A multidimensional scaling study of seven theoretical indices of intervallic similarity and musicians' perceptions among twenty-one pitch-class sets with implications for music teaching and learning

The purpose of this research was to investigate associations between 7 indices of theoretical intervallic similarity and musicians' perceptions among twenty-one pitch-class sets (i.e., T{dollar}sb{lcub}rm n{rcub}{dollar}/T{dollar}sb{lcub}rm n{rcub}{dollar}I-types) compared with trichord 3-1. The 7 indices included Morris's SIM and ASIM (1979-1980), Rahn's MEMB (1980) and AMEMB (Isaacson's 1992 extension of Rahn's MEMB), Lewin's REL (1979-1980), Teitelbaum's s.i. (1965) and Isaacson's IcVSIM (1992). Thirty-three musicians heard 231 paired comparisons of the 21 stimuli and used magnitude estimation to specify the amount perceived similarity in each pair. Multidimensional scaling analyses of the magnitude estimations revealed that subjects' perceptions of similarity among the twenty-one pitch-class sets were affected by variables such as the total number of pitches and intervals, subset content, tonal and atonal attributes, and symmetry. Multiple regression analyses demonstrated that subjects' magnitude estimations were related to values derived using SIM, ASIM, MEMB and s.i. due to the salience of set size and common tones. Subjects' magnitude estimations also were related to values derived using IcVSIM due to the salience of the intervals between the pitches and symmetry. Subjects' magnitude estimations were related to values derived using AMEMB and REL; however, the reason for this relationship was undetected. The results supported the conclusion that relationships existed between these 7 indices and musicians perceptions of similarity among 21 pitch-class sets.