Music multiple simultaneous tones, python

Question

I am working on an interesting project relating solving mathematical problems and music. It is easy to generate a specific note (or tone):

ton = amplitude * sin(2pi * frequency * time / samplerate)

I'm working in python, and have code to do this much from http://code.google.com/p/scitools/.

def note(frequency, length, amplitude=1, sample_rate=44100):
    time_points = numpy.linspace(0, length, length * sample_rate)
    return numpy.sin(2 * numpy.pi * frequency * time_points) * amplitude

Of course, in real music, there are generally multiple tones being played during the same time step. I tried to do this by generating then summing two tones, i.e.:

twotone = note(440, 2)+note(261.63, 2)

but this just gives crap. How would I mathematically encode more than one simultaneous tone?

Answer 1

you should half the individual amplitudes when using two tones, or the total amplitude potentially doubles. If you use more than two, you should mix in a ratio that reflects their relative volume, with a total amplitude of one.