What is permitted? The nature of music
The materials in the music modules of the course are intended to supplement the texts we will be discussing in class. The selection and presentation are neither systematic, nor are they intended to satisfy the standards of musicology. I have made every effort not to assume any previous musical training, and chosen the musical excerpts with the thought of creating a series of linked impressions, rather than providing any systematic account of compositional developments. The selection also presupposes that you do not want to spend more than an hour with each section, which is why I have been so philistine about taking pieces of music outside the context of the total work.
If you do not know how to read musical notes but are willing to devote a half hour or so to understanding music as a semiotic system, a very efficient way to get started would be at musictheory.net. See if you can get as far as generic and specific intervals under "Lessons." Those with some musical knowledge might spend a few minutes toying with the interval ear trainer under "Trainers."
4. Limitations
We mustn't be too quick to simply affirm or deny direct mappings between compositional forms, the production of sound, and the brain's "subjective" processing of musical pleasure or displeasure. Many aspects of subjective musical perception at the level of the brain remain opaque to this day, but for Helmholtz and his contemporaries, the point of entry for scientific study, so to speak, was the ear. The tiny and delicate mechanisms of the inner ear were not readily susceptible to direct investigation, but Helmholtz offered one of the first physically plausible models for how the ear might process sound. In the simplest instance, you might think of the ear as merely a microphone that turns sound waves directly into electric signals for further processing by the brain. It is more rewarding, however, to ask if the ear itself might play a more complex role in filtering and analyzing the sound as it passes from outer ear through the eardrum and middle ear, and on into the intricate coils of the inner ear. Here the so-called basilar membrane detects incoming vibrations. The Organ of Corti rides loosely on the inner part of this membrane and contains more than 20,00 hair cells. Different hair cells are disturbed when different parts of the basilar membrane move, and they initiate signals on the individual fibers of the auditory nerve.
Helmholtz could not replicate this series of mechanisms, and it is extremely difficult to determine the dynamic relations between the parts of the ear through direct examination of human corpses. But he understood the physiology well enough to suggest that different sensations of pitch might be associated with different places on the basilar membrane: one frequency stimulates one place on the membrane and thus a particular nerve ending, another frequency stimulates another place and nerve. Direct experimental confirmation of Helmholtz's theory came only in the late 1920s with the work of the Hungarian-born Georg/György von Bekesy. While working for the Hungarian Telephone and Post Office Laboratory in Budapest, he figured out how to map out basilar membrane response using fresh cadavers, and successfully designed mechanical models to mimic the physiological mechanism. For these investigations he won the Nobel Prize for physiology and medicine in 1961.
It turns out that the ear and brain can play further tricks, like "hearing" missing fundamental tones suggested by a series of overtones but not actually present in a given pitch. In other words, we can also "hear" a frequency that never actually stimulated the appropriate location on the basilar membrane. More complicated theories of pattern recognition relying on the inner workings of the brain have only been available since the 1970s, though Helmholtz's original model still retains some utility.