Vocal mistuning reveals the origin of musical scales

ABSTRACT

Theories of the origin of tonality from the time of Pythagoras onward have assumed that the intervals used in musical scales are defined mathematically based on harmonic ratios. Virtually all such theories are predicated on tunable instruments (e.g. strings), whereas the voice is the most ancestral and universal instrument used to make music. In the present study, we analysed the tuning of sung musical intervals from a familiar song, doing so across both trained and untrained singers. Contrary to the predictions of traditional theories, we found that sung intervals (unlike those of instruments) showed marked overlap with neighbouring interval categories. Furthermore, we found that listeners of these sung productions did not base their aesthetic judgments of singing quality on the precision of tuning of sung intervals. We consolidate these results into a model of tonality based on both vocal and sensory factors that contribute to the formation of sung melodies.

KEYWORDS:

• Tonality
• tuning systems
• singing accuracy
• scales
• birdsong

Acknowledgements

We thank Patrick Savage, Michael Hall, Steven Morrison, David Temperley, Carol Krumhansl, Steven Demorest, Timothy Hubbard and three anonymous reviewers for helpful comments on a previous version of the manuscript. We also thank Steven McAdams for pointing out the link between our work and that of Arom and colleagues.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹Pfordresher and Brown (2007) categorized as VPID any singer for whom the absolute value of mean pitch deviations exceeded 100 cents. Since that time, this criterion has been criticized as being too lax with respect to how many participants may be categorized as accurate, with most researchers now advocating for a 50-cent criterion (see Pfordresher & Larrouy-Maestri, 2015 for discussion). We chose to follow the categorization used in the original paper for purposes of comparison. Nevertheless it is worth noting that 23 of our 27 accurate participants (85%) had error pitch deviation scores between 0 and 50 cents and could thus be considered accurate under either criterion.

Additional information

Funding

This work was supported by National Science Foundation grant BCS-1256964 to PQP and from the Natural Sciences and Engineering Research Council (NSERC) of Canada to SB.