An electrical solution that computes the absolute value of the input signal (an ideal rectifier bridge), i.e. just flips sign on the negative part of the signal will give the same result if the signal is sent to an ADC to measure rms - this obviously only as long as the signal is DC-coupled so there isn't a change of the DC level.

If the input signal is known to be symmetric (doesn't matter if it has distortion or what the overtones looks like), then an ideal diode can remove the negative half of the curve and you then only compute rms for the positive half. The full rms value will be twice the measured value. If the curve isn't symmetric, this concept where you throw away the negative half, will produce the wrong result.

If you know that it's a pure sine wave, your you know that it has one or two overtones and knows the exact phase and procentual relations between the frequencies, then you can measure just the top value and compute everything based on the top value. When the curve is assymetric or you know it has overtones but do not know their phase and relative size, then you must measure at least a half period. A full period if the signal is assymetric.