Using successive nonoverlapping 22.5-ms windows, 16-kHz sampling, no filtering, an automatic algorithm locates five successive windows of minimum spectral velocity, describes a subwindow equal to some multiple of the natural period of F[inf 0], and maps the subwindow onto the unit circle, the interval 0, 2(pi). Consequently, the Fourier analysis is performed on a window where the signal is exactly periodic. Because the spectrum contains no extraneous numerical sidebands it is precise, and consists only of natural harmonics in the acoustic signal. The first 32-integer multiples of F[inf 0] are sufficient to describe the spectrum. J. D. Miller's [J. Acoust. Soc. Am. 85, 2114--2134 (1989)] log F[inf 0][sup 1/3] shift increases recognition of 12 vowels (men, women, and children) in the Hillenbrand et al. [J. Acoust. Soc. Am. 97, 3099--3111 (1995)] data set from 52% to 75% using a Euclidean classifier (EC---with jackknife). Cosine series (12) were used to compare our Betancourt spectrum (EC: 76%) with the Hamming window (EC: 61%). Quadratic discriminant function analysis + log F[inf 0] (79%) adds only 3% to our best EC result. With this spectrum and a log F[inf 0][sup 1/3] shift, most vowel information is clearly captured by a simple EC.