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Notes
- 1.
A “point” of the medium is meant here in the macroscopic sense, still encompassing billions of molecules!
- 2.
“Calibrated” means that we have previously determined how much the spring stretches for a given force, for example, a given weight.
- 3.
This is how the “characteristic frequency” of a neural fiber in the acoustic nerve arises (p. 54): consider a neuron wired to hair cells located at position A of Fig. 3.5. Its response will be related to the amplitude of the local oscillation of the basilar membrane. As the frequency of the test tone gradually rises from a very low value, the entire pattern shown in Fig. 3.5 will move from far right to far left: when the oscillation envelope passes over point A, that neuron’s response capability will gradually increase to a maximum (at the characteristic frequency-see lower graph of Fig. 2.25(b)) and then suddenly drop as the pattern moves away to the left.
- 4.
Note carefully that what is added here are pressure variations, and not absolute values of the pressure!
- 5.
Not true for extremely loud (powerful) sound waves like those from an explosion.
- 6.
The music notation really does not represent an absolute measure of loudness. Musicians for instance will argue that we are perfectly able to perceive fortissimos and pianissimos in music played on a radio with its volume control turned down to a whisper. What happens in such a case is that we use cues other than intensity-particularly if we know the piece-to make subjective judgments of “relative” loudness. On other hand, systematic experiments (Patterson, 1974) have revealed that the interpretation of the musical loudness notation in an actual dynamic context is highly dependent on the instrument and on the pitch range covered.
- 7.
Obtained through “loudness matching” experiments conducted in a way quite similar to pitch matching experiments.
- 8.
A well-known situation, similar to this case, arises with the sensation of pain. If you are pinched in two places very near to each other, the pain may be “twice” that of a single pinch (equivalent to case (1) above). But when the places are far apart, you have difficulty in sensing out what one may call “total pain” (case (3)). Actually, you will tend to focus on the one giving the greater pain sensation.
- 9.
Their addition, of course, also will contribute to a change in timbre (Chapter 4).
- 10.
Many baroque organs had a stop called “Zimbelstern,” sounding very high-pitched miniature cymbals or bells mounted on a rotating star at the top of the organ case; this stop was pulled to reinforce the loudness of a final chord (without in any way interfering with its harmony: frequencies above about 5000 Hz do not contribute to, or interfere with, the periodicity pitch sensation in the normal musical range).
- 11.
Quite generally, there is a physical principle which states that the frequency of a vibration (hence also the associated pitch) cannot be defined more accurately than the inverse of the total duration of the vibration.
- 12.
This should not be confused with acoustic fatigue, a psychological process through which our brain is able to ignore a continuous but otherwise irrelevant sound.
- 13.
For tones of musical instruments complications arise: during tone buildup which may last several tenths of a second, a natural change in intensity and spectrum occurs at the source. Also, reverberation effects are important (Sect. 4.7).
- 14.
We should point out that there is also a shift in pitch when the pressure in the cochlear fluid changes (e.g., pitch shifts perceived during yawning), or when its chemical composition changes (e.g., drug injections into the cerebrospinal fluid).
- 15.
“Sharp tuning” means that the band of frequencies to which the neuron responds is very narrow; “shallow tuning” would mean that responses occur for a wide range of frequencies.
- 16.
Electrophysiological investigations show that the frequencies to which hair cells are most sensitive are inversely related to the lengths of their hair bundles-and it so happens that these lengths increase several times along the basilar membrane from base (high frequency end) to apex (low frequency end). All this is seen in cochleas of lower vertebrates; it is still unclear to what extent it also applies to higher mammals and humans.
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Roederer, J.G. (2008). Sound Waves, Acoustic Energy, and the Perception of Loudness. In: The Physics and Psychophysics of Music. Springer, New York, NY. https://doi.org/10.1007/978-0-387-09474-8_3
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