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The screencast video of illustrates two different approaches to this problem, and demonstrates the perceptual effects that result from treating pitch perception as linear instead of logarithmic.
Perception of sound intensity also logarithmic. When you judge one sound to be twice as loud as another, you actually perceive the ratio of the two sound intensities. For example, consider the case of two people talking with one another. You may decide that one person talks twice as loud as the other, and then measure the acoustic power emanating from each person; call these two measurements ${T}_{1}$ and ${T}_{2}$ . Next, suppose that you are near an airport runway, and decide that the engine noise of one aircraft is twice the intensity of another aircraft (you also measure these intensities as ${A}_{1}$ and ${A}_{2}$ ). In terms of acoustic intensity, the difference between the talkers ${T}_{2}-{T}_{1}$ is negligible compared to the enormous difference in acoustic intensity ${A}_{2}-{A}_{1}$ . However, the ratios ${T}_{2}/{T}_{1}$ and ${A}_{2}/{A}_{1}$ would be identical.
The decibel (abbreviated dB ) is normally used to describe ratios of acoustic intensity. The decibel is defined in :
where ${I}_{1}$ and ${I}_{2}$ represent two acoustic intensities to be compared, and ${R}_{\text{dB}}$ denotes the ratio of the two intensities.
Acoustic intensity measures power per unit area, with a unit of watts per square meter. The operative word here is power . When designing or manipulating audio signals, you normally think in terms of amplitude , however. The power of a signal is proportional to the square of its amplitude. Therefore, when considering the ratios of two amplitudes ${A}_{1}$ and ${A}_{2}$ , the ratio in decibels is defined as in :
Can you explain why "10" becomes "20"? Recall that $\mathrm{log}({a}^{b})=b\mathrm{log}(a)$ .
Often it is desirable to synthesize an audio signal so that its perceived intensity will follow a specific trajectory . For example, suppose that the intensity should begin at silence, gradually increase to a maximum value, and then gradually decrease back to silence. Furthermore, suppose that you should perceive a uniform rate of change in intensity.
The screencast video of illustrates two different approaches to this problem, and demonstrates the perceptual effects that result from treating intensity perception as linear instead of logarithmic.
Musical instruments produce sound composed of a fundamental frequency and harmonics or overtones . The relative strength and number of harmonics produced by an instrument is called timbre , a property that allows the listener to distinguish between a violin, an oboe, and a trumpet that all sound the same pitch. See Timbre: The Color of Music for further discussion.
You perhaps have studied the concept of Fourier series, which states that any periodic signal can be expressed as a sum of sinusoids, where each sinusoid is an exact integer multiple of the fundamental frequency; refer to :
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