I do think it could change the sound. Consider a simple octave interval, with zero phase or 90 degrees out: https://www.wolframalpha.com/input?i2d=true&i=Chart

I do think it could change the sound. Consider a simple octave interval, with zero phase or 90 degrees out: https://www.wolframalpha.com/input?i2d=true&i=Chart+Sin%5C%2840%29x%5C%2841%29%2BSin%5C%2840%292x%5C%2841%29 https://www.wolframalpha.com/input?i2d=true&i=Chart+Sin%5C%2... https://www.wolframalpha.com/input?i2d=true&i=Chart+Sin%5C%2840%29x%5C%2841%29%2BSin%5C%2840%292x%2BDivide%5B%CF%80%2C2%5D%5C%2841%29 https://www.wolframalpha.com/input?i2d=true&i=Chart+Sin%5C%2... The first looks a bit like a sawtooth wave, the second is more like a chain of pulses. Wouldn't that sound different? The Fourier series of Sawtooth wave, Square wave, etc. contain phase info as well as frequency.