1. The reader interested in the basic concepts, objectives, and background of pitch-class set theory can find a general discussion in, for example, these: Allen Forte, The Structure of Atonal Music (New Haven and London: Yale University Press, 1973); John Rahn, Basic Atonal Theory (New York: Schirmer, 1980); Robert Morris, Composition with Pitch-Classes (New Haven and London: Yale University Press, 1987); Joseph Straus, Introduction to Post-Tonal Theory (New Jersey: Prentice Hall, 1990).
2. A pitch-class set is a collection of pitch-classes without duplications, and a set-class is a collection of pitch-class sets mutually related by a transformation or by a group of transformations. The transformation used in this study is transposition (Tn; transpositional classification).
3. See, for example, Robert Morris, "A Similarity Index for Pitch-Class Sets," Perspectives of New Music 18/2 (1979/80): 447; John Rahn, "Relating Sets," Perspectives of New Music 18/2 (1979/80): 494; Mark Hoover, "Set Constellations," Perspectives of New Music 23 (1984): 165-166; Fred Lerdahl, "Atonal Prolongational Structure," Contemporary Music Review 4 (1989): 66; Thomas Demske, "Relating Sets: On Considering a Computational Model of Similarity Analysis," Music Theory Online 1.2 (1995): 16, 17; Richard Hermann, "Towards a New Analytical Method for Post-Tonal Music: A Response to Thomas Demske," Music Theory Online 1.3 (1995): 15, 16, Footnote 2; Eric Isaacson, "Issues in the Study of Similarity in Atonal Music," Music Theory Online 2.7 (1996): 16; Isaacson, "Neural Network Models for the Study of Post-tonal Music," in Mark Leman (ed.), Music, Gestalt, and Computing: Studies in Cognitive and Systematic Musicology (Berlin: Springer-Verlag, 1997): 237-238; David Rogers, "A Geometric Approach to Pcset Similarity," Perspectives of New Music 37 (1999): 78; Marcus Castrén, "Pairs of Chords as Objects Illuminating Set-Class Similarity: Some Viewpoints and a Computer-Assisted Procedure to Create test Material for Listener Experiments," Electronic Journal of Music Theory and Analysis 1/1 (2000).
4. Cheryl Bruner, "The Perception of Contemporary Pitch Structures," Music Perception 2 (1984): 25-39; Don B. Gibson, "The Aural Perception of Nontraditional Chords in Selected Theoretical Relationships: A Computer-Generated Experiment," Journal of Research in Music Education 34 (1986): 5-23; R.C. Lane, A Multidimensional Scaling Study of Seven Theoretical Indexes of Intervallic Similarity and Musicians' Perceptions Among Twenty-One Pitch-Class Sets (Ph.D. diss., University of North Carolina, 1997); Virginia Williamson and Panayotis Mavromatis, "Categorizing Atonal Sonorities: Multidimensional Scaling, Tree-Fitting and Clustering Compared," (Paper presented at the Society for Music Perception and Cognition Conference, Evanston, Illinois, 1999); Arthur Samplaski, A Comparison of Perceived Chord Similarity and Predictions of Selected Twentieth-Century Chord-Classification Schemes, Using Multidimensional Scaling, and Cluster Analysis (Ph.D. diss., Indiana University, 2000); Tuire Kuusi, Set-Class and Chord: Examining Connection between Theoretical Resemblance and Perceived Closeness (Helsinki: Sibelius Academy, 2001); Kuusi, "Semantic Differential as a Method for Collecting Estimations of Chords," (in the Fifth Triennal ESCOM Conference: Proceedings, 2003). Two closely related studies by Gibson examine the effect of octave equivalence (or pitch class) in chord perception: Gibson, "The Aural Perception of Similarity in Nontraditional Chords Related by Octave Equivalence, Journal of Research in Music Education 36 (1988): 5-17; Gibson, "The Effects of Pitch and Pitch-Class Content of the Aural Perception of Dissimilarity in Complementary Hexachords," Psychomusicology 12 (1993): 58-72.
5. David Huron, "Interval-Class Content in Equally Tempered Pitch-Class Sets: Common Scales Exhibit Optimum Tonal Consonance," Music Perception 11 (1994): 289-305. When the Huron consonance values were calculated, the indexes for interval-classes were summed up and the resulting value was divided by the total number of interval-classes in the set-class. In each triad class the total number of interval-classes was 3, and in each pentad class it was 10.
6. I would like to thank Mr. Santtu Valve from the department of Music Technology, Sibelius Academy, for helping to prepare the sound data.
7. Bruner, "The Perception of Contemporary Pitch Structures" (1984); Samplaski, A Comparison of Perceived Chord Similarity and Predictions of Selected Twentieth-Century Chord-Classification Schemes, Using Multidimensional Scaling, and Cluster Analysis (2000); Kuusi, Set-Class and Chord: Examining Connection between Theoretical Resemblance and Perceived Closeness ( 2001), "Semantic Differential as a Method for Collecting Estimations of Chords" (2003).
End of footnotes