source file: mills2.txt Date: Mon, 2 Oct 1995 09:12:35 -0700 From: "John H. Chalmers" From: mclaren Subject: Tuning & Psychoacoustics - Post 9 of 25 --- "A theory should as simple as possible-- but not simpler." -- Albert Einstein --- MYTH: PITCH IS THE LOGARITHMIC FREQUENCY HEIGHT OF A MUSICAL TONE, AND ITS PERCEPTION IS AUTOMATIC AND INNATE. Fact: There are 3 kinds of pitch: physical, mel and perceptual pitch. The 3 differ significantly. Perceptual pitch is never identical to the log of the frequency of the fundamental of the perceived tone, and mel pitch differs radically from both. The perception of all 3 kinds of pitch is strongly influenced by both context and learned experience. --- The perceived pitch of sine tones depends on their duration and their loudness. "A 150-Hz tone increasing from 45 to 90 dB drops in pitch to an extent corresponding to a 12% frequency shift. This is close to 2 semitones in the diatonic scale. The sensitivity to this effect varies considerably between individuals. (...) A funny consequence of this is that a soft sine tone at 300 Hz may sound as a pure octave of a loud sine tone at 168 Hz. The mathematically pure octave, however, has the frequency of 150 Hz. The tone that sounds as a pure octave is 12% too high. This means that mathematically it is a minor seventh! This is a good argument for avoiding confusion of perceptual and physical entities." ["The Science of Musical Sounds," Sundberg, 1992, pg. 46] Pierce explains that "By asking naive subjects to relate frequency changes of sine waves to a halving of pitch, psychologists found a mel scale of pitch (for sine waves). In the mel scale there is no simple relation between frequency and pitch; nothing like the octave shows up. (...) The sounds of orchestral bells are not periodic, and these sounds do not have all the properties of periodic musical sounds. One can play tunes with bells, and the pitches that are assigned to bells can be explained largely in terms of the frequencies of prominent almost- harmonic partials. "Clucking sounds and shushing sounds (bands of noise) have brightness, but no periodicity. Oddly, *we can play a recognizable tune with these sounds, even though they cannot be heard as combining into chords or harmony.* Apparently, in the absence of a clear pitch, brightness can suggest pitch.' ["The Science of Musical Sound," Pierce, J.R. 1992, pg. 37] "Systematical series of experiments have been carried out in which listeners have been asked to adjust the frequency of a variable tone so that it sounds "twice as high" or "half as high" as a reference tone. (...) The mel scale is constructed such that a halving of the number of mels corresponds to a halving of the pitch perceived. As shown in the figure, a tone with the pitch of 1,000 mel sounds twice as high as another tone with the pitch of 500 mel. Examination of the figure tells us this corresponds to a frequency shift from approximately 1,000 to 380 Hz." ["The Scinece of Musical Sounds," Sundberg, 1992, pg. 47] The mel scale of pitch measures what is also sometimes called "ratio pitch." This is drastically different from the ordinary scale of perceptual musical pitch, since the mel scale applies only to sine tones. However, the plot thickens as soon as we realize that *many musical timbres can be modelled as sums of sine waves.* Thus the conceptual basis for conventional harmonic-series models of consonance, as well as for the purported acoustic superiority of small whole-number ratios, comes into doubt as soon as we begin to examine the psychoacoustic evidence in detail. If perceptual pitch is always different from physical logarithmic pitch, how can either equal-tempered or just intonation tunings offer a valid model for musical harmony and musical melody? To make matters even more complex, "In certain cases the amplitude dependence of the pitch of complex tones is the opposite of that shown in Figure 3.4. If the loudness of a complex tone of about 100 Hz fundamental frequency is increased, its pitch may rise rather than drop." ["The Science of Musical Sounds," Sundberg, 1992, Pg. 46] "The pitch of pure tones depends not only on frequency, but also on other parameters such as sound pressure level. (...) Pitch shifts of pure tones can also occur if additional sounds that produce partial masking are presented. Pitch shifts produced by a broad-band noise masker are shown in Fig 5.4, and are given as a function of both frequency and critical-band rate of the pure tones, the level of which is 50 dB. (...) The results display in Fig 5.5 show pitch shifts up to 8% at low frequencies near 300 Hz, and a pitch shift of only 1% at higher frequencies between 1 and 4 kHz, due to the octave ratio of partial-masking tone and test tone." ["Psychoacoustics: Facts and Models," Zwicker and Fastl, 1993, pp. 105-107] The pitch of pure tones is also dependent on their duration. Doughty and Garner (1948) found that pitch is unchanging for tones of 25 msec and longer, but that 12-msec and 6-msec tones have a lower pitch. [See Doughty, J. M and Garner, W.R. "Pitch Characteristics of short tones. II: Pitch as a function of tonal duration," J. Exp. Psychol., Vol. 38, pp. 478-494, 1948] Corso summed up the situation when he concluded that "the pitch of musical sounds is not directly proportional to the logarithm of the frequency and is probably complexly conditioned." [Corso, J.F., "Scale Position and Performed Musical Octaves," Journal of Psychology, Vol. 37, 1954] In short, most of what musicians "know" about pitch is untrue, at least as far as pure sine tones are concerned. This casts strong doubt on tuning theories which ascribe to various pitch relationships "special" characteristics--in particular, the data adduced in this post casts strong doubt on both just and equal-tempered tuning systems, and would tend instead to favor non-just non-equal-tempered tunings. What about complex tones made up of many sinusoidal components and the influence of learning and context? What are the implications for tuning and for music? That's the topic of the next post. --mclaren Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Mon, 2 Oct 1995 19:10 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id KAA17686; Mon, 2 Oct 1995 10:10:07 -0700 Date: Mon, 2 Oct 1995 10:10:07 -0700 Message-Id: Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu