Now that we've covered the physical properties of sound waves, we move on to the first part of Chapter 3, which explores the psychological properties of sound. While they may be related, there are some crucial differences between the two. For one, the physical properties of sound waves are the objective features that are independent of the listener. On the other hand, the psychological properties of sound (see Fig. 1), such as pitch, loudness, duration, and timbre, depend on the phenomenological or first-hand auditory experience of the listener.
Pitch
Pitch refers to how high or low a tone sounds to a listener. Linking it to the physics of sound, pitch can be conceptualised as the perceptual experience related to the frequency of sound waves. Typically, humans can perceive pitches with frequencies ranging from 20 to 20,000 Hz (i.e., cycles per second), but this can be reduced with age. For instance, presbycusis (or age-related hearing loss) can reduce one's sensitivity to the higher end of the range. This normally isn't a problem, though. The authors point out how most music lives in a frequency range of around 20 to 4000 Hz, the higher end of which is way below the limit of human hearing, even with presbycusis.
The simplest account of pitch perception claims that the pitch one hears corresponds to the lowest frequency found in a complex tone. To recap, complex sounds are made up of multiple frequencies, the lowest of which is called the fundamental. If the fundamental is what we pick up to perceive pitch, then the higher frequencies contribute to the distinctive quality of the sound, or timbre.
Unfortunately, we face some issues here. For example, most telephones have limited frequency ranges that don't transmit lower frequencies, hence implicating the fundamental. Despite this limitation, we are still able to perceive the pitch of someone singing over the phone. This phenomenon of hearing an identifiable pitch even without the presence of a fundamental frequency is known as 'residue pitch' (Terhardt, 1974). It has been argued that, in these cases, individuals perceive the pitch by detecting the higher frequencies of the complex tone. In other words, we can infer the fundamental from harmonics.
The authors end this section with a discussion of consonance and dissonance, which simply refer to how pleasing or displeasing, respectively, simultaneously played tones sound. For example, a perfect fifth (e.g., playing C and G together) gives a stable and pleasing sound. On the other hand, a C7#9b13 (i.e., C, E, Bb, D#, Ab) might be described as crunchy, unstable, and, depending on the context, displeasing.
What makes some tone combinations consonant or dissonant can be explained using the concept of a critical bandwidth. Simply put, this refers to a range containing frequencies that trigger a similar response pattern in the auditory system. The idea here is that, given that frequency is a continuous variable, it makes no sense for an auditory system to have a unique response to each of these (theoretically infinite) frequencies. To make the auditory system more efficient, we can instead get it to give similar responses to frequencies that are close together. To reiterate, these frequencies are then described as being part of the same critical bandwidth.
Let's bring this back to consonance and dissonance. To be honest, I'm not fully certain of the logic here either, but in a nutshell, Plomp & Levelt (1965) show that consonant intervals arise when they have identical frequencies (and hence share a large proportion of the critical bandwidth; right side of Fig. 2) or when they do not belong to the same critical bandwidth (see left side of Fig. 2). Deviations from these two extremes give increasing dissonant sounds, with maximal dissonance occurring when the tones contain frequencies that have an 25% overlap in critical bandwidth.
Fig. 2 Consonance and dissonance as a function of proportion of critical bandwidth overlap (Plomp & Levelt, 1965)
Loudness
If pitch is related to sound wave frequency, then loudness can be described as the perceptual experience of a tone related to sound wave amplitude. Another term for physical loudness (note: physical, not perceived, loudness) is sound intensity level (apparently, this is different from just intensity), which is measured using a decibel scale. I won't go into the mathematics here, but briefly, you get a decibel measure by taking the energy contained within a sound wave (i.e., its intensity), plugging it into a logarithmic function, and poof, you get your decibel measure. Here, 0 dB corresponds to the faintest discernible sound, defined as a sound with a sound wave with a specific amount of energy (FYI, it's 10-16 watts/cm2).
The problem with the decibel scale is that it's not exactly intuitive, and it doesn't measure what many people think it measures. Remember that the decibel scale is concerned with the intensity of a sound wave. Even though this is a section on the psychological experience of loudness, the decibel scale actually measures the physical signal, that is, the sound wave. It is not a measure of subjective auditory experience!
This is made more problematic when we realise that there is no linear correlation between sound intensity level (as measured by the decibel scale) and perceived loudness. While sound intensity level depends on wave intensity (which is proportional to amplitude), perceived loudness is a function of both amplitude and frequency. For an idea of how unintuitive the decibel scale is, consider the following: An increase of 3 dB corresponds to a doubling of wave intensity. Meanwhile, you would have to see an increase of 10 dB for one to perceive a doubling of loudness!
Duration
Tone duration refers to how long a listener perceives a note to be. Anecdotal experience tells us that humans are incredibly sensitive to minute variations in note length. Indeed, this has allowed us not only to appreciate more conventional Western music with straighter and more metronomic timings, but also music with more varied and complex rhythmic modes and meters, such as jazz or Balkan music.
That being said, tone duration is not strictly related to the duration of the acoustic signal. Schulz & Lipscomb (2007) demonstrated this when they got an internationally acclaimed percussionist to play the same piece of music twice -- once with short arm gestures and the other with longer ones. Here, no difference in physical signal duration or perceived tone duration was revealed by an acoustic analysis or by listeners who had heard the recordings without visuals, respectively.
However, when listeners were allowed to listen to the piece while watching the percussionist perform, they perceived the notes to be shorter when accompanied with short gestures, and longer when played with longer gestures! Clearly, we can see that, similar to how watching someone's lips can influence the words we hear, a performer's actions can influence the note duration perceived by listeners.
Timbre
Finally, we have timbre, which the authors define as 'the intrinsic and distinctive quality of sound". Perceiving timbre is what allows us to distinguish between musical instruments or singing voices. In this way, it can be viewed as the unique signature of a given sound. The rest of this section covers two important sources of variation in perceived timbre, namely frequency content and temporal changes.
Recall that the pitch of a tone is typically related to the fundamental frequency of a complex sound wave. On top of this fundamental are many more higher frequencies that all combine to give the characteristic complex wave pattern for a particular sound. In Fig. 3, we can see how different complex wave patterns underlie the unique sound quality of different instruments. A really cool thing about this figure is that you can also see properties of the fundamental frequency in the overall pattern of vibration of the sound. Here, the fundamental is associated with the number of times each discrete complex wave pattern occurs (over the same time period across the instruments). For instance, the double bass plays a lower pitch (and frequency) than the violin, and we can see each unit of its complex waveform repeating fewer times compared to that of the violin over a period of 50 ms.
Fig. 3 Complex waveforms from different instruments (Plack, 2018)
In Fig. 4, we can use a power spectrum analysis to look at differences in intensity at different frequencies for different instruments. Here, the double bass and vibraphone have higher sound intensity levels at lower frequencies than at higher frequencies, giving them fuller, mellower, and more resonant timbres. Meanwhile, the guitar and violin have high intensity levels at higher frequencies, hence giving them brighter and more piercing timbres.
Fig. 4 Power spectral analyses (Plack, 2018)
Finally, we have temporal changes, where we look at 3 segments of a musical signal, namely attack, sustain, and decay. I also know of a fourth segment not mentioned, release, so I'll include it here for the sake of completion (see Fig. 5). Briefly, attack refers to the initial part of sound production, defined as the time it takes for a sound to go from its lowest to maximum volume. Next, sustain refers to the volume level at which a tone will remain if you, for example, held a piano key without letting it go. In between the attack and sustain stages, we have decay, which refers to the time it takes for the sound to go from its peak volume to sustain levels. Finally, release is the time taken for the note to fade out after you release it.
Fig. 5 The attack-decay-sustain-release envelope (Source: link)
The key idea here is that sounds from different instruments have different combinations of attack, decay, sustain, and release parameters. These also contribute to the overall timbre of the sound and aid in the identification of the sound source.
Concluding remarks
We'll continue covering the rest of the chapter in a separate post. There, we'll move away from the properties of sound waves and tones and start looking at the neuroanatomy of our auditory system
References
Plack, C. J. (2018). The sense of hearing. In Routledge eBooks. https://doi.org/10.4324/9781315208145
Plomp, R., & Levelt, W. J. M. (1965). Tonal consonance and critical bandwidth. The Journal of the Acoustical Society of America, 38(4), 548–560. https://doi.org/10.1121/1.1909741
Schutz, M., & Lipscomb, S. (2007). Hearing gestures, seeing music: vision influences perceived tone duration. Perception, 36(6), 888–897. https://doi.org/10.1068/p5635
Tan, S., Pfordresher, P., & Harré, R. (2010). Psychology of Music: From Sound to Significance. http://ci.nii.ac.jp/ncid/BB01824497
Terhardt, E. (1974). Pitch, consonance, and harmony. The Journal of the Acoustical Society of America, 55(5), 1061–1069. https://doi.org/10.1121/1.1914648
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