Don Gibson - Pitch-class Set Theory and Perception (original) (raw)
The perceptibility of various set-theoretic concepts has received considerably experimental attention. Pertinent experiments include Thrall (1962), Largent (1972), Millar (1984), Lannoy (1972), Bruner (1984), and Gibson (1986, 1988, 1993). All of these experiments raise significant questions for the perceptibility of various concepts in set theory.
The following summary reviews four pertinent cognitive experiments. This summary was prepared by Dr. Paul von Hippel.
**Question:**Do listeners' similarity judgments correspond to Robert Morris'(1979/1980) index of set similarity?
**Overview:**There were two stages to the study. The first stage consisted of "seven preliminary studies;" the second stage consisted of "one larger scale experiment."
**Listeners:**Most of the listeners in the preliminary studies were "musical experienced." The listeners in the larger-scale experiment are not described, nor is the number of listeners given.
**Stimuli:**In the large-scale experiment, listeners heard all possible pairs of trichords, presented as block chords in inverted normal form. (In the preliminary studies, listeners also heard pairs of tetrachords; in addition, the sets were presented as melodies and arpeggios as well as block chords.)
**Task:**For each pair of sets, listeners were asked to rate numerically how similar the two sets sounded.
**Results:**Morrison's index was neither a strong nor a consistent predictor of listeners' similarity judgments. Instead, similarity judgments were correlated with three other factors:
- consonance or tonal associations
- number of tones that the two sets have in common
- harmonic construction -- tertian vs. quartal/quintal
**Question:**Like Bruner, Gibson (1986) compared listeners' similarity judgments to Robert Morris' index of set similarity. In addition, Gibson (1986) considered similarity relationships defined by Allen Forte (1973). Forte's relationships are based on transformations like transposition and inversion, as well as close resemblances between pc sets (Rp) or ic vectors (Z-relationships, R1, R2, R0).
**Listeners:**198 listeners, of whom 173 were music students or faculty. The subjects were distinguished according to general musical training, musical instrument, and "experience in the atonal idiom." No significant differences were found between listener groups.
**Stimuli:**Each item consisted of two pairs of block tetrachords played by synthesizer. Tetrachords with tonal connotations were excluded. The voice-leading between consecutive chords was standardized.
**Task:**For each item, listeners were asked which pair of tetrachords sounded more similar.
**Results:**Among the 39 experimental items, for only 3 did listeners' responses exhibit a significant correspondence to Forte's and Morris' theories.
**Question:**Is the notion of octave-equivalence ("pitch classes") relevant to the similarities that listeners hear among nontonal chords?
**Listeners:**51 undergraduate music majors, 50 undergraduate non-music majors, and 32 members of the Texas Society for Music Theory.
**Stimuli:**Each item consisted of two pairs of nontonal block chords. In one pair, the chords had identical pitch-class content; in the other, they did not. (Supplementary information: All chords were played by synthesizer. The number of pitch-classes was consistent within each item. No pitch-classes were doubled. The voice-leading between consecutive chords were standardized.
**Task:**As in Gibson's (1986) earlier study, for each item listeners were asked which pair of chords sounded more similar.
**Results:**For each group, only 55-57% of the responses were in agreement with the theories. N.B. If the theories bore no relationship to the responses, 50% would have been in agreement.
**Question:**As he asked in 1988, in 1993 Gibson asked whether the notion of octave-equivalent "pitch-classes" is relevant to the similarities that listeners hear among nontonal chords.
**Listeners:**50 undergraduate music majors, 57 undergraduate non-music majors
**Stimuli:**Each item consisted of two pairs of nontonal block hexachords. Within each pair, the two hexachords were complementary. In one pair there were shared pitch-classes; in the other there were not. In 12 of the 24 experimental items, the shared pitch _classes_were also shared pitches.
**Task:**As in Gibson's earlier studies, for each item listeners were asked which pair of chords sounded more similar.
**Results:**For each group, only 56-57% of the responses were associated with shared pitch-classes. When the effect of shared pitches was excluded, only 49-52% of the responses were associated with shared pitch classes. Again, a 50% association would be expected by chance alone.
References:
Bruner, C.L. (1984).
The perception of contemporary pitch structures.
_Music Perception,,_Vol. 2, No. 1 pp. 25-39.AbstractForte, A. (1973).
The Structure of Atonal Music
New Haven: Yale University Press.Gibson, D.B., Jr.
The aural perception of nontraditional chords in selected theoretical relationships: A computer-generated experiment._Journal of Research in Music Education,_Vol. 34, No. 1 (1986) pp. 5-23.AbstractGibson, D.B., Jr.
The aural perception of similarity in nontraditional chords related by octave equivalence.
_Journal of Research in Music Education,_Vol. 36, No. 1 (1988) pp. 5-17.AbstractGibson, D.B., Jr.
The effects of pitch and pitch-class content on the aural perception of dissimilarity in complementary hexachords.
_Psychomusicology,_Vol. 12, No. 1 (1993) pp. 58-72.AbstractKrumhansl, C.L., Sandell, G.J., and Sergeant, D.C.
The perception of tone hierarchies and mirror forms in twelve-tone serial music.
_Music Perception,_Vol. 5 (1987) pp. 31-78.Lannoy, C. (1972).
Detection and discrimination of dodecaphonc series.
_Interface,_Vol. 1, pp. 13-27.Largent, E.J. (1972).
An investigation into the perceptibility of twelve-tone rows. Ohio State University, PhD Dissertation.Millar, J.K. (1984).
The aural perception of pitch-class set relations: A computer-assisted investigation.
North Texas State University, PhD dissertation.AbstractMorris, R. (1979/1980).
A similarity index for pitch class sets.
_Perspectives of New Music,_Vol. 18, pp. 445-460.Pedersen, P.R. (1970).
The perception of musical pitch structure. University of Toronto, PhD Dissertation.Rahn, J. (1979). Aspects of musical explanation.
Perspectives of New Music
Vol. 73, pp. 1-14.Rahn, J. (1980).
Basic Atonal Theory
New York: Longman Inc.Thrall, B. (1962).
The audibility of twelve-tone serial structure. Ohio State University, PhD Dissertation.