Theories of the origin of musical scales from the ancient Greeks to the present day have assumed that the intervals comprising scales are defined by specific mathematical ratios. Such theories are predicated on pre-tunable instruments, and yet the voice is almost certainly the original musical instrument. Therefore, the analysis of vocal scales offers a more naturalistic approach to understanding the origin of musical scales. In the present study, we conducted a large-scale computational analysis of vocal pitch-class properties and their implications for scale structure. We analyzed 417 field recordings of solo, unaccompanied songs from across 10 principal musical-style regions of the world. The results revealed a mean vocal pitch-class imprecision of approximately 1.5 semitones, and comparable results were obtained across all regions. These results suggest that vocal imprecision is universal and is mainly derived from the physiological limitations of the voice. Such vocal imprecision fundamentally constrains the formation of musical scale structure: it provides a lower limit on the spacing between adjacent scale tones, and thereby an upper limit on the number of scale tones that an octave can contain. We discuss these results in terms of an Interval Spacing model of the evolution of musical scales.