Summing N oscillators multiplies amplitude by N; dividing by N after summing prevents clipping

In an additive synthesis patch, each of N oscillators contributes to a single output sum. If every oscillator outputs at amplitude 1.0, the summed signal has amplitude N — which exceeds the ±1 digital range and clips. The standard fix is to multiply the final summed signal by 1/N (e.g., divide by 10 for a 10-oscillator patch), returning the peak amplitude to the 0–1 range. Alternatively, set each oscillator to amplitude 1/N from the start. Individual oscillator amplitude multipliers then shape the spectrum (timbral mix), while the master normalizer prevents distortion regardless of how the spectral weights are distributed.

Examples

10 oscillators, each at amplitude 1 → sum = 10 → clip. Add *~ 0.1 after the mixer → peak = 1 → no clip. With partial amplitudes [1, 0.5, 0.25, …] the sum is smaller, but the 1/10 normalizer still guarantees safety.

Assessment

A patch adds 6 oscillators, each with amplitude set by a slider from 0 to 1. At what multiplier should the master output be set to guarantee no clipping regardless of the slider positions?