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Vibrato is a type of low-frequency frequency modulation. After learning about vibrato produced by the singing voice and musical instruments, you will experiment with the vibrato effect using an interactive LabVIEW VI and learn how to model the vibrato effect mathematically.
Vocalists and instrumentalists will introduce vibrato -- a low-frequency variation in pitch -- into long sustained notes primarily to add musical interest. Listeners are drawn to sounds with dynamic (changing) spectral characteristics, and vibrato makes a sustained note sound much more interesting than a constant frequency. Moreover, sustaining a long note at a constant frequency with sufficient accuracy to avoid drifting "out of tune" is challenging for vocalists and wind-based instruments. Vibrato is produced in a variety of ways, depending on the instrument. Trombonists wiggle the slide slightly to change the overall tube length that sets pitch. A violinist will rock his or her left hand that presses the string to slightly alter the effective string length.
Download and run the LabVIEW VI vibrato.vi to demonstrate the vibrato effect applied to a sinusoidal oscillator. This VI requires the TripleDisplay front-panel indicator. Vibrato normally requires two controls: rate determines how quickly the frequency should fluctuate, and depth establishes the amount of frequency fluctuation. The third control adjusts the pitch of the sinusoidal oscillator.
Vibrato is a type of low-frequency frequency modulation . In this section the mathematical equations necessary to model the vibrato effect will be developed.In addition, two important effects associated with the singing voice will be discussed to produce a more realistic model.
The screencast video develops the mathematical equation needed to model the vibrato effect in perhaps an intuitively-obvious (but unfortunately incorrect) way. After watching the video, try the interactive front panel VI below that is part of the demonstration, then respond to the exercise questions to ensure that you understand the main concepts.
Download and run the LabVIEW VI vibrato_naive.vi .
What is the main auditory effect produced by the intuitively-obvious approach to modeling vibrato?
The amount of frequency fluctuation (deviation) increases with time rather than remaining constant.
When modifying the basic sinusoidal oscillator equation, which part -- frequency or phase - requires the most attention?
Phase; the entire argument to the sine function must be considered as a time-varying phase function $\varphi (t)$
How should the phase function $\varphi (t)$ be designed to achieve vibrato?
A ramp function with a superimposed sinusoidal variation.
The screencast video develops the mathematical equation needed to model the vibrato effect for a constant low-frequency variation.
Refer again to the LabVIEW VI vibrato.vi you downloaded earlier.
Several effects become immediately apparent when listening to an opera singer:
These effects are also evident when listening to expressive instrumentalists from the strings, brass, and woodwind sections of the orchestra. The mathematical model for vibrato can therefore be improved by (1) making the vibrato depth track (or be proportional to) the intensity envelope of the sound, and by (2) making the vibrato rate track the intensity envelope. Modeling the "brightness" effect would require adding overtones or harmonics to the sound.
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