A team of scientists at Queen Mary University of London (QMUL) focus on bringing individuals closer to understanding the musical experience through a unique approach used to study a common musical effect called vibrato.
Vibrato is the up-down oscillation in pitch introduced during vocal or instrumental performance in order to include expressivity and enable sound projection. Vibrato is commonly used in opera. A vibrato that is skillfully executed and perfectly timed can immensely improve the sound quality of a note, and induce powerful emotional responses in the listener.
The Journal of Mathematics and Music features a report on this new approach to vibrato analysis. This report describes the use of the Filter Digitalization Method (FDM) for the first time in music signal processing. The approach is used to analyze nuclear magnetic resonance and molecular dynamics and has origins in quantum physics.
We are now one step closer to understanding the mechanics of music communication, the nuances that performers introduce to the music, and the logic behind them.
Professor Elaine Chew, Centre for Digital Music at QMUL's School of Electronic Engineering and Computer Science (EECS)
The ability of the new technique to identify and estimate characteristics from extremely fine slivers of information is specifically used in vibrato analysis and also enables researchers to study music signals with increased precision than before.
Typically, vibratos oscillate with a period of 125 - 250 milliseconds per cycle, or at a rate of 4 - 8 cycles per second. The degree to which the pitch is bent down or up can be up to half a semitone.
Vibratos happen extremely fast and because of this the traditional techniques requiring a comparatively large window for examining the music signal have till now faced difficulties in accurately capturing their characteristics.
The FDM algorithm was initially developed to efficiently and effectively explore the complicated quantum dynamical resonances of atoms and molecules. Although musical signals are very different from their quantum counterparts, mathematically they share many similarities, including the characteristics of their resonances. In fact, we found that, because they oscillate with time, the harmonics in musical signals can be more complicated to analyse than their quantum counterparts.
Dr Khalid Rajab, QMUL's School of Electronic Engineering and Computer Science (EECS)
The research developed from a project to model the variations existing between playing on violin and erhu, a two-stringed Chinese fiddle.
Professor Chew said: "When music for a folk instrument like the erhu is performed on a violin, it lacks the stylistic and expressive qualities of the original. One of the major sources of these differences lies in the way in which notes are elaborated (with vibrato) and the way in which the instrumentalists make their transitions between notes (using portamentos). We were interested in creating computing tools that can help reveal these differences."
The research is part of the PhD project of Luwei Yang, first author and a China Scholarship Council doctoral candidate and Research Assistant in EECS.
Being an ardent erhu player, Yang stated that, "In erhu, as in violin playing, vibrato is frequently employed to mimic the liveliness and colorful expressivity of the human voice. Contemporary erhu vibrato styles were deeply influenced by violin techniques, so it is fascinating to dig deeper into characterizing the differences between them."
The researchers anticipate that the new technique will help music teachers and musicians in their mission to attain the perfect vibrato, and assist sound artists in developing sounding vibrato effects that are more natural in audio production. They also hope that the new technique will enable researchers to map stylistic trends in vibrato use across time and cultures.