Exponential (not linear) envelope segments sound perceptually linear because hearing is logarithmic

When visualized on a graph, most envelope diagrams show straight lines (linear segments). But human hearing is logarithmic: equal ratios of amplitude are perceived as equal steps, not equal differences. A linearly rising amplitude envelope sounds like it jumps to volume instantly then stalls, because most of the perceptible change happens early. An exponentially rising amplitude — which rises slowly at first and accelerates — sounds like a steady, linear increase in loudness. Because pitch is also perceived logarithmically, cutoff and frequency envelopes should use exponential segments too. Best practice: use exponential segments for musical envelope applications. Caveat: standard envelope diagrams still depict straight lines even when the implementation is exponential.

Examples

Compare: a 500ms linear attack on a 220 Hz sine (sounds like instant jump then flat) vs. a 500ms exponential attack (sounds like steady fade-in). Most software synths default to exponential curves for exactly this reason.

Assessment

A student sets a 1-second linear attack on an amplitude envelope and complains ‘the volume jumps instantly then doesn’t change much.’ Diagnose the problem and prescribe a fix.