source file: mills2.txt Date: Sun, 17 Nov 1996 11:58:47 -0800 Subject: From Brian McLaren From: John Chalmers From: mclaren Subject: a blizzard of misinformation -- Paul Erlich is a very smart fellow who has done commendable work in looking up valuable references. Alas, Paul often has a tendency to shoot from the hip, based on incomplete or out-of-date info. Such an example occurred when Paul Erlich wrote that "the preference for stretched intervals only occurs in melodic, not harmonic, intervals" (or words to that effect). This is a common enough canard, and it turns out to be untrue. In actual fact unbiased listeners uniformly tend to hear *both* melodic *and* vertical intervals which are stretched as "pure" and "just," while they tend to hear unstretched small-integer ratio harmonic *and* melodic intervals as "too narrow" and "impure." (I mention "unbiased" because it is always possible to train yourself to recognize any kind of interval from its beat structure if you confine yourself to a narrow range of very restricted integer-harmonic timbres. This is why A-B-X tests using a wide variety of different timbres in an objective psychoacoustic experiment are so important. Simply setting up a synthesizer and playing such-and-such and interval and saying, "Oh, I can hear that the interval is [fill in the blank]" is useless in probing the human auditory system, since you know what to listen for and thus have unwittingly biased yourself.) The evidence that listeners hear *both* stretched harmonic *and* melodic intervals as "pure" is cumulative, the data have been confirmed by hundreds of experiments, and the evidence goes back more than 160 years. C.J. Delezenne in "Memoires sur les valeurs numeriques des notes de la gamme," in Recueil des travaux de la Societe des Sciences de Lille, 1826-1827, was the first researcher to identify *both* melodic *and* harmonic preference for stretched intervals. Delezenne used an adjustable monochord and meticulously recorded the values his test subjects heard as "pure" intervals in terms of fractions of a Pythagorean comma (cents were not yet a measurement in use). The next researchers who duplicated these results were Cornu and Mercadier, who used a phonautograph (as scholars, you know what this instrument is and require no explanation) and by examination of the tracings on the lampblack-coated camphorated cellulose strips Mssrs. C & M were able to calculate with precision the frequency of sounds impinging on the phonautograph. Cornu & Mercadier found that the mean intonation for a vertical dyad heard as a "pure" major third was 1.251, close to but sharper than the just 5/4; a consecutive-tone series of tests on musical subjects yielded the much sharper value of 1.2666 for melodic "just" thirds. See Cornu & Mercadier, "Sur les intervalles musicaux," Comptes Rendus de l'Academie Royale des Sciences, 1869a, pp. 301-308 for proof. In 1876 Preyer found that vertical intervals as large as 397 cents were still identified by some subjects as "pure major thirds." Preyer's results are suggestive, but not conclusive, since he gave his data in terms of an "index of sensitivity" to intervals rather than in terms of analysis of variance, as would be done today. Preyer's value for the "pure" major third represents a weighted average of the minimum and maximum values cited by test subjects. For details, see Preyer, W. T., Ueber die Grezen der Tonwahremung, Jena, 1876. In 1897-8 the extremely underrated acoustician and music theorist Carl Stumpf studied perception of the minor third by test subject under 3 conditions: melodic ascending, melodic descending, and simultaneous dyad. His results show a marked asymmetry in the spread of sharp vs. flat intervals judged "pure." For the minor third, this means that the test subjects were more inclined to accept considerable flatting that slight sharping. Stumpf concluded that the "point of subjective purity" shifted toward flat minor thirds. He conducted the same series of tests with major thirds and found exactly the opposite tendency. For major thirds, the point of subjective purity shifted toward sharp thirds. Melodic intervals had to be tuned significantly sharper to be perceived as "pure" than simultaneous dyad major thirds, but *both* had to be sharper than just to be perceived as "pure." See Stumpf, C., and H. F. Meyer, "Massbestimmungen ueber die Rienheit consonanter Intergvals," in Beitraege zur Akustik und Musikwissenschaft, Vol. 2, 1898, for full details. Moran and Pratt tested melodic and vertical intervals but didn't give detailed breakdowns: they state merely that there is an average error of 18 cents for the intervals of the 12-TET scale. They did, however, find that subjects were more likely to hear intervals chosen from equal temperament as "pure" and "just" than intervals chosen because they exhibited small integer ratios. It's unclear whether this was due to the effect of familiarity with 12-tet, however. See Moran , H. and C. C. Pratt, "Variability of Judgments On Musical Intervals," J. Exp. Psych., Vol. 9, 1926, for more info--but not much more. The article is very short on details, alas. P.C. Greene cites exhaustive stats shows a marker preference for melodic Pythaogrean thirds: see Greene, P.C., "Violin Performance with Reference to Tempered, natural and Pythaogrean Intonation," Iowa Studies in Muisc, Vol. 4, pp. 232-251, 1937, also see Greene's JASA study published in the same year. Incidentally the entire University of Iowa Studies series supervised by Seashore remain a remarkable resource. I heartily recommend these to *every* microtonalist as a compendium of what performers actually *do*, as opposed to the intervals they *claim* they play. The second world war pretty much shut down psychoacoustic research, so the next significant papers on the subject are from the late 1940s and the 1950s. J. F. Nickerson, in "A Comparison of Performance of the Same Melody in Solo and in Ensemble with Reference to Equi-Tempered, Just and, Pythagorean Intonation," PhD thesis, University of Minnesota, 1948, found the same perception of stretched melodic *and* harmonic intervals as "pure" (although as usual melodic intervals had to be stretched more widely than vertical dyads before they were heard as "pure" or "just" or "in tune."). There are so many studies from the 1950s and 1960s and 1970s that I will cite only 3 more: Ward, W. D., "Music Perception" in Foundations of Modern Auditory Theory, Ed. J. V. Tobias, 1970--more support for my statement and more contradiction of Paul Erlich's claim that listeners do not perceive stretched vertical dyads as "just" and just vertical dyads as "too narrow" and "impure." In 1975 Terhardt and Zick published an extremely interesting paper which links the accompaniment of a melody with the intervals heard as "pure." Some types of accompaniment required intervals be stretched to be heard as "pure," while other types of accompiment required that all intervals be contracted to be heard as "pure." This applies to the vertical intervals of the accompaniment as well as to the consecutive intervals of the melody. See Tehardt, E., & Zick, M., "Evaluation of the Tempered Tone Scale in Normal, Stretched and Contracted Intonation," Acustica, Vol. 32, 1975, pp. 268-274. The most recent reference which refutes Paul Erlich's claims and proves my statement of fact is Sundberg, Johan, "The Science of Musical Sounds," The Academic Press: New York, 1991, page104: "In the case of the octave, the craving for stretching has been noticed for both dyads and melodic intervals." Table 4.12 on Sundberg's page 102 gives "Average sizes and standard deviations for dyads between vibrato tones adjusted by musically experienced listeners." Average for M2nd is 199 cents, for Major third was 402 cents, for perfect fifth 704 cents, for octave 1204 cents. Notice that these are in fact dyads. As mentioned, Paul Erlich is a smart fellow with good intentions but occasionally he does miss the mark by making a claim which isn't based on fact. His posts contain more errors than other people's posts merely because Erlich posts more useful information than most other subscribers. The total amount of incorrect information in Erlich's posts as a percentage is actually quite low. --mclaren Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Sun, 17 Nov 1996 23:09 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA11043; Sun, 17 Nov 1996 23:10:31 +0100 Received: from eartha.mills.edu by ns (smtpxd); id XA13095 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id OAA19919; Sun, 17 Nov 1996 14:10:29 -0800 Date: Sun, 17 Nov 1996 14:10:29 -0800 Message-Id: <961117170850_1419612455@emout19.mail.aol.com> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu