Audio Cheatsheet

Amplitude
In general: Amplitude_dB = 20 log10(intensity/intensity_ref) If we measure relative to a full scale signal: Amplitude_dB = 20 log10(intensity) intensity   = 10^(Amplitude_dB*0.05) So, for example: Amplitude_dB( 1.0 )      = 20 log10(1)         = 0 dB Amplitude_dB( 0.0 )       = 20 log10(0)         = -infinity dB Amplitude_dB( 0.5 )       = 20 log10(0.5)       ~ -6 dB Amplitude_dB( sqrt(0.5) ) = 20 log10(sqrt(0.5)) ~ -3 dB intensity( -6 ) = 10^(-6*0.05) ~ 0.5

Mid/side Processing
From stereo til M/S: side = 0.5 * (left - right) mid = 0.5 * (left + right) From M/S to stereo: left = mid + side right = mid - side Derivation: mid + side = 0.5 * (l + r) + 0.5 * (l - r)           = 0.5 * l + 0.5 * r + 0.5 * l - 0.5 * r = l mid - side = 0.5 * (l + r) - 0.5 * (l - r)            = 0.5 * l - 0.5 * r + 0.5 * l + 0.5 * r = r

Exponential Cross-fade
Exponential / logarithmic cross-fades can be performed with this general formula, where out is the result of mixing in_a and in_b from t=0..1 with power p: out = in_a t^p + in_b (1-t)^p Different values of p result in different fade shapes: p = 0.5 is an equal power fade (at t=0.5, inputs are multiplied with sqrt(0.5) ~ 0.707, ~ -3dB) p = 1.0 is a linear fade      (at t=0.5, inputs are multiplied with 0.5, ~ -6dB) p = 2.0 is an exponential fade (at t=0.5, inputs are multiplied with 0.25, ~ -12dB)

Durations
Given that tempo is beat/minute and sample_rate is smp/s: beat_duration  = 60/tempo s/b sample_duration = 1/sample_rate s

Examples (assumes sample_rate = 48000 smp/s): beat_duration(120) = 60/120 = 0.5  s/b = 24000 smp beat_duration(140) = 60/140 ~ 0.428 s/b ~ 20571 smp

Examples (assumes sample_rate = 44100 smp/s): beat_duration(140) = 60/140 ~ 0.428 s/b = 18900 smp

Relative Frequency
If we want to adjust the pitch of a sound a given number of semitones (positive or negative): relative_frequency = 2^(semitones/12)

Examples: relative_frequency(+12) = 2^(12/12) = 2    # octave relative_frequency(-12) = 2^(-12/12) = 0.5 # octave down relative_frequency(+7) = 2^(7/12)   ~ 1.50 # fifth relative_frequency(+4) = 2^(4/12)   ~ 1.26 # major third

Wave length
Speed of sound: 343.21 m/s

Examples: wavelength(50 Hz) = 343.21 m/s /    50 per/s ~ 7 m/per wavelength(20 KHz) = 343.21 m/s / 20000 per/s ~ 0.017 m/per = 1.7 cm/per