The perceived height of octave-related complexes Diana Deutsch Department of Psychology, University of California, SanDiego, La Jolla,California 92093 F. Richard Moore and Mark Dolson Department of Music University of California, San Diego, La Jolla, California 92093 (Received 28 January 1986; accepted for publication 18July 1986) Subjects werepresented with two-part patterns consisting of tones whose partials stood in octave, or near-octave relation. The perceived heights of the tones in thepatterns were found to varydepending on theirpositions along theehroma circle, so that thepatterns were perceived quite differently depending onwhich of twokeys they were in. Implications of these findings are discussed. PACS numbers: 43.66.Hg, 43.75.Cd INTRODUCTION It hasbeen argued, on both psychological and music- theoretic grounds, that the pitchof a toneshould be repre- sented alongtwo dimensions. First, the rectilinear dimen- sion of height defines the position of a tone on a continuum from high to low. Second, the circulardimension of the chroma, or pitchclass, defines the position of a tonewithin the octave (Meyer, 1904, 1914; Revesz, 1913; Ruckmiek, 1929; Baehem, 1948; Babbitt, 1960, 1965; Shepard, 1964, 1982; Deutsch, 1969, 1982; Forte, 1973; Ward and Burns, 1982).Thisbid imensional representation isimplicitin Wes- tern musical notation. Here, a noteis designated firstby a lettername, whichrefers to its position within the octave, andthenby a number, which refers to theoctave in which it isplaced. Thus, forexample, D2, D3, and D4 designate notes having the same chromas or pitch classes which are placed in different octaves, and C3, F•3, and A3 designate notes haw ingdifferent chromas or pitch classes which areplaced in the same octave. As evidence for thepsychological reality of thechroma dimension, people with absolute pitchsometimes make oc- taveerrors whileassigning thecorrect letternames to notes (Baird, 1917; Bachem, 1954; Ward and Burns,1982). Con- ditioning studies employing both/iumanand animal sub- jects have obtained generalization of response to tones that stand in octave relation (Humphreys, 1939;Blackwelland Schlosberg, 1943). Interference effects in short-term mem- ory for pitchexhibit octave generalization (Deutsch, 1973). Tone pairs thatare presented in a musical context are judged as closely similar when they are separatedby octaves (Krumhansl, 1979). In order to accommodate the dimensions of height and chroma in a single spatial representation, it has been suggest- edthatpitch be described as a helix which completes one full termper octave, so that tones which areseparated by octaves are represented as in spatialproximity (Drobisch, 1855; Shepard, 1965, 1982). It has alternatively beensuggested that the monotonic dimension of heightand the circulardi- mension of chroma be represented as two separate arrays, the chromaarray beingformedout of projections from the height array(Deutsch, 1969, 1982).Both of theabove mod- els assume (as has generally been assumed) that the per- ceived heights of tones are invariant with respect to pitch class. However, there is verylittle experimental evidence on this issue. One study which addressed the relationship of pitch class to perceived height was performed by Shepard (1964). He generated a series of tones, each of which consisted of ten octave-related sinusoidal components. The amplitudes of these components differed according to a fixedbell-shaped spectral envelope, such thatthose in themiddle ofthe musi- cal range werehighest, and those at the extremes were low- est. Thepitch classes ofthe tones were then varied byshifting the components up and downin log frequency. Since the spectral envelope remained fixed, Shepard argued, the per- ceived heights of thetones would beexpected to remain un- changed as thesinusoidal components shifted along thelog frequency continuum. Subjects were presented with ordered pairs of such tones, and they judged for each pair whether it formed an ascending or a descending sequence. When the tones were separated by one or twosteps along thechroma circle, judg- ments of relativeheightwere found to be almostentirely determined byproximity (see also Burns, 1981; Risset, 1971; Schroeder, 1986). Thus,when thesecond tone was displaced oneor two steps clockwise from the first,the sequence was judged to beascending. Similarly, when thesecond tone was displaced one or two steps counterclockwise fromthefirst, the sequence was judged to be descending. With increasing distance alongthe chromacircle,the tendency for judg- ments to bedetermined by proximity lessened, but stillper- sisted. When,however, the tones were separated by exactly a haft-octave, ascending anddescending judgments oocurred equally often. Shepard concluded that for such octave-related com- plexes, the perceived attribute of height was entirely sup- pressed, with pitchclass alone remaining. However, since judgments in this situation were overwhelmingly deter- mined by proximity, other factors which might have given rise to differences in perceivedheight could have been masked.Further, the resultswere obtainedby averaging overbothsubjects andpitchclasses, so that individual differ- ences in perceived height would have been lost in theaverag- ing process. 1346 J. Acoust. Soc.Am. 80 (5), November 1986 0001-4966/86/111346-08500.80 ¸ 1986 Acoustical Society of America 1346