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Hence that clan was noble, we can conclude Uchiha's won't have blood relationships with other clans through the creation of the Uchiha clan itself, because other clans were not as high as this one, talking about social status and blood purity (like what happens with Royal families).
In other terms, there was no way being an Uchiha that you could have a son with non-Uchiha powers. If we talk from the statement that the Sage got two sons 'naturally' then they both would have the Sage's DNA (dominant and recesive genes of the sage). The Elder Son would have Yin dominant genes and Yang recesive genes, the Younger son would have Yang dominant genes and Yin recesive genes...
So with the flow of time (in the Uchiha branch) there had to be an Uchiha who was born naturally with Yang powers (because even being recesive genes, they have the probability to be manifested as consequence of fenotype).
But this wasn't the case until Madara implanted the Senju (Yang) genes manually to awake the Rinnegan...
So the conclusion is that even if these sons had the Sage's DNA, their Yin and Yang powers couldn't be so pure through the time by coincidence... there had to be something else that divided them perfectly to be mantained without the Rinnegan being manifested again "naturally".
- By the way, sorry for the slackness... but I hate to repeat myself, and I kinda hate people who call me a slacker when they don't even do the job to read all my posts before criticizing me.