In Search of the Missing Fundamental: by Richard K. Jones
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Time and Place

How does the human auditory system work? A full explanation is beyond the scope of this book, but a condensed explanation of simple auditory transduction follows.

Once acoustic energy is collected by the outer ear, it is transformed into mechanical energy, i.e. vibrational energy via the eardrum upon where the three bones in the middle ear, colloquially known as hammer, anvil and stirrup efficiently convey this vibrational energy to the fluid filled inner ear. The coiled basilar membrane of the inner ear detects the amplitude and frequency of the vibrational energy; those vibrations are converted to electrical impulses and sent as neural information along a bundle of nerve fibers (the auditory nerve) to the primary and secondary auditory cortex of the brain responsible for processing and interpreting incoming auditory information known as the Heschl’s gyrus.

Auditory Transduction (2002)
courtesy of

The duplicity continues with the two main theories of how the auditory system is believed to code the pitch of a sound once it has reached the inner ear: the pitch place theory and the pitch temporal theory.

The place theory of pitch is based on the fact that different frequency components of the input sound stimulate different places along the basilar membrane (as shown in the video above) and in turn stimulate auditory nerve fibres with different characteristic frequencies. The vibrational energy is carried by the inner ear fluid and travels the length of the membrane. The wave stops at particular places along the length of the membrane, where the greatest vibration of the membrane occurs, corresponding to different frequencies. High frequencies are sensed at the membrane near the middle ear while low frequencies are sensed at the farther end. The sound wave excited by a high-frequency sound does not reach the far end of the basilar membrane. However, a low-frequency sound will pass through all high frequency places to reach the far end.

The basis for the temporal theory of pitch perception is the timing of neural firings, which occur in response to vibrations on the basilar membrane. It is a time-domain mechanism which is event-based; i.e., it tries to detect the time interval between events, which may be peaks or overall envelope of the input waveforms. These events determine the periodicity of the waveform, and the reciprocal of the periodicity is the same as the fundamental frequency. As the basilar membrane vibrates, each clump of hair cells along its length is deflected in time with the sound components as filtered by basilar membrane tuning for its position. The more intense this vibration is, the more the hair cells are deflected and the more likely they are to cause nerve firings. Temporal theory supposes that the consistent timing patterns, whether at high or low average firing rate, code for a consistent pitch percept.

The auditory processing parts of the brain (Heschl’s gyrus) is supplied with information concerning the place of stimulation on the basilar membrane (place theory) and neural firing patterns (temporal theory). The importance of both types of information depends on the frequencies present and the type of sound. Place coding is believed to dominate for frequencies above 5000 Hz, below this temporal information is believed to be dominant.

One might ask why a study of Place Theory vs. Temporal Theory is important to timpani sound production.  Perhaps not to the production of timpani sound, but to the perception of that sound.  The sound of timpani can range from C2 65 Hz to C4 262 Hz, which is at the low end of the human hearing spectrum. Since the quasi-harmonic spectrum of a timpano falls well below 5000 Hz and does not contain a fundamental, is it possible that no two people hear timpani pitch the same way? The science of the missing fundamental adds yet another intriguing dimension to the production and perception of timpani sound.

Chapter 4: References