Edosenke is a school established by Fuhaku KAWAKAMI, who was ordered by Yoshimune TOKUGAWA to become a disciple of the Omotesenke, so does not have a blood relationship to the Sansenke.
江戸千家は徳川吉宗の命を受けて表千家に弟子入りした川上不白が興したもので、三千家との血縁関係はない。