Understanding Loudness and Pitch Differences in Sound
The human ear is capable of discerning multiple characteristics of sound, significantly enhancing our auditory experience. Among these characteristics, loudness and pitch stand out, each contributing uniquely to our perception of sound. These attributes are not merely physical phenomena but are intricately linked to the auditory sensations experienced by the listener.
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. Although a wave repeats in time, its motion during an oscillation can be simple or highly complex.
A foghorn located adjacent to the Sumburgh Head lighthouse in the Shetland Islands of Scotland. The frequency of a sound wave is a measurement of how quickly the individual waves are following one another. This measurement is usually expressed using the SI unit Hertz (Hz). 1 Hz is equivalent to one wave per second.
Figure 1: A simple waveform with measurements included. The amplitude of a sound wave is a measurement of how intense the wave is. It is often helpful to visualize sound waves using a graph called a waveform. In this graph, the horizontal axis represents time, and the vertical axis can be understood as the position of a single particle in relation to its resting position.
When two or more sounds happen simultaneously, their sounds waves combine, so what reaches our ears is a single, complex sound wave.
Figure 2: Two waveforms which reinforce one another. If two sound waves are identical but offset by half a cycle - so one waveform peaks when the other bottoms out - the frequencies will cancel each other out, resulting in silence. If the frequencies of two sound waves are slightly different, the combined sound wave will alternate between periods of reinforcement and periods of cancellation, producing pulsing beats of sound which slow as the frequencies get closer.
Loudness: The Perception of Sound Intensity
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.
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 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.
Humans can generally hear frequencies from around 20 Hz to around 20,000 Hz, and can hear differences in frequency of about 3.6 Hz, meaning that humans are capable of discerning over 5,000 discrete pitches. Musical pitch is a continuous scale: given any two frequencies, there are an infinite number of different frequencies between them. Because listeners are usually unable to hear infinitesimally small differences - humans are typically capable of hearing frequency changes as small as 1 Hz - most musical systems make use of a discrete set of pitches.
Most musicians hear frequencies at octave apart as being so consonant with one another as having a shared identity. Most musicians train themselves to recognize the intervals between two different pitches. With this capability, given a named reference pitch, one can identify any other pitch by hearing the interval between them. Most musicians train themselves to fluently identify the interval between two notes, a capability called relative pitch. Some people are able to identify pitches independently, without a reference pitch, a capability called absolute pitch or perfect pitch.
Although for most practical purposes, the pitch of a sound can be said to be simply a measure of its frequency, there are circumstances in which a constant frequency sound can be perceived to be changing in pitch. One of most consistently observed "psychoacoustic" effects is that a sustained high frequency sound (>2kHz) which is increased steadily in intensity will be perceived to be rising in pitch, whereas a low frequency sound (<2kHz) will be perceived to be dropping in pitch.
The perception of the pitch of short pulses differs from that of sustained sounds of the same measured frequency. If a short pulse of a pure tone is decaying in amplitude, it will be perceived to be higher in pitch than an identical pulse which has steady amplitude. Interfering tones or noise can cause an apparent pitch shift. Further discussion of these and other perceptual aspects of pitch may be found in Chapter 7 of Rossing, The Science of Sound, 2nd. Ed.
Timbre: The Color 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.
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.
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
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.
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?
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.
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?
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.