What determines the pitch of a sound?

We naturally use the terms "high pitch" and "low pitch" in everyday life. While pitch is an important element in audio development, frequency is used to objectively represent the difference between them. Frequency is a value that represents how many times a sound vibration is repeated per second, and its unit is Hertz (Hz). Slower vibrations are perceived as low pitches, and faster vibrations are perceived as high pitches.

For example, the lower-pitched keys on a piano produce relatively low-frequency sounds, while the higher-pitched keys produce higher frequencies. The note "A," used as a tuning standard in music, is 440Hz, which means it vibrates 440 times per second. In this way, frequency is a common language for numerically expressing the pitch of a sound. Therefore, in audio development, sound is captured objectively, not in subjective expressions such as "a slightly high-pitched sound," but in terms of "components around 2kHz."

However, there's something interesting here. We can easily distinguish between a 440Hz note played on a piano and a 440Hz note played on a guitar, even though they are the same pitch.

Why can't frequency alone explain the differences in sound?

Frequency is a very useful indicator of pitch. However, it cannot describe all the characteristics of a sound. For example, consider the case of playing the same "A" note on a piano and a guitar. Both produce the same pitch, and their fundamental frequency is 440Hz. Nevertheless, we can easily distinguish between the two sounds.

The same can be said for human voices. Even if multiple people sing at the same pitch, it's rare to mistake their voices. This is because the impression of the sound changes greatly depending on the voice quality and the characteristics of the instrument. If sound were determined solely by frequency, then all sounds at the same 440Hz frequency should sound the same. However, this is not the case. What this shows is that while frequency is important information that represents pitch, it alone cannot represent the sound itself.

The differences we usually perceive as "soft," "bright," or "powerful" sounds are created by factors other than pitch. To understand these differences, we need to view sound not as a single frequency, but as a component of multiple frequencies.

How do differences in tone color arise?

The reason why the same pitch sounds different depending on the instrument or human voice is that sound is not composed of only a single frequency. For example, when a piano plays a 440Hz note, that sound contains not only 440Hz, but also multiple frequency components such as 880Hz and 1320Hz. Similarly, a guitar also produces a sound based on 440Hz, but the balance of the frequency components it contains is different. This difference is what creates the "timbre" that we perceive.

The fundamental frequency that determines the pitch of a sound is called the "fundamental frequency," and frequency components that are integer multiples of the fundamental frequency are called "harmonics." Actual musical instruments and human voices contain multiple such frequency components, and their combinations create their unique sounds. For example, even if a piano and a guitar play the same pitch, we can instantly distinguish between them because the way they contain harmonics is different. The same is true for human voices; even if people speak at the same pitch, their voices sound different because the composition of their frequency components is different.

In other words, to understand sound, we need to look not only at "what frequency the sound is in Hz," but also at "what frequency components it contains." The key here is to think of actual sound not as a single frequency, but as a collection of multiple frequency components. Adopting this perspective allows us to understand why sounds have different characteristics.

What does a spectrum represent?

As we've seen, actual sound is not made up of a single frequency, but rather a combination of multiple frequency components. So, how can we determine what frequency components are contained in a sound? That's where "spectrums" come in.

A spectrum represents the frequency components contained in a sound and the distribution of their intensity. For example, if a sound contains components at 440Hz, 880Hz, and 1320Hz, a spectrum can visualize how loud each frequency is. When sound is displayed as a waveform, we can see how it changes over time. However, simply looking at the waveform does not make it easy to intuitively understand what frequency components make up the sound. On the other hand, with a spectrum, by plotting frequency on the horizontal axis and intensity on the vertical axis, it becomes easier to grasp the components contained in the sound. For example, in the case of a human voice, the frequency bands that characterize the voice will appear, and in the case of musical instrument sounds, the unique frequency configuration of each instrument will appear.

Furthermore, if unwanted noise is present, it's possible to identify the frequency band in which that noise resides. In other words, while a waveform represents the "temporal changes of sound," a spectrum can be seen as representing the "components of sound." Features that are not apparent simply by listening to sound can be objectively understood by viewing them as a spectrum. For this reason, in audio development, it is common practice to analyze and evaluate sound using spectra, in addition to recording and playing it back.

Figure 1. The spectrum visualizes the contents of the sound.

Why is spectral analysis used in audio development?

We can form impressions such as "muffled," "overly bright treble," or "noticeable noise" simply by listening to sound. However, subjective evaluations alone are insufficient in audio development. For example, if a product is evaluated as "muffled," what aspects should the developer improve? Also, if a product is described as "clear," how can the difference be shared with other team members? In situations like these, a common metric that can objectively describe sound is necessary.

That's where spectra come into play.

By using spectra, the characteristics of sound can be expressed as frequency components. For example, it becomes possible to quantitatively confirm things like "lack of low frequencies," "noise concentrated in a specific frequency band," or "emphasized high frequencies," thus transforming subjective evaluations into concrete discussions. This approach is used in various audio development situations. For example, in microphone evaluation, it can be used to check which frequency bands the microphone excels at. In speaker development, it can be used to evaluate which frequency bands are being reproduced adequately. Furthermore, in noise reduction and sound quality adjustment, it provides clues to identify problematic frequency bands and focus improvements on those areas.

In other words, what developers want to know is not "whether or not there is sound," but "what characteristics the sound has." Spectra is used as a means to translate the impression perceived by the ear into objective information. For this reason, the concepts of frequency and spectrum are widely used as a common language in audio development.

Summary

We usually perceive sound in terms of "high" or "low," but in audio development, frequency is used to objectively represent its characteristics. Furthermore, actual sound is not composed of a single frequency; timbre and characteristics are created by a combination of multiple frequency components. The spectrum is a visualization of this composition.

By utilizing the spectrum, it becomes possible to grasp characteristics that are difficult to discern simply by listening to sound, and this is useful in various audio development situations, such as sound quality evaluation and noise analysis. The concept of understanding sound as frequency components can be said to be an important first step in learning audio technology.

Related Information

In audio development, various technologies such as filtering, equalization, noise reduction, and audio processing algorithms are utilized, based on the frequency and spectral concepts introduced here. In actual development, the characteristics of the sound are confirmed while designing and evaluating these signal processing methods.

DSP Concepts' audio development platform, "Audio Weaver," provides an environment for designing and evaluating audio signal processing using a GUI.

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