Various observers have noted that the fluctuation of pitch in the normal vocal vibrato is accompanied by a fluctuation of loudness and of timbre. Although this coupling is an implicit outgrowth of the formant principle, the point does not appear to have been explicitly pointed out in the literature, and seems to have been missed by some. Consider any single partial lying on the slope of a resonance peak, such as a vowel formant. If the slope is positive, an increase in frequency leads to an increase in intensity; if negative, the converse is true. Since the voice has many partials randomly located with respect to the formants, the loudness may be expected to vary with pitch, but with sometimes a positive and sometimes a negative phase relation. The overtone structure will also vary though the vibrato cycle. This timbre vibrato is clearly shown in a motion picture made some years ago at Bell Telephone Laboratories. Several other interesting points concerning the practical utility of the vibrato in singing are also mentioned.

LETTERS TOTHE EDITOR function for the case treated and the directivity function of the elementY This means that if the pattern function of the element is less than A, at any value of 0 less than 90 ø the sector coverage of that array is necessarily limited to that angle. The results here are limited to the case of uniform spacing. Since it is conceivable that a nonuniformly spaced array could be steered, the method might be extended to include this case. However, the analyses on the nonuniform array of the many authors who have treated the problem of arrays of arbitrary spacings thus far have not led to results that seem amenable by an extension of the method presented here. For such arrays, the procedure remains "cut and try." z S. Several investigators have derived expressions for the pressure spectrum of the sonic-boom N wave. Where the rise time is zero, Howes has shown that the pressure spectrum is a published spherical Bessel function. The present analysis shows that the spectrum with a finite rise time, not exceeding onetenth of the duration, can be closely approximated by multiplying two spherical Bessel functions, or, equivalently, by adding their logarithmic curves. WITI-I RECENT INTEREST IN TI-IE SUPERSONIC TRANSPORT AND TI-IE associated sonic-boom problem, several investigators--notably Zepler and Hard/Young, TM Howes, 4 and AustinS--have derived expressions for the spectrum distribution of N waves. Young •' has published curves for the case of zero rise time and has also shown a Volume 43 Number 4 1968Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 160.36.178.25 On: Sat

This is the third report on the acoustics of the singing voice based on Sonograph measurements carried on at Westminster Choir College and Columbia University. Previous reports discussed certain discontinuities or register changes, and the significance of higher formants in the 2000–4000 cycle region. The present discussion will center around observations on the vibrato pattern. Several types of patterns deviating from the norm as described by Seashore and others are represented in these measurements, including vibratos principally of amplitude, uneven rates and extents, and angular and asymmetrical patterns. The relation of vibrato to rapid scale singing, and its implications for vocal pedagogy are also discussed.

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The formants which determine vowel quality lie largely in the range of 250–1850 Hz. Since normal speech, male or female, rarely has fundamentals higher than 250 Hz, it is generally assumed in speech studies that the formants modify the harmonics of the laryngeal tone. The same assumption is valid for the lower singing voices with occasional exceptions. The fundamental pitch of the soprano singer however often goes as high as 1320 Hz, and sometimes in the coloratura voice, considerably higher. Very little attention has been given by voice scientists to the interaction of formants and laryngeal tone in this region. The present study has been addressed to the question of whether harmonics of the formants modify the fundamental of the glottal tone in this range (sometimes called the “whistle register”). The presentation will include videotapes of one of the authors (EC), singing tones between 1000 and 1500 Hz, using vowel positions of most of the usual singing vowels. Each vowel had formants whose harmonics reinforce the fundamental pitch, but there is virtually no audible difference in the vowel character of the resulting sounds.