El

I

¾ ¾• total volume to be scaled by the rat•io of the tangents of the half-angles qb/2 and •2 as might be expected from the expression for the cross-sectional area.

The above expression for the intersection volume has been checked for right circular cones and for various values of 0 and r•. against results obtained with the nu- merical computer program described in Ref. 2 and has been shown to provide good agreement.

FIG. 2. Representative cross section.

and L is the distance between the apex points of the two beams.

If instead of elliptical cones, right circular cones are employed, then •b = • and only the expression for B is changed. In particular for a fixed 6, this causes the

1R. A. Rasmussen and N. E. Head, "Characteristics of High Frequency Sea Reverberation and Their Application to Tur- bulence Measurement," J. Acoust. Soc. Am. 59, 55-61 (1976).

2E. J. Sullivan and K. A. Kemp, "The Significance of Beam Pattern Side Lobes in Fluid Flow Measurement," J. Acoust. Soc. Am. 66, 1494-1498 (1979).

3p. F. Smith, A. S. Gale, and J. H. Neelley, New AnalyHc GeomeD'y (Ginn, New Yo•k, 1928), p. 317.

"Practically perfect pitch": Some comments Donald E. Hall

Physics and Music Departments, California State University, 6000 J Street, Sacramento, California 95819 (Received 7 December 1981; accepted for publication 9 December 1981)

A plea is made against use of the popular but unscientific term "perfect pitch," and for greater care to exclude use of relative pitch ability in experiments intended to test absolute pitch ability.

PACS numbers: 43.66.Hg, 43.75. -- z [JH]

A recent article in this Journal (Lockhead and Byrd, 1981) illustrates with unusual clarity a pitfall which has long plagued the literature on absolute pitch ability (AP).

The problem is partly one of terminology. The phrase "perfect pitch" is commonly regarded among the uninit- iated as synonymous with AP. But of probably equal (perhaps even greater) importance to musicians is rela- tive pitch ability (RP), i.e., interval-recognition abil- ity. Use of the term "perfect pitch" is undesirable be- cause one may have varying degrees of AP, accom- panied by quite different degrees of RP, though nobody will ever be truly "perfect" in either. It is especially common among trained musicians to have rather poor AP but quite good RPo Lockhead and Byrd made clear in their first paragraph that they were using "perfect pitch" to mean AP, but I would much prefer to see everyone avoid this usage in the future.

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The second, and more substantial, problem is in methodology. Since the difference between AP and RP

is mainly one of long-term versus short-term memory, it is crucial in any experiment intended to test AP that the subject be denied the opportunity to use the short- term memory. Lockhead and Byrd used visual feed- back of the correct response, followed by the next test tone after only a 1/4-s pause. Thus all but the first in each of their blocks of 25 trials seem most likely to have tested RP, not AP. The entire discussion of their results might better be addressed to RP with sine waves, not to AP.

This problem hides under a different guise when feed- back is not given: a sequence of responses that are all incorrect by the same number of semitones in the same direction may reveal that the subject is using RP, not AP. Any such data should be rejected in an experiment that is supposed to be testing APo Unfortunately, such culling still leaves us in the dark as to how many of the correct answers were due to RP rather than AP. Some

investigators have properly noted this effect (e.g., Weinert, 1929; Ward, 1963). But more often, silence on this subject leaves the reader to worry that no tests

754 J. Acoust. Soc. Am. 71(3), March 1982; 0001-4966/82/030754-02500.80; ¸ 1982 Acoust. Soc. Am.; Letters to the Editor 754

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of correlation between successive answers were made

to protect against this misinterpretation (e.g., Riker, 1946; Cuddy, 1970).

Rather than trying to untangle AP from RP in such circumstances, it would seem as if experiments on AP should always be designed with either very long inter- stimulus intervals or RP defeating interstimulus dis- tractors. The work of Rakowski (1978) suggests that the main decay of RP may take as long as five to thirty minutes, so that a mere few seconds of silence is prob- ably quite inadequate to force the subject back upon his AP resources. Relatively few experimenters have ever played it truly safe on the basis of time alone, as did Brady (1970) with a 24-h ISI.

Several investigations have included distraction tech- niques, as discussed by Ward and exemplified in Hart- man (1954) and Terman (1965). But Wickelgren (1966), by using a pure tone rather than a noise for a distract- or, leaves us with some doubt as to whether this tone could have served as a temporary intermediate refer- ence standard instead of "interference" as intended.

Some readers may think I am harping on a nonexis- tent problem, since Ward remarks that a review by Pet- ran (1932) gives "some evidence that relative pitch simply is not used in AP experiments." In terms of my own musical experiences, however, I find that ex- tremely hard to believe. Until I see a strong experi- mental demonstration that RP is not used even though

readily available, I will prefer to read of very careful precautions to exclude RP before any results are dis- cussed in terms of AP.

Brady, P. T. (1970). "Fixed-scale mechanism of absolute pitch," J. Acoust. Soc. Am. 48, 883-887.

Cuddy, L. L. (1970). "Training the absolute identification of pitch," Percept. Psychophys. 8, 265-269.

Hartman, E. B. (1954). "The influence of practice and pitch distance between tones on the absolute identification of pitch," Am. J. Psychol. 67, 1-14.

Lockhead, G. R., and Byrd, R. (1981). "Practically perfect pitch," J. Acoust. Soc. Am. 70, 387-389.

Petran, L. A.. (1932). "Experimental study of pitch recogni- tion," Psychol. Monogr. 42, #6, 1-120.

Rakowski, A. (1978). "Investigations of absolute pitch," Pro- ceedings of t he Research Symposium on the Psychology and Acoustics of Music, edited by E. P. Asmus, Jr. (Univ. Kansas), pp. 45-57.

Riker, B. L. (1946). "The ability to judge pitch," J. Exp. Psychol. 36, 331-346.

Terman, M. (1965). "Improvement of absolute pitch naming," Psychon. Sci. 3, 243-244.

Ward, W. D. (1963). "Absolute pitch," Sound 2 (3), 14-21, and 2 (4), 33-41.

Weinert, L. (1929). "Untersuchungen fi•er das absolute GehiJr," Arch. Gen. Psychol. 73, 1-128.

Wickelgren, W. A. (1966). "Consolidation and retroactive interference in short-term recognition memory for pitch," J. Exp. Psychol. 72, 250-259.

Practically perfect performance Gregory R. Lockhead

Department of Psychology, Duke University, Durham, North Carolina 27706 (Received 7 December 1981; accepted for publication 9 December 1981)

People who can identify piano notes with essentially no errors are often said to have absolute, or perfect, or relative pitch. But it is not pitch that these people identify so well; it is musical notes.

PACS numbers: 43.66.Hg, 43.75. -- z

Many people use the terms perfect pitch (PP) and absolute pitch (AP) interchangeably and often discrim- inate these from relative pitch (RP). The most com- mon interpretation I have been offered by musicians is that a person has RP if he or she can sing a capella after a reference note has been sounded, and perfect or absolute pitch if no beginning note is needed. These are descriptive statements or a sort of street language. No theory is intended.

Commenting on a paper by Lockhead and Byrd (1981) in which AP and PP were used as just described, Hall (this issue) defines those terms theoretically and states that the report by Lockhead and Byrd "illustrates with unusual clarity" the sorts of confusions one can have concerning these issues. Hall interprets that there are

two processes by which tones are judged, absolute and relative (AP and RP), and that either process might be done perfectly (PP). Thus one ought not to use AP and PP indiscriminately.

Consistent with this thesis, Hall is further concerned that, while Lockhead and Byrd talked about AP, they conducted their studies in a manner that was conducive

of RP. Subjects were given feedback after every re- sponse, which could aid them in keeping their response scale aligned, and the time between successive tones was brief, which could allow use of the memory of the previous tone as a referent for judging the current tone.

Concerning the distinction between RP and AP, Ward's (1963, p. 20) example is relevant. Suppose that a per- son has a persistent tinnitus which is used as a refer-

755 J. Acoust. Soc. Am. 71(3), March 1982; 0001-4966/82/030755-02500.80; (D 1982 Acoust. Soc. Am.; Letters to the Editor 755

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