Vibrato

Three Attributes of Vibrato

Vibrato is characterized by three attributes: the extent or depth of the variation, the rate of the variation, and the waveshape of the variation.

Vibrato depth is the deviation in fundamental frequency either side of the note, and it is usually quoted or measured in “cents,” where one cent is one hundredth of an equal-tempered semitone. Because an equal tempered semitone has a frequency ratio of the twelfth root, or 2(1/12) = 1.05946, one cent will have a frequency ratio of the twelve hundredth root of 2, or 2(1/1200) = 1.0005778.

Vibrato rate is the frequency of variation in pitch, indicated by the number of oscillations or cycles per second, and is measured in Hertz (Hz). Typical vibrato rates in musical context lie approximately between 4 and 7 Hz, and rates between 5.5 Hz and 6.0 Hz are quite common. Vibrato rates below 4 Hz are usually heard as pitch undulations as the ear follows the rising and falling pitch variations.

[Page 1166]The vibrato waveshape of the underlying pitch variation is often observed as close to sinusoidal, but some skewing of the underlying sinusoidal pattern, along with additional high frequency undulations, are observed in practice.

The perceived pitch of a tone with vibrato is taken as the geometric mean of the fundamental frequency excursion, according to J. I. Shonle and K. E. Horan. It has been suggested that this is only appropriate for notes with at least four cycles of vibrato, as related by C. d'Alessandro and M. Castellengo, suggesting that the use of the geometric mean is only appropriate for notes that are (assuming a vibrato rate of 5.5 Hz) at least (4/5.5) = 0.73 second in length. This would, in musical terms, be a long note, and the majority of notes in music are considerably shorter than this. It would only be by chance that an exact whole number of vibrato cycles will be completed during a given note (again assuming a vibrato rate of 5.5 Hz, one cycle would last (1/5.5) = 0.182 second; 2 cycles would be twice this as 0.364 second; and 3 cycles would last 0.545 second).

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