Shaping envelope curvature (exponential / linear / logarithmic) changes the feel and function of a rise or fall stage

A rise or fall stage is not just a duration — it has a shape. MATHS offers three curvature modes per stage: exponential (fast initial movement, slow tail — aggressive, percussive character), linear (constant rate of change — mechanical, steady), and logarithmic (slow initial movement, fast arrival — smooth, swelling feel). Percussive sounds like kick drums rely on exponential decay for snap. Pads and swells use logarithmic attack for the characteristic bloom. Choosing the curve is therefore choosing the musical function of a stage, independent of its length.

Examples

Kick drum: short exponential fall on amplitude envelope — fast snap. Pad swell: logarithmic rise. Mechanical, even movement: linear rise and fall.

Assessment

Describe the audible difference between an exponential and a logarithmic decay on a drum hit. Explain why curve shape, not just duration, determines the character of a stage.