At first sight, it seems obvious what loudness is. A sound is loud when the acoustical wave carries a lot of energy. But if we think about it in details, we quickly encounter difficulties. One obvious thing is that if we play the same sound at different levels, then clearly the feeling of loudness directly correlates with the amplitude of the sound, and therefore with the energy of the sound. But how about if we play two completely different sounds? Which one is louder? Should we consider the total energy? Probably not, because this would introduce a confusion with duration (the longer sound has more energy). So perhaps the average energy? But then what is the average energy of an impact sound, and how does it compare with a tone? Also, how about low sounds and high sounds, is there the same relationship between energy and loudness for both sounds? And does a sound feel as loud in a quiet environment as in a noisy environment? Does it depend on what sounds were played before?

I could go on indefinitely, but I have made the point that loudness is a complex concept, and its relationship with the acoustic signal is not straightforward at all.

Let us see what can be said about loudness. First of all, we can say that a sound is louder than another sound, even if the two sounds are completely different. This may not be true of all pairs of sounds, but certainly I can consider that a low amplitude tone is weak compared to the sound made by a glass breaking on the floor. So certainly there seems to be an order relationship in loudness, although perhaps partial. Also, it is true that scaling the acoustical wave has the effect of monotonically changing the loudness of the sound. So there is definitely a relationship with the amplitude, but only in that scaling sense: it is not determined by simple physical quantities such as the peak pressure or the total energy.

Now it is interesting to think for a while about the notion of a sound being “not loud enough” and of a sound being “too loud”, because it appears that these two phrases do not refer to the same concept. We say that a sound is “not loud enough” when we find it hard to hear, when it is difficult to make sense of it. For example we ask someone to speak louder. Thus this notion of loudness corresponds to intelligibility, rather than acoustical energy. In particular, this is a relative notion, in the sense that intelligibility depends on the acoustical environment – background noise, other sources, reverberation, etc.

But saying that a sound is “too loud” refers to a completely different concept. It means that the sound produces an uncomfortable feeling because of its intensity. This is unrelated to intelligibility: someone screaming may produce a sound that is “too loud”, but two people screaming would also produce a sound that is “too loud”, even though intelligibility decreases. Therefore, there are at least two different notions regarding loudness: a relative notion related to intelligibility, and a more absolute one related to an unpleasant or even painful feeling. Note that it can also be said that a sound is too loud in the sense of intelligibility. For example, it can be said that the TV is too loud because it makes it hard to understand someone speaking to us. So the notion of loudness is multiform, and therefore cannot be mapped to a single scale.

Loudness as in “not loud enough” (intelligibility) is rather simple to understand. If the signal-to-noise ratio is too low, then it is more difficult to extract the relevant information from the signal, and this is what is meant by “not loud enough”. Of course there are subtleties and the relationship between the acoustical signals and intelligibility is complex, but at least it is relatively clear what it is about. In contrast, it is not so straightforward what “too loud” means. Why would a sound be unpleasant because the acoustical pressure is large?

First of all, what does it mean that something is unpleasant or painful? Something unpleasant is something that we want to avoid. But this is not a complete characterization: it is not only a piece of information that is taken into account in decision making; it has the character of an uncontrollable feeling, something that we cannot avoid being subjected to. In other words, it is an emotion. Being controlled by this emotion means acting so as to escape the unpleasant sound, for example, by putting one’s hands on the ears. Consciously trying not to act in such a way would be considered as “resisting” this emotion. This terminology implies that loudness (as in “too loud”) is an involuntary avoidance reaction of the organism to sounds, one that implies attenuating the sounds. Therefore, loudness is not only about objective properties of the external world, but also about our biological self, or more precisely about the effect of sounds on our organism.

Why would a loud sound trigger an avoidance reaction? We can speculate on different possibilities.

1) A loud sound may indicate a threat. There is indeed a known reflex called “startle reflex”, with a latency of around 10 ms (Yeomans and Frankland, Brain Research Reviews 1996). In response to sudden unexpected loud sounds, there is an involuntary contraction of muscles, which stiffens in particular the neck during a brief period of time. The reflex is found in all mammals and involves a short pathway in the brainstem. It is also affected by previous sounds and emotional state. However, this reflex only involves a small subset of sounds, which are sudden and normally very loud (over 80 dB).

2) A very loud sound can damage the cochlea (destroy hair cells). At very high levels, it can even be painful. Note that a moderately loud sound can also damage the cochlea if it lasts long. Thus, the feeling of loudness could be related to the emotional reaction aimed at avoiding damage to the cochlea. Note that while cochlear damage depends on duration, loudness does not. That is, a continuous pure tone seems just as loud at the beginning as 1 minute into it, and yet because damage depends on continuous exposition, an avoidance reaction should be more urgent in the latter case than in the former case. Even for very loud sounds, the feeling of loudness does not seem to increase with time: it may seem more and more urgent to avoid the sound, but it does not feel louder. We can draw two conclusions: 1) the feeling of loudness, or of a sound being too loud, cannot correspond to an accurate biological measurement of potential cochlear damage, as it seems to have a feeling of constancy when the sound is stationary; 2) the feeling of a sound being “too loud” probably doesn’t correspond to the urgency of avoiding that sound, since this urgency can increase (emotionally) without a corresponding increase in loudness. It could be that the emotional content (“too loud”) comes in addition to the perceptual content (a certain degree of loudness), and that only the latter is constant for a stationary sound.

3) Another possibility is that loudness correlates with the energy consumption of the auditory periphery (possibly of the auditory system in general). Indeed when the amplitude of an acoustical wave is increased, the auditory nerve fibers and most neurons in the auditory system fire more. Brain metabolism is tightly regulated, and so it is not at all absurd to postulate that there are mechanisms to sense the energy consumption due to a sound. However, this is not a very satisfying explanation of why a sound would feel “too loud”. Indeed why would the organism feel an urge to avoid a sound because it incurs a large energy consumption, when there could be mechanisms to reduce that consumption?

In this post, I have addressed two aspects of loudness: intelligibility (“not loud enough”) and emotional content (“too loud”). These two aspects are “proximal”, in the sense that they are determined not so much by the sound source as by the acoustical wave at the ear. In the next post, I will consider distal aspects of loudness, that is, those aspects of loudness that are determined by the sound source.