source file: mills2.txt Date: Mon, 9 Oct 1995 07:52:48 -0700 From: "John H. Chalmers" From: mclaren Subject: Tuning & psychoacoustics - post 16 of 25 --- The evidence for a universal human preference for stretched intervals is so overwhelming that it appears throughout the length and breadth o`e psychoacoustic literature, both with Western and non-Western musicians: "Dowland has reported that measurements of Western and non-Western fixed pitch instruments suppprt Ward's conclusion that the perceptual octave is some 15 cents larger than the physical or mathematical octave. Western musical practice supports these conlusions (play sharp in higher octave). Balinese gamelan tunings take advantage of this apparently widespready characteristic of pitch perception to create a multi-octave beating ocmplex in their fixed pitch instruments." [Erickson, Robert, "Timbre and the Tuning of the Balinese Gamelan," Soundings, pg. 100, 1984] Particularly revealing is "The 1215-Cent Octave: Convergence of Western and Non-Western Data on Pitch Scaling," W. J. Dowling, Abstract QQ5, 84th meeting of the Acoustical Society of America, Friday, December 1, 1972, p. 101 of program. Yet more evidence for a universal preference for stretched octaves comes from Sundberg, who found that the octave was as a rule played significantly sharp by performing musicians, and was also preferred sharp of the 2:1 in adjustment tests: "Evidently the octave intervals in such stretched scales will exceed a 2:1 frequency ratio slightly. Thus, it is necessary to distinguish between the *physical octave * (PO) which is defined as a 2:1 frequency ratio, and the *subjective (musical) octave * (MO) that is perceived as pure. (...) As a rule, the perceptual octave corresponds to a fundamental frequency ratio exceeding 2:1." [Sundberg, J. and Lindqvist, J., "Musical Octaves and Pitch," JASA, 54(4), 1973, pp. 973-929] Among the many implausible arguments which attempt to explain away this mountain of experimental evidence for a preference for an octave interval larger than the purportedly "pure" 2:1, most prevalent is the claim that these "laboratory experiments do not represent real musical practice." If this objection is correct, why does computer analysis of the frequencies of pitches played during actual performances which show a uniform stretch of the octave also show the same results as the laboratory psychoacoustic experiments? And why do psychoacoustic measurements and experiments stretching back over 150 years uniformly produce the same results? "This disparity between the physical and subjective octaves is not a new discovery. Stumpf and Meyer, using the method of constant stimuli, had 18 subjects judge pairs of successive tones as greater than, less than, or equal to an octave. They lower tone was 300 cps and the upper tone was varied around 600 cps. They found that 602 cps (the higher upper tone used) received 52 percent "less," 43 precent "equal," and 5 percent "greater" responses from the group, indicating that the mean subjective octave of 300 cps was somewhere above 602 cps (the present Fig. 4 gives about 605 cps). Later von Maltzew, in an investigation on the identification of intervals in the upper frequency range, found that a physical octave was more often called a major seventh or below than a minor ninth or above. See C. Stumpf and M. Meyer, Beit. Akust. Musikw., Vol. 2 ppg. 84-167, 1898. C. v. Malzew, Z. Psychol. Vol. 64, pp. 16-257, 1913. [Ward., W.D., "Subjective Musical Pitch," Journ. Acoust. Soc. Am. , Vol. 26, No. 3, May 1954, pg. 374] "The average standard deviation of repeated adjustments of sequential or simultaneous octaves composed of sinusoids is on the order of 10 cents (Ward, 1953, 1954; Terhardt, 1969; Sundberg & Lindquist, 1973). A range of average deviations from 4 to 22 cents for adjustments of the other intervals of the chromatic scale (simultaneous presentation) has been reported by Moran and Pratt (1926). Rakowski (1976) reports variability--in interquartile ranges--of 20 to 40 cents for both ascending and descending melodic versions of the 12 chromatic intervals. Other general trends evident from the results of adjustment experiments are...a tendency to 'compress' smaller intervals (adjust narrower than equal-tempered intervals) and "stretch" wider intervals (adjust wider)." [Burns, E. M., and Ward, W.D., "Intervals, Scales and Tuning," in The Psychology of Music, ed. Diana Deutsch, 1982, pg. 250.] "A number of measurements have been made of the intonation of musicians playing variable-tuning instruments under actual performance conditions (e.g., Greene, 1937; Nickerson, 1948; Mason, 1960; Shackford, 1961, 1962, a, b). The results of these measurements have been summarized by Ward (1970). They show a fairly large variability for the tuning of a given interval in a given performance--ranged of up to 78 cents, interquartile values of up to 38 cents. The mean values of interval tunings, in general, show no consistent tendency to either just intonation or Pythagorean intonation in either melodic or harmonic situations. The general tenedency seems to be to contract the semitone and slightly expand all other intervals relative to equal temperament. There is also some evidence of context- dependent effecst (e.g., to play F# sharper than Gb (Shackford, 1962 a,b)]. Those results mirror, to a certain extent, the results of the adjustment and identification experiments using isolated intervals (discussed in Sections III A and III B) which showed a tendency to compress the scale for small intervals and stretch the scale for large intervals, in both ascending and descending modes of presentation. "The above measurements were obtained for Western classical music, but the same general tendencies are evident in intonation form a military band (Stauffer, 1954), Swedish folk musicians (Fransson, Sundberg & Tjernland, 1970), and jazz daxophonists (Owes, 1974). Measurements of intonation inperformance for Indian (Hindustani) classical music (jairazbhoy & Stone, 1963; Callow and Shepard, 1972) show similar variability." [Burns, E. M., and Ward, W.D., "Intervals, Scales and Tuning," in The Psychology of Music, ed., Diana Deutsch, 1982, pg. 258.] "Even the ubiquitous 5th itself is played, on the average, sharper than the 702 cents predicted; indeed, in Shackford's study, it is played sharpest in a harmonic context, where the minimization-of-beat forces would be expected to be the most active." (...) Thus evidence indicates strongly that in musical performances the target pitch for frequencies actually produced in response to a given notation is one that is just a shade sharper than that called for by Et. In the 500 and 1000 Hz regions, even the subjective octave (sacrosanct 2:1 in all theoretical systems) is about 1210 cents for pure tones (Ward, 1954). In his studies, Shackford (1962 a,b) measured harmonic 10th, 11th and 12th and found that they were sharped to about the same extent as 3rd, 4tha nd 5th. "Boomsliter and Creel (1963) too have provided striking confirmation of this theory. (...) ...it is clear from the sample dat they present aththe preferred scale almost always is composed of tones consistently higher in frequency than those of ET. For example, in three classical numbers (the Marseillaise, a Bartok dance, and Mozart's Serenta Notturna), all notes above "do" are preferred 4 to 23 cents sharp." [Ward, W.D., "Musical Perception," in "Foundations of Modern Auditory Theory," ed. J.V. Tobias, Vol. 1, pp. 420- 421] cent 2:1. The next post will examine data bearing on the third theory of hearing-- a model of the ear so far not dealt with as extensively as the other two. --mclaren Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Tue, 10 Oct 1995 02:20 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id RAA12768; Mon, 9 Oct 1995 17:20:34 -0700 Date: Mon, 9 Oct 1995 17:20:34 -0700 Message-Id: <951010001440_71670.2576_HHB24-3@CompuServe.COM> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu