The right prospective

On the pages regarding sound waves, we dealt with the sound phenomenon touching exclusively on questions pertinent to physics. In particular, we focused on the first two phases of the phenomenon; i.e. the production and propagation of sound waves.

Moving on to the next two phases, the receiving and processing of sound, we are forced to leave the field of physics and mention concepts and notions pertaining to other disciplines including physiology, psychology, music theory, etc.

We do not intend to elaborate on all aspects but simply to show how the complexity of the sound phenomenon makes impossible any hope of "reducing" all its aspects to an approach based exclusively on Physics.

The problem of perception

First of all, let's focus on the difference between the physics approach to the sound object and an approach that also takes perceptual factors into consideration.

From the physics point of view, the typical questions are:

1. What characteristics of sound waves are measurable objectively?
2. What are the laws of physics that govern them?

From the perception point of view, we should ask:

1. What are the subjective parameters that allow people to appreciate sound?
2. What are the subjective characteristics of sound that people perceive?

In the end, trying to link the two approaches, we could ask:

• What objective characteristics of the receiving (ear) and processing (brain) systems give rise to perceived characteristics starting with the given objective physical properties of sound waves?

If we take this point of view, we realise that the sound phenomenon is composed of the interaction of many different phenomena that take place on many distinct planes:

1. the physical plane of the vibration of the medium and the propagation of the sound wave;
2. the physical-physiological plane of the interaction between the sound wave and the ear;
3. the physiological plane of the transformation of the signal by the auditory system;
4. the physiological-psychological plane of the recognition and cognition of the signal and its emotional correlations.

And with regards to music (see the section on from sound to music):

1. the cognitive-linguistic plane of the interpretation and attribution of meaning to the sounds;
2. the linguistic-formal plane of the recognition of the musical structure of sounds;
3. the anthropological-cultural plane regarding the development of particular musical forms and languages by various human societies;

... and from here, you can take the discussion further in any direction you like.

Focusing our attention on musical instruments, we can ask ourselves similar questions:

1. What objective characteristics of a musical instrument influence its quality?
2. What are the perceptual factors?
3. What are the cultural components?

In this section, and in those on musical instruments, we will deal with this topic emphasising the part that concerns physics.

Attributes of perceived sound

On the page about sound waves, we have listed some measurable objective characteristics that are typical of sound waves and undulatory phenomena.

However, everyday language uses other terms to define the qualities of sound. Generally, these terms do not refer to objective sound characteristics but to perception characteristics of the sound phenomenon, even when they accidentally have the same name as a physical property (such as intensity).

We have all heard about:

• low pitch or high pitch sounds, which are the characteristics of perceived sound that allow us to order sounds in a scale from low pitch to high pitch called sound pitch. For musicians, this is the sound characteristic that distinguishes the "notes" (e.g. an A instead of a C);
• loud or soft sounds, which are what we commonly call sound "volume" or loudness. This is what musicians regulate based on notations on their sheet music that come from "dynamics" and range from the Italian terms "più che pianissimo" (ppp) to "più che fortissimo" (fff);
• sounds of different timbre, which is basically the perceived quality that allows us to distinguish the sound of a piano from that of a guitar when they are emitting the same note, which is actually a sound with the same pitch.

Links between attributes of perceived sound and the properties of sound waves

Let's get back to the role of physicist-musician (see the paragraph "On the perceived pitch of a complex sound" for a dialogue between a physicist-musician and a curious-navigator).

Obviously, we ask ourselves:

is it possible to establish simple relationships between the physical properties of sound waves and the attributes of sound that we perceive?

The answer is yes. However, these relationships are usually not simple due to the complexity of our auditory and nervous systems.

This question is often answered in the following terms:

If we investigate more deeply (for more on this, visit the pages on the perception of loudness, perception of pitch, perception of timbre and physiology of the auditory system), we will discover that these relationships are only approximately valid and only when they refer to pure sounds.

In the case of more "realistic" sounds, the correlation is much more complex than the one illustrated here. Human perception introduces notable complications into this correlation, therefore, the pitch of a sound may also depend on the loudness of the sound and vice versa, or the timbre may vary with the variation of the frequency, loudness and mode of excitation of the vibrating source by the performer, etc.

Some concrete examples, discussed further in the pages cited:

• at equal sound intensity, a sound of 50 Hz seems much weaker than one of 1000 Hz: the sensitivity of the ear depends strongly on frequency (see the isophonic curves);
• doubling the intensity of a sound does not make it sound "twice as loud": this requires about ten times the intensity, that is, 10 dB more;
• a sound made only of the harmonics 200, 300 and 400 Hz is perceived with the pitch of a note at 100 Hz, even though that frequency is not present: this is virtual pitch;
• timbre does not depend only on the spectrum, but also on how the sound evolves in time, in particular on the attack: removing the attack from a piano note makes it hard to recognise the instrument (see perception of timbre).

Virtual laboratory

If you wish to experiment with the simple correlation illustrated in the previous paragraph, you can do experiments in our virtual laboratory, where it is possible to vary the parameters of a (sound) wave as you like. The app is very intuitive and easy-to-use. Several guided experiments are illustrated on the following pages. We encourage you to freely experiment with them based your curiosity.

Change wave frequency, in which you will perceive a change in sound pitch;

Change wave amplitude, in which you will perceive a change in sound "volume";

Change sound timbre, in which you will perceive a variation in sound quality. This app also contains sounds with predefined timbres (e.g. oboe, clarinet) built with sound spectra.

Check your understanding

In-depth study and links

• For further study on the first phase of the sound phenomenon, visit the pages on musical instruments.
• For further study on the phase related to the receiving and perceiving of sound, visit the pages on the perception of sound and physiology of the auditory system
• If you are interested in discovering a partial physical foundation for the consonance and dissonance of sounds, visit the page on critical bands;
• If you are interested in the more "musicological" aspects of consonance and dissonance, you can visit this page.