Computer Realization of Extended Just Intonation Compositions
George T. Kirck · Computer Music Journal · 1987
If a superposition of two or more periodic frequencies within the audible spectrum can be expressed in terms of simple ratios of the form fl /f2 = n/m (where n, m are integers), the subjective perception of the degree of blend or consonance of the superposition is inversely proportional to the magnitude of the integers required to represent it. Thus, the Just perfect fifth (3/2) is perceived as being more than the Just major third (5/4), which is more than the septimal minor third (7/6), and so on. A superposition is considered perfectly when there is a coincidence of all harmonic spectra (unison and octave), consonant when the frequencies are separated by an interval greater than the critical band (a frequencydependent minimum separation between activated regions along the basilar membrane beyond which beating or roughness is no longer perceived), and nonconsonant or dissonant when the frequencies differ by about 5%-50% of the corresponding critical bandwidth (Roederer 1979). An intonation system based on ratios thus allows for the establishment of musical structures re-