Patterns of Ratio Relationships in Melody
Paul C. Boomsliter, Warren Creel · The Journal of the Acoustical Society of America · 1963
Musicians selected their preferred tunings for specific melodies, using an instrument that allows choice of intonation. In this critical listening situation, their choices were found to represent a number of variations on a principle of organization by simple whole-number ratios to tonal centers. Even without modulation, these melodic choices shift away from direct relation to the tonic to relation to other tonal centers. These acting tonal centers stand in small-whole-number ratios to other centers, which in turn have the same class of relation to the tonic. The instances presented do not match any known scale; they indicate structural importance for variant tunings of the same note, and for what is here called “extended reference,” a tendency to avoid direct relationship to the tonic until resolution is desired. Thus, they indicate that tuning preferences are the result of the operation of structural principles embodied in a melody rather than in a scale.