source file: mills2.txt Date: Fri, 20 Oct 1995 07:57:41 -0700 From: "John H. Chalmers" From: mclaren Subject: Tuning & psychoacoustics - post 25 of 25 --- As an empirical science, psychoacoustics is largely concerned with measuring the reactions of the ear/brain system to specific acoustic stimuli. However, human hearing is a hierarchical process made up of many layers of abstraction. Small acoustic stimuli shade imperceptibly into larger ones, leading inexorably to such large-scale percepts as "key center," "cadence," and "discordance" and "concordance." As Eberhard Zwicker points out, "It is clear that psychoacoustics plays an important role in musical acoustics. There are many basic aspects of musical sounds that are correlated with the sensations already discussed in psycoacoustics. Examples may be different pitch qualities of pure tones and complex sounds, perception of duration, loudness and partially-masked loudness, sharpness as a an aspect of timbre, perception of sound impulses as events within the temporal patterns leading to rhythm, roughness, and the equivalence of sensational intervals. For this reason it can be stated that most of this book's contents are also of interest in musical acoustics. At this point we can concentrate on two aspects that have not been discussed so far: musical consonance and the Gestalt principle." [Zwicker, E. and H. Fastl, Psychoacoustics: Facts and Models, 1990, pg. 312] Zwicker characterizes the hierarchical perception of musical tones by drawing a distinction between sensory consonance (perceived roughness, sharpness, and noisiness of the tone) and harmony, (perceived tonal affinity, tolerability, and root relationship of tones or sequences of tones to a scale). So doing, he posits that both modes of perception are hierarchically involved in the sensation of musical consonance. Both experience and experiment tell us that the process of listening to music involves levels of neural organization above the purely physical acoustic operation of the inner ear. While the point of maximal stimulation on the basilar membrane indicates a simple mechanical Fourier analysis of sounds entering the ear, the firing pattern of neural fibers in the auditory nerve encodes pitch and spectral information in the nerve system in a complex way. The path between primary auditory nerve and cerebral cortex is not a simple one. Many feedback loops control the processing of auditory information, and there are many opportunities for higher brain centers to alter the raw input travelling up the auditory nerve--and vice versa. The anatomy of the pathway between the auditiory nerve and the cerebral cortex is complex: the cells of the primary neurons (that is, those in the auditory nerve) are located within the modiolus of the cochlea; these primary nurons terminate in the cochlear nucleus, a mass of gray matter located in the dorsal and lateral portion of the medulla oblongata. Here the physical nerve connection breaks. From this point there is a synpatic connection (mediated by neurotransmitters) to the neurons of the inferior colliculus. After another synpatic gap in the neural pathway, the third- order neurons converge on the medial geniculate body, the final relay station on the auditory path to the cerebral cortex. It's worth nothing that the medial geniculate body not only collates fibers from the audtiory nerve, but also from other sensory systems and from the cerebral cortex as well. Thus the geniculate body serves not as a passive relay station so much as an active filtering and integrating locus. >From the geniculate body, the fourth-order auditory neurons connect with the cerebral conrtex by way of a thin sheet of radiating nerve fibers. These radiations include corticofugal fibers running from the cortex back to the medial geniculate body. Thus the auditory neural pathway contains a complex feedback loop, controlled by several sets of higher brain loci, running between the auditory nerve and the cerebral cortex. Most of the fourth-order neurons enter a small region ofthe posterial half of the horizontal wall of the Sylvian fissure, which acts as a focal zone for the entire auditory cortex. The complexity of the auditory region of the Sylvian fissure is daunting: each cochlear fiber makes connections with thousands of other neurons grouped in at least thirteen regions, and populated by many different types of neurons. To make the process even more complex, not all of these neurons respond identically. Some produce strong signals when presented with tones in a particular frequency range but do not respond to tones in other frequency ranges. A small fraction of neurons emit strong signals when two different frequencies are sounded together, but these same neurons produce little or no response when either frequency sounds alone. Some neurons are most strongly stimulated by sounds at specific amplitudes: sounds outside this narrow amplitude window cause no resopnse from suchneurons. For yet other auditory nerve fibers, the higher the sound's amplitude, the stronger the response, until a satuation point is reached. Some neurons respond best toe amplitude-moedulated tones, others to frequency-modulated tones. Some neurons respond with paritcular vehemence to sounds coming from a particular region of space, and some neurons respond best to sounds that are moving in space. Because these cortical loci consist of neural pathways, they are formed by learned response and can be changed. Thus, the impact of culture and experience on musical perception is at least as great as the physical sensory correlates of musical tone--if not greater. "I once attended...a concert in Bangkok that was totally mystifying. I could see that the audience was utterly enraptured, swooning at moments of apparently overwhelming emotional beauty that made no impression on me whatsoever; not only that, I couldn't distinguish them from any other moments in the piece." [Eno, Brian, "Resonant Complexity," Whole Earth Review, May 1995, pg. 42] This points to a important caveat. While the results adduced so far provide evidence for this or that musical tuning system ont he basis of sensory consonance, psychoacoustics cannot describe or validate the higher levels of musical organization implicit in a tuning system. Thus the internal structure of a tuning is different from the sensory consonance produced by intervals within that tuning. For example: Risset's, Pierce's and Sethares' timbral mapping procedure, following the implications of research by Plomp and Levelt and Kameoka and Kuriyagawa, allow a composer to control the level of *sensory consonance * in a given tuning, but mapping the component partials of a sound into a given maximally consonant set for a specific scale does *not * change the inherent tonality of the scale, its Rothenberg propriety, the Barlow harmonicity or the Wilson efficiency of the scale. In short, by changing timbre, note duration, and compositional style one can change the surface affect of music produced in a given tuning: but the deeper structural elements of the tuning remain invariant. Ivor Darreg described one of the deeper structural invariants in a given tuning as its "mood:" "In my opinion, the striking and characteristic moods of many tuning-systems will become the most powerful and compelling reason for exploring beyond 12-tone equal temperament. It is necessary to have more than one non-twelve-tone system before these moods can be heard and their significance appreciated." [Darreg, Ivor, "Xenharmonic Bulletin No. 5, 1975, pg. 1] David Rothenberg proposed that the Rothenberg propriety of a scale explains some aspects of the scale's deep structure; Clouth and Douthett duplicated some of this work in their article "On Well-Formed Scales." John Chalmers has speculated that Rothenberg propriety explains the sense of tension in such tunings as Ptolemy's intense diatonic. In addition to the "mood" or overall "sound" of a given tuning, Darreg and McLaren (1991) pointed out that each tuning exhibits some degree of inherent bias toward melody or harmony. The Pythagorean intonation and 13-tone equal temperament, for example, are both strongly biased toward melody, while 31-tone equal temperament and 13-limit just intonation are strongly biased toward harmony. Douglas Keislar made this same point in his 1992 doctoral thesis. In it, Keislar describes research which demonstrates that altering the surface characteristics of the music--timbre, tempo, spatialization--does not change the deeper structural characteristics of the tuning. Thus, while mapped overtones will make a comopsition in 13-tone equal temperament sound more acoustically smooth, it does not change the essentially atonal character of the 13-tone scale, nor does it materially affect the scale "mood." Similarly, changing the timbres of a composition in Ptolemy's intense diatonic tuning will alter the degree of sensory roughness or smoothness; adding reverberation will mask to greater or lesser degree some of the overall "sound" of the composition. But the sense of aesthetic tension created by scale intervals which are, in Rothenberg's usage, improper, will remain unchanged. Thus the implications for tuning suggested by psychoacoustic research must be viewed as separate from larger musical and perceptual questions. Because current psychoacoustic experiments focus on questions of sensory perception, there remains a dichotomy between what Easley Blackwood has called "concordance and discordance" and sensory consonance and dissonance. In fact sensory consonance is a misnomer: the effects are more accurately described as sensations of auditory roughness or smoothness. Depending on the tuning or the composition, intervals which are perceived as rough may prove concordant, while intervals which prdouce the auditory sensation of smoothness may strike the listener as discordant--that is, out of place musically. In Western music, the best example of this phenomenon is the perfect fourth, which sounds acoutically smoother than the major third but which by itself generally constitutes an unstable and musically discordant interval. In Balinese and Javanese music, the best example is the stretched 1215- cent octave, which sounds acoustically rough but which produces as sense of musical concordance when performed by a gamelan. The most striking example in my own experience was a 1990 concert by the Women's National Chorus of Bulgaria. One of the duets (a folk song from the Thracian plains) ended on a large major just second (9/8). The Western audience sat without moving forwhat seemed a long time: only when the singers bowed did the audience realize the duet was over, and applaud. In this case the contradiction between learned perceptions of concordance and cadence, and the sensory perception of roughness in the cadential intervals, prevented the audience from correctly perceiving the cadence. It is important not to confuse sensory roughness or smoothness, as measured by psychoacoustical experiments, with higher-level perceptions of musical consonance and dissonance. Many advocates of just intonation have baselessly conflated the two categories, while advocates of Fetis' model (viz., all auditory responses are predominately learned responses) excessively emphasize the abstract levels of hierarchical auditory perception while unjustifiably discounting the purely physical processes at work in the human ear/brain system--in particular the frequency-analysis operations of the basilar membrane and the periodicity-extraction mechanism of the neurons in the auditory nerve. Ultimately, what Zwicker calls Gestalt musical perception is mediated not only by the physics and acoustics of the inner ear, but also by primary, secondary, third-order and fourth-order neurons, a variety of different brain locations, and the operant conditioning imposed by experience, culture and musical tradition. The conclusions of this series of posts must be taken in that context, and understood in that larger framework. --mclaren Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Sat, 21 Oct 1995 01:16 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id QAA08509; Fri, 20 Oct 1995 16:16:08 -0700 Date: Fri, 20 Oct 1995 16:16:08 -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