So for reference, we end up with Kahak roughly 200 years after parting with Hisame. It took roughly 40 years between Hayase and Hisame, going through 2 generations and 1"inheritor". We've gone through 5 more inheritors, assumedly 40 years apiece, hence 200 years. Then again, the time between generations can vary quite a lot so its a rough estimate at best.