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From Shirlee Emmons:
Some Science Background on Vibrato, Tremolo, and Wobble
If you are not interested in the scientific studies of vibrato, feel free to skip this section, although reading it will undoubtedly clarify your thinking on the subject.
As long ago as the 1930s, Carl E. Seashore initiated a study of the vibrato. Until only very recently when the issue was raised again, by Ingo R. Titze among others—without conclusions as yet—the results have stood as a hallmark. Seashore’s definition of a vibrato is the traditionally accepted one: “A good vibrato is a pulsation of pitch, usually accompanied by synchronous pulsations of loudness and timbre, of such extent and rate as to give a pleasing flexibility, tenderness, and richness to the tone.” Several important points were revealed in the Seashore study, among which were these, roughly extracted from that study:
1. The vibrato is a fundamental attribute of the artistically effective singing voice.
2. With the exception of trills, and an occasional note, every tone of every artist registers vibrato, whether long or short, gliding or steady, high or low, pianissimo or fortissimo. The upper and lower limits of each vibrato pulse...are always present.
3. Most singers cannot sing a tone that would have any semblance of desirability without using the vibrato.
4. It is this fact--that the vibrato is not heard even by the best musician as it really is--that lies at the bottom of the confusion which has prevailed on this subject.
5. The impression that a vibrato disappears in pianissimo is false. When a vibrato is not detected in pianissimo tones, it is a fault in the ear of the listener. The vibrato is actually present in production.
6. Both the extents and rates of the vibratos of excellent singers are in a continual state of flux.
7. The whole problem of the prominence of the vibrato in a voice revolves around auditory fusion. Probably the fusion of the slower vibrato rates is not as perfect as the fusion of the faster. At the slower rate...the vibrato is less of a unity since it is completely broken...Too fast a rate, such as in a flutter, also attracts attention more than the artistic vibrato rates.
8. Although the vibrato consists of a frequency pulsation in the sound wave, it has only one salient pitch in perception. This perceived pitch is approximately midway between the extremes. There are individual differences. The vibrato that one person hears as in tune may be appear to be out of tune to another person, pitch discrimination being equal.
9. Those who are most critical of the vibrato are generally those with very sharp ears for pitch discrimination. To those, a vibrato that is too slow or too wide is undesirable because the two notes cannot blend into one.
Dr. Friedrich Brodnitz, a leading New York otolaryngologist of the fifties, stated: “A well-trained voice exhibits always a certain amount of vibrato that gives changes, both in pitch and volume. By vibrato we understand small rhythmical changes in pitch and volume. These oscillations are more noticeable in forte than in piano....If the wavering becomes excessive—up to twelve times per second—it is called tremolo.”
Later scientific authorities also do not disagree with Seashore’s earlier findings: Vennard (1971), Large (1971), Shipp and Izdebski (1975), Shipp, Leandersen, and Sundberg (1981), and Hirano (1985) all consider a vibrato of from five to eight regular pulsations per second to be that of a good singer.
The ordinary and extraordinary tasks for which a singer is often responsible present a variety of problems that impinge upon the desired stability of the vibrato.
1. The extent of the vibrato decreases when rapid pitch changes take place. If the vibrato frequency could be matched to the rate of pitch change in an agility passage, this difficulty could be avoided, but the singer must choose his/her tempo with that principle in mind.
2. Jazz singers commonly change from straight tones to a vibrato tone by altering vibrato extent.
3. Sustained, slow moving music accepts more vibrato than fast-moving music.
4. Middle Eastern music asks that the vibrato extent be reduced even further in order to distinguish between melody and vibrato.
5. Whatever we perceive, neither the straight tone nor the vibrato tone is rock-steady, although they are more steady than a tremolo.
6. When pitches vary, intensity and timbre fluctuate greatly.