2.3 Amplitude, Loudness, and Dynamic Range

Amplitude, loudness, and dynamic range are crucial concepts in sound design. They determine how we perceive volume and intensity in audio. Understanding these elements helps create balanced, impactful mixes and shape the emotional impact of sound.

Measuring amplitude involves decibels and sound pressure levels. We'll explore peak and RMS levels, loudness perception, and Fletcher-Munson curves. We'll also dive into dynamic range compression, a key tool for controlling volume and shaping sound in modern audio production.

Measuring Amplitude

Decibel Scale and Sound Pressure Level

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• Decibel (dB) logarithmic unit used to express the ratio of two values of a physical quantity, often power or intensity
  • Comparing sound pressure level (SPL) to a reference level, typically the threshold of hearing at 1kHz ($2 \times 10^{-5}$ Pa)
  • Formula: $SPL = 20 \log_{10}(\frac{p}{p_0})$, where $p$ is the RMS sound pressure and $p_0$ is the reference pressure
• Sound Pressure Level (SPL) measure of the effective pressure of a sound relative to a reference value, expressed in decibels (dB SPL)
  • 0 dB SPL corresponds to the threshold of hearing at 1kHz, while 120 dB SPL is the threshold of pain
  • Every increase of 6 dB SPL approximately doubles the sound pressure and perceived loudness

Peak and RMS Levels

• Peak level maximum absolute value of the waveform in a given time interval
  • Represents the highest point the waveform reaches, either positive or negative
  • Does not provide information about the average loudness or energy of the signal
  • Used to determine the headroom and prevent clipping (digital distortion caused by exceeding the maximum level)
• RMS (Root Mean Square) level average level of a signal over time, calculated by squaring the signal, finding the mean, and taking the square root
  • Provides a better indication of the perceived loudness and energy of the signal compared to peak level
  • RMS level is always lower than the peak level, with the difference depending on the crest factor (ratio of peak to RMS level) of the signal
  • Signals with a high crest factor (transient-rich sounds like drums) have a larger difference between peak and RMS levels compared to signals with a low crest factor (sustained sounds like synth pads)

Perception of Loudness

Fletcher-Munson Curves and Hearing Thresholds

• Fletcher-Munson curves (equal-loudness contours) represent the sound pressure level required for pure tones at different frequencies to be perceived as equally loud by human ears
  • The curves demonstrate that human hearing is most sensitive around 3-4 kHz and less sensitive at low and high frequencies
  • At lower sound pressure levels, the curves are more compressed, indicating that the perceived loudness difference between frequencies is more pronounced
• Threshold of hearing lowest sound pressure level that can be perceived by human ears at a given frequency, typically around 0 dB SPL at 1 kHz for young, healthy individuals
  • The threshold of hearing varies with frequency, as described by the Fletcher-Munson curves
  • Age, exposure to loud sounds, and other factors can increase the threshold of hearing over time
• Threshold of pain sound pressure level at which sound becomes painfully loud, typically around 120-140 dB SPL
  • Exposure to sounds above this level can cause immediate hearing damage and should be avoided
  • The threshold of pain is relatively consistent across frequencies, unlike the threshold of hearing

Dynamic Range Compression

Compression Parameters

• Compression ratio relationship between the input and output levels above the threshold
  • Ratio of 2:1 means that for every 2 dB increase in input level above the threshold, the output level increases by 1 dB
  • Higher ratios (4:1, 8:1, 20:1) result in more aggressive compression, while lower ratios (1.5:1, 2:1) provide gentler compression
• Threshold of compression input level at which the compressor starts to reduce the gain of the signal
  • Signals below the threshold pass through the compressor unaffected
  • Lower thresholds result in more of the signal being compressed, while higher thresholds affect only the loudest parts of the signal
• Peak level and RMS level detection methods used by compressors to determine the input level and apply gain reduction
  • Peak level detection responds to the instantaneous peak levels of the signal, resulting in faster attack times and more aggressive compression
  • RMS level detection averages the input signal over a short time window, providing a more accurate representation of the perceived loudness and resulting in smoother, more natural-sounding compression

Attack and Release Times

• Attack time duration between when the input signal exceeds the threshold and when the compressor reaches its target gain reduction
  • Faster attack times (1-10 ms) catch transients and provide more aggressive control, while slower attack times (20-100 ms) allow transients to pass through and sound more natural
  • The appropriate attack time depends on the material and the desired effect (punchy vs. smooth compression)
• Release time duration between when the input signal falls below the threshold and when the compressor returns to its normal gain
  • Faster release times (20-100 ms) can cause pumping and breathing artifacts, as the compressor rapidly adjusts the gain
  • Slower release times (100-500 ms) provide a smoother, more transparent compression, but may not react quickly enough to sudden level changes
  • The release time should be set in relation to the tempo and rhythm of the material to avoid unnatural-sounding gain changes