source file: mills2.txt Date: Fri, 16 Aug 1996 07:30:17 -0700 Subject: Another post from Brian From: John Chalmers From: mclaren Subject: Hucksters, shysters and other suspicious doyens of intonational "research" -- Many and mutually contradictory are the results of psychoacoustic research on tuning in the early years of this century. And still, occasionally, in the badly thought-out articles which appear now and then. As one who believes along with H. L. Mencken that "Man, at his best, remains a sort of one-lunged animal, never completely rounded and perfect, as a cockroach, say, is perfect," this is perhaps only to be expected. Nevertheless it behooves me to point out some of the more glaring errors perpetuated in the name of early 20th-century intonational "research." (These errors are filched straight from "How to Lie with Statistics," by Darrell Huff, W. W. Norton and Co., 1954. This book ought to be taught in every college curriculum.) The first classic error of the intonational "researcher" is the biased sample. Consider, for example, a paper which stands out for sheer wackiness as perhaps the worst piece of microtonal "research" ever done: namely, "Scale, Key and contour in the discrimination of tuned and mistuned approximations to melody" by Anthony J. Watkins, Perception & Psychophysics, 1985, Vol. 37, No. 4, pp. 275-285. Watkins makes sure to build in a huge bias into his test sample of listeners, because he defines "mistuned" melodies as the closest approximation to a 12-TET melody in another equal temperament. The problem with this sort of microtonal "research" should be obvious: if you inform your test subjects that, say, red is a distorted version of blue, and then show your test subjects a lot of paintings with red in 'em, you will obtain the predictable result that "the subjects reported that all paintings which were not monochromatically blue were perceived as significantly distorted." This kind of "research" is just a nudge away from the infamous political "push polls," in which quondam "phone researchers" call up voters for the opposition and ask: "Would you change your vote if you learned that your candidate is a child molester?" (It's worth mentioning that Richard Nixon is the father of this infamy, in the 1947 Jerry Vorhees senate race.) In the microtonal realm, a more subtle form of biased sample is found when researchers choose 1st year music students as test subjects for intonational listening studies. SInce most of these music students are constantly being run through an exhaustive regimen of 12-TET listening tests, the sample is a priori tainted, and might even be unusable. John Chalmers has pointed this out--the problem is much less severe with upper division music students, since they've been exposed to real music in so many intonational real-life situations that their ears are bound to be more flexible. They also have presumably passed the early ear- training tests and thus are not constantly being bombarded by 12-TET brainwashing.) [2] The well-chosen average is a second source of error in intonational research. Mean and median "averages" are often quite different, particularly with small sample sizes and large variances. Most insidious of all is the quoted "average" deviation from some hypothetical "target tuning" as measured by the preferences of a group of listeners. If the averages are given as unsigned scalars, the study is often worthless. Don Hall et al. made this error in their 1985 article "The Perception of Musical Intervals." Hall and co. also chose their deviations from values which slyly sit atop just ratios, so that the implication was that the listeners judged deviations based on an innate desire for small integer ratios. Franz Loosen's articles corrected this error by showing that the direction of the error bars of perceived deviations changed systematically depending on which instrument the listener used. Loosen's studies tell us: [1] different listeners perceive deviations from different types of intervals--pianists from ET intervals, violists from Pythagorean intervals; and [2] that pianists and violinists tolerate different error ranges skewed toward different triadic pitch heights, showing that they are measuring "deviation" primarily in terms of the triads they've become used to hearing. [3] "The little figures that are not there" bedevil small group studies of intonational perception. If you've got 4 or 6 listeners, it's no more meaningful to report that "75% of listeners perceived the stretched intervals as..." than it is to report that "75% of dentists surveyed prefer Crest." (What this really means is that the fourth dentist disagreed.) Carol Krumhansl's studies use very small sample sizes--yet her results purport to be statistcally significant. A much earlier researcher, Carl Seashore, used truly mammoth sample sizes, and his results hold up. Heinz Werner's studies are also a excellent model in this regard; his results were primarily *qualitative*, and Werner's main interest was in eliciting descriptions of perceived intervals. This is a valid procedure even with very small sample sizes. But Krumhansl's statistical approach seems highly suspect when only a dozen or twenty-some listeners are involved, yet the results are generalized to sweeping grandiosities involving "Western tonal hierarchical perception," etc. [4] "Much ado about practically nothing" is the problem of making a big deal out of small differences which probably don't exist. This can be seen in Partch's insistence and more recently Ezra Sims's insistence that inaccuracies in the realm of 2 cents, 1 cent, 1.8 cents, etc., are lethal to the peformance and audition of just intonation music. This error also crops up in intonational research. Comparing standard deviations of interval preference, for example, may not be valid unless the sample size is very large and/or the results have been replicated by many different reserachers over many different years. Another way of saying this is: (number of intonational studies) * (difference in standard deviations) is the quantity that ought to be compared. This works in reverse. Many intonational advocates have tried to claim that small differences in standard deviation of interval perception are merely a statistical error caused by sampling noise--yet they ignore the fact that these small differences are (A) small when compared with the octave, but not when compared with the intervals being perceived, and (B) the results have been replicated by so many hundreds of researchers over more than 150 years of quantitative tests that it's clear a real effect is involved, not mere statistical noise. [5] The last error and one of the most insidious in intonational research is the classic "post hoc" fallacy. This fallacy is aptly summed up by the case in which there are two clocks in the town square. When clock #1 points to 5 o'clock, clock #2 rings its bell. Therefore clock #1 caused clock #2 to ring. Right? This kind of error can be seen in study after study of ethnic scales in non- western cultures. Most of these studies find predominantly 7 or 5 tones. No suggestion is ever made that because of Miller's limit to the channel capacity of the human sensorium and short-term memory (see Miller, G. A., "The Magic Number 7 Plus or Minus Two," Journ. Psych. 1956), 7 notes represents a practical near-upper limit to the number of tones which can be distinguished in a fluid musical context. Instead of arriving at *that* conclusion, intonational researchers in the early part of the century reasoned: since the piano has 7 white keys and 5 black keys, clearly this indicates that the tuning preferences throughout all the world's cultures are caused by an unconscious desire for the western 7-note white piano keys. Right? Alternatively, this fallacious argument is used by just intonation fans (most notably, Lou Harrison--a very fine composer but a less than entirely rigorous scholar) to argue that since errors are distributed approximately evenly around this or that set of just ratios for all of the 7-tone and 5-tone scales used by other cultures, clearly this indicates that the tuning preferences throughout all the world's cultures are caused by an unconscious desire for small whole number ratios. Right? And thunder causes the lightning, right? And smoke causes the fire...right? Researchers like Frederic Voisin, who use retunable synthesizers to measure the *process* of tuning by native experts in other musical cultures, are now beginning to torpedo these specious "post hoc, propter hoc" notions of the origins of ethnic tunings. Shockingly, researchers like Voisin are discovering that there's very little preference for even such purportedly "universal" and "basic" units of intonational measure as the 2:1 octave, the 3:2 fifth, etc. See Voisin, F. "Musical Scales in Central Africa and Java: Modelling by Synthesis," Leonardo Music Journal, Vol. 4, 1994, pp. 85-90; also Kubik, G. "African Tone-Systems: A reassessment," Yearbook for Traditional music, Vol. 17, 1985, pp. 31-63; Schneider, A. and Beurmann, A. "Notes on the Acoustics and Tunings of Gamelan Instruments," Performance in Java and Bali: Studies of Narrative, Theater, Music and Dance, London: B. ARPS, 1993, pp. 197-218; Tracey, H. "Towards an Assessment of African Scales," African Music, Vol. 2, No. 1, 1958, pp. 15-23; Ellis, "Pre- Instrumental Scales," Ethnomusicology, 1962;Vetter, R., "A Retrospect On A Century of Gamelan Tone Measurements," Vol. 33, No. 2, Ethnomusicology, 1989, pp. 217-227; Rahn, Jay, "Javanese Pelog Tunings Reconsidered," Yearbook of the International Folk Music Council,1978, Vol. 10, pp. 69-82; Wachsmann, K., "A Study of Norms in the Tribal Music of Uganda," Ethnomusicology, Vol. 1, No. 11, 1957, pp. 9-16; Hood, Mantle, Hood, M., "Slendro and Pelod Redefined: With a Note on Laboratory Methods, by Max Harrell," Selected Reports on Ethnomusicology, 1966, Vol. 1, No. 1, pp. 28-48; "Hatch, Martin, F. "Lagu, Laras, Layang: Rethinking Melody in Javanese Music," PhD. dissertation, Cornell University, 1980, und so weiter. Lou Harrison has been a prime mover in the misguided attempt to describe *all* ethnic tunings throughout world musical cultures as departures from this or that set of small integer ratios. Alas, the data accumulated over the last century make it clear that most of the world's intonational usage *cannot* be adequately explained in this way. In fact, as Ellis' article and Voisin's research makes clear (along with much other research), many cultures do not even think in terms of subdividing a 2:1 ratio, much less in terms of small-integer ratios. Many cultures think musically in terms of adding constant Herz intervals, irregardless of whether the sum comes out to a 2:1 or not. In fact the Banda Linda, Banda Ndopka, Ngaka-Manza and Banda Gbambiya peoples of Central Africa prefer an "octave" of 1150 cents. Lou Harrison has not explained how to reconcile these facts with the notion that just intonation forms the basis of world music. In the 1920s H. L. Mencken lamented: "Today the old pegagogy has gone out, and a new and complicated science has taken its place. Unluckily, it is largely the confection of imbeciles, and so the unhappiness of the young continues. In the whole realm of human learning there is no faculty more fantastically incompetent than that of pedagogy. If you doubt it, go read the pedagogical journals. Better still, send for an armful of the theses that Kandidaten write and publish when they go up for their Ph.D's. Nothing worse is to be found in the literature of astrology, snake oil salesmanship, or Christian Science." [Mencken, H. L., "The Vintage Mencken Gathered by Alistair Cooke," Vintage Press: New York, 1956, pg. 184] This is nowhere more true than in early intonational "research." Fortunately, there are signs that the woeful tide of error may be receding--somewhat. --mclaren Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Fri, 16 Aug 1996 18:22 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA01772; Fri, 16 Aug 1996 19:05:01 +0200 Received: from eartha.mills.edu by ns (smtpxd); id XA01771 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id KAA21639; Fri, 16 Aug 1996 10:05:00 -0700 Date: Fri, 16 Aug 1996 10:05:00 -0700 Message-Id: <199608161603.RAA05161@gollum.globalnet.co.uk> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu