source file: mills2.txt Date: Sat, 7 Oct 1995 07:42:06 -0700 From: "John H. Chalmers" From: mclaren Subject: Tuning & psychoacoustics - post 14 of 25 --- "In the case of the octave, the craving for stretching has been noticed for both dyads and melodic intervals. The amount of stretching preferred depends on the mid frequency of the interval, among other things. The average for synthetic, vibrato-free octave tones has been found to be about 15 cents. Thus, subjects found a just octave too flat but an octave of 1215 cents just." [Sundberg, J. "The Science of Musical Sounds," 1992, pg. 104] MYTH: "The interval is just or not at all." [Harrison, "Lou Harrison's Music Primer," 1971, pg. 48] FACT: "For centuries, musical folklore has held that the simplest ratios are the best ratios, in musical intonation. Thus the interval betwen two frequencies having a ratio of 3:2 is the "perfect" fifth; 4:3 gives a "perfect" fourth, etc. (...) These philosophical and a priori views of temperament, however, are hardly supported by empirical evidence." [Ward, W.D. and Martin, W.D., "Psychophysical Comparison of Just Tuning and Equal Temperament in Sequences of Individual Tones," JASA, Vol. 33, No. 50, 1961, pg. 586] MYTH: "This 2 to 1 relationship is a constant one...the fact is that nature does not offer one tone and its doubling (200 to 400) as a given quality of relationship, and the same quality of relationship in two tones which are not a ratio of doubling (200 to 600, for example)" [Harry Partch, "Genesis of a Music," 2nd. Ed., 1974, pg. 77.] FACT: "If a frequency of 8 kHz is chosen for f1, subjects produce for the sensation of `half pitch' not at a frequency of 4 kHz, but a frequency of about 1300 Hz." [E. Zwicker and H. Fastl, "Psychoacoustics: Facts and Models," 1993, pg. 103.] MYTH: "If, through some terrestrial disaster, our [equal-tempered] musical system were completely lost, it would sooner or later be inevitably redicsovered, just as it exists today, after having passed through transformations identical or similar those those it has undergone." [Ducup de Saint-Paul, quoted in Matthys Vermeulen, "Hic et Nunc, Jacobe," Djawa, Vol. 12, 1932, pp. 146-149] FACT: "It is quite remarkable that musicians seem to prefer too wide or "stretched" intervals." [Johan Sundberg, "The Science of Musical Sounds," 1992, pg. 103.] MYTH: "Notice that these frequency clumps are arranged in a harmonic series based on a fundamental frequency half that of tone M, and also that any lack of accuracy in setting an exact 3/2 frequency ratio will be called to our attention... " [Benade, A. H., Fundamentals of Musical Acoustics, 1975, pg. 272] FACT: "The experimental results very convincingly show that, on the average, singers and string players perform the upper notes of the major third and the major sixth with sharp intonation (Ward 1970)...The same experiments revealed that also fifths and fourths and even the almighty octave were played or sung sharp, on the average! (A reciprocal effect exists. Pure octaves are consistently judged by musicians to sound flat!) Rather than revealing a preference for a given scale (the Pythagorean), these experiments point ot the existence of a previously unexpected *universal tendency to play or sing sharp all musical intervals.* (italics in original text)" [Juan Roederer, "Introduction to The Physics and Psychophysics of Music," 1973, pg. 155.] MYTH: "Consequently, these statements can be conclusively made; the ear consciously or unconsciously classifies intervals according to their comparative consonance or comparative dissonance; this faculty in turn stems directly form the comparative smallnesss or comparative largeness of the numbers of the vibrational ratio..." [Harry Partch, "Genesis of a Music," 2nd. Ed., 1974, pg. 87.] FACT: "Therefore it must be concluded that even just or pythagorean intonation cannot be considered as ideal. Rather, optimum intonation of a diatonic scale probably depends on the structure of the actual sound in the same manner as has been previously discussed with respect to tempered scales." [E. Terhard and S. Zick, "Evaluation of the Tempered Tone Scale In Normal, Stretched, and Contracted Intonation," Acustica, Vol. 32, 1975, pg. 273.] MYTH:"The reason that the ratio does not change is simply and wholly because physiogically the ear does not change excpet over a period of thousands and millions of years." [Partch, Genesis of a Music, 2nd ed., 1974, pg. 97] FACT: "The degree of consonance depends on the quality or spectrum of the component tones, i.e., the relative intensity of dissonant vs. consonant upper harmonics." [Juan Roederer, "The Physics and Psychoacoustics of Music," pg. 143.] MYTH: "Long experience in tuning reeds on the Chromelodeon convinces me that it is preferable to ignore partials as a source of musical materials. The ear is not impressed by partials as such. The faculty--the prime faculty--of the ear is the perception of small-number intervals, 2/1, 3/2, 4/3, etc., etc., and the ear cares not a whit whether these intervals are in or out of the overtone series." [Harry Partch, "Genesis of a Music," 2nd. Ed., 1974, pg. 87.] FACT: "In 1987 IPO issued a wonderful disc by Houtsma, Rossing and Wagenaars...illustrating the effects of a moderate stretching...of scale frequencies and/or partial spacings. Part of a Bach chorale is played with synthesized tones. When neither scale nor partial frequencies are stretched, we hear the intended harmonic effect. When the scale is unstretched but the partial frequencies are stretched, the music sounds awful. Clearly, intervals in the ratio of small whole numbers are in themselves insufficient to give Western harmonic effects." [John R. Pierce, "The Science of Musical Sound," 2nd Ed., pp. 91-92.] MYTH: "In the previous section of this chapter, I made a definition: we would henceforth reserve the word *tone* to refer to sounds having harmonic partials. For emphasis, I will often refer to such sounds as musical tones...to underline the fact that harmonically related complexes of partials have a very special perceptual status that happens also to make them useful in music." [Benade, A.H., Fundamentals of Musical Acoustics, 1975, pg. 264] FACT: "Clearly the timbre of an instrument strongly affects what tuning and scale sound best on that instrument." [Wendy Carlos, "Tuning: At the Crossroads," Computer Music Journal, 1987.] "Most instruments in our music culture produce harmonic spectra, as mentioned. However, in the contemporary computer-aided electroacoustic music studios, is not a necessary constraint any longer. One would then ask if this does not open up quite new possibilities also with respect to harmony. If one decides to use one particular kind of inharmonic sepctra for all tones, it should be possible to tailor a new scale and a new harmony to this inharmonicity." - Johan Sundberg, "The Science of Musical Sounds," pg. 100. "By using a digital computer, musical tones with an arbitrary distribution of partials can be generated. Experience shows that, in accord with Plomp's and Levelt's experiments with pairs of sinusoidal tones, when no two successive partials are too close together such tones are consonant rather than dissonant, even though the partials are not harmonics of the fundamental. For such tones, the conditions for consonance of two tones will not in general be the traditional ratios of the frequencies of the fundamentals... [The 8-TET scale] is, of course, only one example of many possible scales made up of tones whose upper partials are not harmonics of the fundamental and having unconventional intervals, which nonetheless can exhibit consonance and dissonance comparable to that obtained with conventional musical intstruments (which have harmonic partials) and the diatonic scale. It appears that, by providing music with tones that have accurately specific but nonharmonic partial structures, the digital comptuer can release music from the constraint of 12 tones without throwing consonance overboard." [John R. Pierce, "Attaining Consonance in Arbitrary Scales," Journal of the Acoustical Society of America, 1966, p. 249.] "The physical correlate of an interval is not a ratio, anymore than the physical correlate of a pitch is a frequency. Intervals and pitches both have thresholds, ranges of variability," [Moran, H. and C. C. Pratt, "Variability of Judgments on Musical Intervals," Journal of Experimental Psychology, Vol. 9, 1926] Evidence for this conclusion is so voluminous and so detailed that it cannot be contained in a single series of 22 posts. However, the next post scratches the surface of this body of evidence, and hints at the enormous extent of the experimental data showing a universal human preference for stretched octaves, fifths, thirds, etc. --mclaren Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Sun, 8 Oct 1995 03:26 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id SAA22621; Sat, 7 Oct 1995 18:25:50 -0700 Date: Sat, 7 Oct 1995 18:25:50 -0700 Message-Id: <951008012346_71670.2576_HHB23-1@CompuServe.COM> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu