaics.

Working with colleagues at Stanford and The Dow Chemical Company, researchers at the University of Illinois at Urbana-Champaign fabricated 3-D birefringent...

Im Focus: Quantum Particles Form Droplets

In experiments with magnetic atoms conducted at extremely low temperatures, scientists have demonstrated a unique phase of matter: The atoms form a new type of quantum liquid or quantum droplet state. These so called quantum droplets may preserve their form in absence of external confinement because of quantum effects. The joint team of experimental physicists from Innsbruck and theoretical physicists from Hannover report on their findings in the journal Physical Review X.

“Our Quantum droplets are in the gas phase but they still drop like a rock,” explains experimental physicist Francesca Ferlaino when talking about the...

Im Focus: MADMAX: Max Planck Institute for Physics takes up axion research

The Max Planck Institute for Physics (MPP) is opening up a new research field. A workshop from November 21 - 22, 2016 will mark the start of activities for an innovative axion experiment. Axions are still only purely hypothetical particles. Their detection could solve two fundamental problems in particle physics: What dark matter consists of and why it has not yet been possible to directly observe a CP violation for the strong interaction.

The “MADMAX” project is the MPP’s commitment to axion research. Axions are so far only a theoretical prediction and are difficult to detect: on the one hand,...

Im Focus: Molecules change shape when wet

Broadband rotational spectroscopy unravels structural reshaping of isolated molecules in the gas phase to accommodate water

In two recent publications in the Journal of Chemical Physics and in the Journal of Physical Chemistry Letters, researchers around Melanie Schnell from the Max...

All Focus news of the innovation-report >>>

Anzeige

Anzeige

Event News

ICTM Conference 2017: Production technology for turbomachine manufacturing of the future

16.11.2016 | Event News

Innovation Day Laser Technology – Laser Additive Manufacturing

01.11.2016 | Event News

#IC2S2: When Social Science meets Computer Science - GESIS will host the IC2S2 conference 2017

14.10.2016 | Event News

 
Latest News

High-precision magnetic field sensing

05.12.2016 | Power and Electrical Engineering

Construction of practical quantum computers radically simplified

05.12.2016 | Information Technology

NASA's AIM observes early noctilucent ice clouds over Antarctica

05.12.2016 | Earth Sciences

VideoLinks
B2B-VideoLinks
More VideoLinks >>>