An entirely transparent
A mapping function transforms the input gesture to the output sound.
Each gesture / input is mapped directly to one output. Clear and simple. Not terribly exciting.
One input controls multiple outputs. Higher level control but less control over details. Powerful.
Many inputs coupled to produce one musical parameter. Allows for greater expressive control and mastery. Finer degree of control. (e.g. Frequency and Detune knob).
Non-linear, non-deterministic control can add intrigue and interest to your interface, but too much of it will make the interface feel arbitrary and non-responsive.
Dimensionality and parameterization are important concepts for interactive music. Often times users are given an interaction an a specific dimension. The higher-level the dimension (i.e. “energy” vs “loudness”, “dance-ability” vs “tempo”), the more engaging and approachable the interaction.