Simple frequency ratios naturally make precisely perceived melodies

Almost all human music is built on discrete scales of pitch.¹ Culturally prominent scales, such as the diatonic major scale of Western music, make use of the simple frequency ratios 2:1, 3:2, and 4:3 between notes.² It is generally believed that these ratios were chosen to optimize the consonance of simultaneous notes.^3,4,5,6,7 Alternatively, or in addition, it is conceivable that these ratios are intrinsically advantageous for the perceptual encoding of melodies.^8,9,10,11,12 Here, we provide behavioral support for this hypothesis. In three experiments, young Western adults had to detect pitch anomalies ("sour notes") in partly random pure-tone melodies based on various musical scales, including novel ones. The task did not require any musical knowledge. Most importantly, the listeners were extensively trained in order to saturate familiarity with the scales: for a given scale and listener, more than 2,000 (up to 5,280) trials were run. Practice largely improved performance. This occurred even for the diatonic major scale, suggesting that performance in our task was not biased by previous musical enculturation.^13,14 Frequency ratio simplicity also favored performance. Crucially, its benefit was not smaller in the final test sessions, when performance for each scale was presumably optimal and no longer improvable by practice, than in the initial test sessions. Thus, frequency ratio simplicity appeared to be intrinsically advantageous, rather than advantageous merely due to familiarity. The naturalness of melodic intervals defined by simple frequency ratios is likely to have contributed to the cultural selection of musical scales.