I think I did this exercise before but cannot find it so have repeated it.
I did an orange red through to blue green to start, using a little white to try and keep the tonal values. I then did orange to violet and was surprised that the middle broken colours where almost the same as previously. The violet to green felt more tricky, as the colours went very dark, almost black however that was a useful thing to know!
I think the tertiary colours would be useful to use when painting in shadows, as shadows are not really just black and grey when you really look at them . I shall try to use this within my own work.