Musashi-shichito (seven parties of samurai in Musashi country) wielded power from the last Heian-era to the Kamakura-era (12-13th century). Shichito (seven parties) included Noyo, Murayama, Yokoyama, Inomata, Tan, Nishi, Tsuzuki, Kisai party and so on bisides KODAMA PARTY, then that didn't mean strictry seven parties.
KODAMA PARTY was the most powerful and had the most blood relative in these Musashi-shichito.
"The fourth grandson of Arimichi (or Udo) Tomine who was Fujiwara Korechika's secound son was Musashi-gonnokami Ieyuki. Ieyuki came this country originally. His son, KODAMA Shotaro Iehiro, called himself as KODAMA associated with his place of residence. His posterity extended more than fifty branches all affiliated with KODAMA PARTY and was prospering in this country."
"This country" indicates Musashi country, and the name of KODAMA PARTY is derived from KODAMA area in this country. The area is now KODAMA country in Saitama prefecture, and so it remains the name of KODAMA.