Figure 4 Two-dimensional configuration of single instruments positioned by a professor of musicology on the basis of mental image of timbre (Bb4). Dimension 1 (left to right) was “nasal” to “not nasal” and dimension 2 (top to bottom) was “rich” to “brilliant.” From Kendall & Carterette (1991).
Ian Cross, Irene Deliege · 2004
We submitted the entire set of scalings over all contexts to INDSCAL (INdividual Differences SCALing), which provided a summary solution. The two dimensions gave essentially as good a fit as three; we present the two-dimensional solution here (Figure 3). The result was a circumplex with a notable gap on both sides of the oboe dyads. Other well-known circumplexes are those for pitch chroma (Shepard, 1964) and visual colors (Shepard, 1962). In terms of verbal attributes, left to right along dimension 1 (Figure 3) is “nasal” to “not nasal”; top to bottom is “rich” to “brilliant.” A circumplex like Figure 3 might arise from the vector sum of the positions of single instruments arranged in two dimensions (Figure 4): Nasal-not nasal and brilliant-rich. In fact, the results of positioning single instruments in such a space by a professor of musicology generated a quasi-circumplex similar to Figure 3 (Kendall & Carterette, In Press, a, b).