Intonation of tone scales: psychoacoustic considerations - TERHARDT, Ernst (Archives of Acoustics, 1988)
Conventional music theory ordinarily is based more or less explicitly on the concept that intonation of musical tones can with sufficient precision be described by one physical parameter, i.e. "tone frequency". Ratios of "tone frequencies" play a predominant role in theories of consonance and tone scales. Closer inspection of the physical nature of musical tones, and particularly of pitch-dependent auditory effects, reveals, however, that the aforementioned classical concept is insufficient. A psychoacoustically-oriented dualistic approach to intonation is suggested maintaining that "correct" intonation of a musical tone interval basically depends on (1) harmonic purity, and (2) sensory purity. Harmonic purity depends on memorized pitch-interval templates which in turn are partly of natural, partly of cultural origin. Sensory purity largely depends on perception of fluctuations, and its basic aspects are independent of cultural effects. It is concluded that optimal intonation is a compromise which at every moment of a musical performance must be achieved by active evaluation of the two aforementioned criteria. Theories of perception of pitch and fluctuations readily explain why this is so, and provide promising tools for achieving that compromise.