Understanding Loudness, Pitch, and Timbre: The Building Blocks of Sound
To begin our discussion, we will consider the attributes or characteristics of any kind of wave. The most noticeable aspect of a wave is that it repeats in time. Whether it is a vibrating string on a violin or waves breaking at the shore, something is repeating.
There are many ways to describe a sound, but the perceptual attributes of a sound can typically be divided into three main categories-namely, loudness, pitch, and timbre. These attributes are not merely physical phenomena but are intricately linked to the auditory sensations experienced by the listener. Let's delve into each of these characteristics to better understand how we perceive sound.
Loudness: The Perception of Sound Intensity
Besides the pitch of a musical note, perhaps the most noticeable feature in how loud the note is. The loudness of a sound wave is determined from its amplitude. While loudness is only associated with sound waves, all types of waves have an amplitude. Waves on a calm ocean may be less than 1 foot high. Good surfing waves might be 10 feet or more in amplitude.
Sound waves with different amplitudes.
The most direct physical correlate of loudness is sound intensity (or sound pressure) measured close to the eardrum. However, many other factors also influence the loudness of a sound, including its frequency content, its duration, and the context in which it is presented. Loudness is a subjective attribute that allows us to differentiate between sounds that are perceived as soft or loud. This characteristic is fundamentally dependent on the amplitude of the sound wave.
Simply put, the amplitude of a sound wave correlates with its loudness: a greater amplitude results in a sound that is perceived as louder. This relationship highlights the sensitivity of the human ear to variations in sound wave amplitude.
It’s noteworthy to mention that the standard unit for measuring sound level is the decibel (dB). The decibel scale is logarithmic, meaning that a sound that is perceived as twice as loud as another is not simply twice as high in amplitude but is about 10 decibels higher. This logarithmic scale reflects the human ear’s nonlinear response to changes in sound intensity.
A great deal of time and effort has been spent refining various measurement methods. Some of the earliest psychophysical studies of auditory perception, going back more than a century, were aimed at examining the relationships between perceived loudness, the physical sound intensity, and the just-noticeable differences in loudness (Fechner, 1860; Stevens, 1957). These methods involve techniques such as magnitude estimation, where a series of sounds (often sinusoids, or pure tones of single frequency) are presented sequentially at different sound levels, and subjects are asked to assign numbers to each tone, corresponding to the perceived loudness. Other studies have examined how loudness changes as a function of the frequency of a tone, resulting in the international standard iso-loudness-level contours (ISO, 2003), which are used in many areas of industry to assess noise and annoyance issues.
Pitch: The Musical Quality of Sound
Musical notes or tones have a pitch. The pitch of a particular note is often given as a number. For example, the note "A" in the middle of a piano is designated A=440. Now, the question is 440 what? will vibrate or oscillate back and forth and will have a certain pitch. all of the time, so a shorthand has been developed. Each way of writing this gets progressively more compact. Since frequency always refers to some number of oscillations, we do not have to keep writing "oscillations". Also, "per second" is more easily written as /second, and second is abbreviated as sec.
What may be more unfamiliar is the designation that "/sec" = "Hz". Hz is an abbreviation of the unit Hertz, named after the physicists Heinrich Hertz. Once we understand the meaning of a pitch or frequency of 440 Hz, we can ask a related question: how long does 1 oscillation of the vibrating string take? If the string oscillates 440 times in 1 second, then each oscillation will take (1/440) seconds. Another way to look at this is the following: if each oscillation takes (1/440) seconds then 440 oscillations will take 1 second. Again, we have used some shorthand notation. If the period is rather small, we don't want to keep writing lots of zeros after the decimal point, so we use scientific notation, instead. 10-3 seconds corresponds to 1 millisecond and 1 millisecond is abbreviated as 1 msec.
Pitch is crucial to our perception and understanding of music and language. Pitch plays a crucial role in acoustic communication. Pitch variations over time provide the basis of melody for most types of music; pitch contours in speech provide us with important prosodic information in non-tone languages, such as English, and help define the meaning of words in tone languages, such as Mandarin Chinese.
Pitch is essentially the perceptual correlate of waveform periodicity, or repetition rate: The faster a waveform repeats over time, the higher is its perceived pitch. The most common pitch-evoking sounds are known as harmonic complex tones. They are complex because they consist of more than one frequency, and they are harmonic because the frequencies are all integer multiples of a common fundamental frequency (F0). For instance, a harmonic complex tone with a F0 of 100 Hz would also contain energy at frequencies of 200, 300, 400 Hz, and so on. These higher frequencies are known as harmonics or overtones, and they also play an important role in determining the pitch of a sound.
In fact, even if the energy at the F0 is absent or masked, we generally still perceive the remaining sound to have a pitch corresponding to the F0. This phenomenon is known as the “pitch of the missing fundamental,” and it has played an important role in the formation of theories and models about pitch (de Cheveigné, 2005).
We hear pitch with sufficient accuracy to perceive melodies over a range of F0s from about 30 Hz (Pressnitzer, Patterson, & Krumbholz, 2001) up to about 4-5 kHz (Attneave & Olson, 1971; Oxenham, Micheyl, Keebler, Loper, & Santurette, 2011). This range also corresponds quite well to the range covered by musical instruments; for instance, the modern grand piano has notes that extend from 27.5 Hz to 4,186 Hz.
Pitch gives sound a musical quality, allowing us to perceive it as either high (sharp) or low. The determining factor of pitch is the frequency of the sound wave; this means the number of wave cycles that occur in one second. Instruments like the violin, which produce high-frequency sounds, are perceived as having a high pitch, whereas instruments like the bass drum, known for their low-frequency sounds, are perceived as having a low pitch.
The intricacy of pitch perception lies in its ability to convey the harmonic context of music or speech, significantly influencing how sound is interpreted and appreciated. The human ear’s ability to detect frequency variations is what enables us to distinguish between different musical notes, voices, and the subtleties within complex sounds.
Timbre: The Color of Sound
Although a wave repeats in time, its motion during on oscillation can be simple or highly complex. In fact, their amplitudes are also the same. Thus, if these two waves represented sound waves, the pitch and loudness would be the same in both cases. But would they sound exactly the same? The answer is No, because there is one more attribute to sound waves that you are familiar with, and that is tone quality. This is what makes different instruments sound different. A violin and a trumpet can play the same pitch with the same loudness, but we can easily tell them apart, because they have a different tone quality. In fact, the same instrument can create different tone qualities. If you pluck a guitar in different ways, you can get quite different tones. Try it! The technical musical term for this is timbre.
Timbre refers to the quality of sound, and is often described using words such as bright, dull, harsh, and hollow. Technically, timbre includes anything that allows us to distinguish two sounds that have the same loudness, pitch, and duration.
An important aspect of timbre is the spectral content of a sound. Sounds with more high-frequency energy tend to sound brighter, tinnier, or harsher than sounds with more low-frequency content, which might be described as deep, rich, or dull. Other important aspects of timbre include the temporal envelope (or outline) of the sound, especially how it begins and ends. For instance, a piano has a rapid onset, or attack, produced by the hammer striking the string, whereas the attack of a clarinet note can be much more gradual. Artificially changing the onset of a piano note by, for instance, playing a recording backwards, can dramatically alter its character so that it is no longer recognizable as a piano note.
Each sound has its own unique tone color or timbre. Even if it’s sometimes hard to describe, most people can readily hear whether a note is played on a piano or on a violin, or if there’s thunder during a rainstorm. To understand this better, we need to learn about harmonics.
When a pipe or string vibrates along its full length, this is the first harmonic. But a vibrating body does not just vibrate along its full length but also in halves, thirds, fourths, fifths and so on. At half its total length, this creates the octave, the second harmonic. When it vibrates in thirds, this creates the interval of a fifth above the octave, the third harmonic.
Each tone color has a sonic fingerprint created by the relative strengths of the harmonics. When the full-length vibration is very strong compared to the harmonics, the fundamental pitch is predominant. A tuning fork is a good example of this. It has no strong upper harmonics affecting its sound wave; we want a tuning fork to give a strong fundamental to which we can tune our voice or an instrument. If there were strong harmonics at other frequencies, the pitch for tuning would not be as clear. But other sound waves have stronger harmonics and this creates distinctive timbres.
The different strength of harmonics produces an amazing tapestry of sound. Adding to loudness and pitch, timbre is another crucial characteristic that plays a significant role in our perception of sound. Timbre, often referred to as the “color” or “quality” of sound, is what allows us to distinguish between different instruments playing the same note at the same loudness and pitch. It is influenced by factors such as the sound wave’s form, the harmonics, and other complex aspects of the sound.
The quality of timbre is what enriches our auditory experience, allowing for a rich tapestry of sound that is capable of conveying emotions, atmosphere, and nuanced musical expression.
Together, loudness, pitch, and timbre form a trio of characteristics that are essential for the complex and nuanced experience of hearing. They allow us to navigate and appreciate the auditory world, from the simplest sounds to the most complex musical compositions.
Worked Examples
The human ear is capable of discerning multiple characteristics of sound, significantly enhancing our auditory experience.
Example 1: The Concert Experience
During a live concert, you notice that the sound of the lead guitarist’s solo seems much louder than the rhythm guitarist’s chords, even though both are playing their instruments energetically. Assuming the amplification settings for both guitars are identical, explain why the solo might be perceived as louder. Consider the characteristics of sound in your explanation.
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The perception of the lead guitarist’s solo being louder could be due to several factors related to loudness and timbre. If the solo contains higher-pitched notes, more sustained notes, or utilizes specific effects that add harmonics or overtones, it might stand out more prominently against the rhythm guitar’s chords. The human ear is more sensitive to certain frequencies, and the added harmonics or sustained high notes in the solo could make it more attention-grabbing. Additionally, the timbre of the lead guitar, possibly altered by effects pedals, could make its sound more distinct and thus perceived as louder within the mix of the concert’s sound.
Example 2: The Mystery of the Quiet Alarm
You set your alarm clock to the same volume every day, but some mornings it sounds quieter and doesn’t wake you up as effectively. Without changing the volume setting, how can the pitch and timbre of the alarm sound affect its perceived loudness in the morning?
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The perceived loudness of the alarm can be affected by its pitch and timbre. If the alarm sound has a higher pitch, your ears might be more sensitive to it, making it more effective at waking you up. Conversely, a lower-pitched sound might not be as easily perceived, especially if you are in a deeper stage of sleep. Additionally, the timbre of the alarm-if it includes more complex overtones or varies from day to day-can affect how the brain processes the sound, making it seem more or less urgent. A richer, more complex timbre might catch your attention more effectively than a simpler, purer tone.
Example 3: The Choir Conundrum
A choir is performing a piece with a wide range of notes, from very low to very high. All singers are equally distant from you, but the high-pitched soprano voices seem to stand out more than the bass voices, even when all are singing at the same volume. Explain why the sopranos are more discernible based on the concepts of pitch and loudness.
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This phenomenon can be explained by the frequency sensitivity of the human ear, which is more attuned to certain frequencies. High-pitched sounds, like those produced by sopranos, are generally more noticeable to human listeners because our ears are more sensitive to higher frequencies. Even though all singers are producing sound at the same volume, the higher frequency of the soprano voices makes them stand out more prominently against the lower-pitched bass voices. This selective sensitivity helps to explain why certain notes or tones are more perceptible in complex auditory environments.
Example 4: The Recording Riddle
An audio engineer records the sound of a flute and a clarinet playing the same note at the same volume. When played back, the flute’s recording sounds softer than the clarinet’s, even though the volume levels were not altered. What could explain this difference in perceived loudness, considering the concepts of loudness, pitch, and timbre?
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The difference in perceived loudness between the flute and clarinet recordings, despite being at the same volume, can be attributed to their distinct timbres. The clarinet produces a sound that is rich in harmonics, giving it a fuller and more complex timbre compared to the flute. This richness in the clarinet’s sound can make it seem louder or more present in the recording. Even though both instruments are playing at the same volume and pitch, the clarinet’s complex overtones engage the ear more effectively, leading to a perception of greater loudness.