MusicReasonProduction, Synthesis, and Audio Math
How does this time constant compare to the beat?
Declare a tempo, a note division, and an attack or release time in milliseconds. This tool shows what fraction of that note's duration the time constant represents and how much of a declared illustrative envelope would be reached by then. It never claims any specific hardware or plug-in compressor follows this exact curve.
Answer
Want to learn more? Musical Time in Delay, Reverb, and Modulation
Understand
A one-pole envelope never fully reaches its target instantly; it approaches it exponentially, covering a large share of the distance quickly and the remainder ever more slowly. The time constant, tau, is the time at which the envelope has covered roughly 63.2% of the total distance, a standard reference point for comparing different attack or release settings against each other or against the beat.
Worked examples
At a time equal to the time constant itself, the illustrative envelope has always reached about 63.2% of its total travel, regardless of what that time constant's actual value is. Increasing the time constant while holding the observation time fixed always slows the response, reaching a smaller percentage at that same fixed time, since a larger tau stretches the same exponential curve out further.
Method and limitations
The envelope percentage at time t is (1 − e^(−t/tau)) × 100, a standard one-pole illustrative curve, evaluated here at multiples of the stated time constant. The note division's own duration comes from the stated tempo using the identical formula Tempo-Synced Delay Calculator uses, giving a musical reference window to compare the time constant against. Real compressors use a range of topologies, including ones that are not simple one-pole filters at all; this tool states its illustrative curve explicitly rather than implying it matches any specific device's actual response.
The evidence table's five checkpoints, at zero, one, two, three, and five time constants, are chosen because the curve's remaining distance to travel shrinks by roughly two-thirds at every additional time constant: about 63% covered at one tau, about 86% at two, about 95% at three, and effectively complete by five. A time constant set far shorter than the target note division reaches its target well before the next pulse arrives; one set far longer barely moves within that same window.