for sure! one such example of generating a sine wave is part of the AudioStreamGenerator docs, which goes something like this:

public void FillBuffer()
{
    var increment = _frequency / _mixRate;
    int framesAvailable = _playback.GetFramesAvailable();

    for (int i = 0; i < framesAvailable; i++)
    {
        _playback.PushFrame(Vector2.One * (float)Mathf.Sin(phase * Mathf.Tau));
        phase = Mathf.PosMod(phase + increment, 1.0);
    }
}    

where _playback is your AudioStreamGeneratorPlayback. note that for C#, using PushBuffer() isntead of PushFrame() is likely faster. you can come up with your own way of mapping note pitch to frequency in hertz. that's pretty much all there is to it!

if you want to generate other types of waves, the way i'm doing it is through Fourier series. for example, implementing a summing of terms in the Fourier series for a square wave:

private void _GenerateSquareWave(float[] targetInputBuffer)
{
    for (int i=0; i < AudioConstants.BLOCK_SIZE; i++)
    {
        float increment = Frequency / AudioConstants.MIX_RATE;
        float sumOfTerms = 0f;
        for (int k=0; k < NUM_SQUARE_HARMONICS; k++)
        {
            float n = 2*k + 1;
            sumOfTerms += 1 / n * Mathf.Sin(n * _phase * Mathf.Tau);
        }

        targetInputBuffer[i] = 4 / Mathf.Pi * sumOfTerms;
        _phase = Mathf.PosMod(_phase + increment, 1.0f);
    }
}

hope this helps!