The naturalness factor of sustained vowels has been mainly attributed to a fundamental frequency fluctuation called jitter. However, sustained human vowels, with a fundamental frequency that is made to be constant, still sound natural [Ifukube et al., J. Acoust. Soc. Jpn. 47, 903--910 (1991)]. In order to investigate this fact, 128 pitch periods of the sustained vowel /a/ were analyzed. The maximum peak amplitude of each pitch period, which was placed at relatively the same position through 128 pitch periods, was extracted to make a time series that is called shimmer. Using FFT analysis, the shimmer turned out to have a 1/f fluctuation characteristic. This time series characteristic is often found in the biomedical signal processing area. This finding is thought to be classified as one of these signals. Not only does the maximum peak shimmer show 1/f fluctuation characteristics, but other peak shimmers show the same characteristics. In order to investigate the role of 1/f shimmer, a psychoacoustic experiment was conducted. Acoustic stimuli that sound like the vowel /a/ were made by means of a PARCOR synthesizer with various kinds of shimmer. The results showed that the stimulus with 1/f shimmer was recognized to be more humanlike.