I am not sure if you can access the values using Python or not, but those values aren't impossible to recreate. In fact there is mathematical formula for each type, they are called Color Harmonies. So you can get the current color value, and do the math to get the other two.
Color choose types in C4D:
http://c4d.cn/help/r17/US/html/54503.html
The math:
This can be complex, as you have to change the color value from RBG to HSL, then you can change the HSL value using some formulas.
Discussion includes the conversations:
https://stackoverflow.com/questions/14095849/calculating-the-analogous-color-with-python
Math formula for all the types:
https://www.ethangardner.com/articles/2009/03/15/a-math-based-approach-to-color-theory-using-hue-saturation-and-brightness-hsb/