An analysis is made of the perception of musical intervals. Two kinds of stimuli were used; intervals consisting of two simultaneous simple tones (sinusoids) and intervals consisting of two simultaneous complex tones (fundamental plus harmonics). Subjects judged the stimuli by the method of triadic comparisons in an incomplete balanced design. Multidimensional analysis was performed according t...

In the first part of this paper, we consider 3 × 3 × 3 arrays with complex entries, and provide a complete self-contained proof of Kruskal’s theorem that the maximum rank is 5. In the second part, we provide a complete classification of the canonical forms of 3× 3× 3 arrays over F2; in particular, we obtain explicit examples of such arrays with rank 6. In 1989, Kruskal [6, page 10] stated witho...