In the first style to descend from Hachijō-daiko, what is the title of the drum player who provides the underlying beat?
Hachijō-daiko (八丈太鼓, trans. "Hachijō-style taiko") is a taiko tradition originating on the island of Hachijō-jima. Two styles of Hachijō-daiko emerged and have been popularized among residents: an older tradition based on a historical account, and a newer tradition influenced by mainland groups and practiced by the majority of the islanders.The Hachijō-daiko tradition was documented as early as 1849 based on a journal kept by an exile named Kakuso Kizan. He mentioned some of its unique features, such as "a taiko is suspended from a tree while women and children gathered around", and observed that a player used either side of the drum while performing. Illustrations from Kizan's journal show features of Hachijō-daiko. These illustrations also featured women performing, which is unusual as taiko performance elsewhere during this period was typically reserved for men. Teachers of the tradition have noted that the majority of its performers were women; one estimate asserts that female performers outnumbered males by three to one.
The first style of Hachijō-daiko is thought to descend directly from the style reported by Kizan. This style is called Kumaoji-daiko, named after its creator Okuyama Kumaoji, a central performer of the style. Kumaoji-daiko has two players on a single drum, one of whom, called the shita-byōshi (下拍子, "lower beat"), provides the underlying beat. The other player, called the uwa-byōshi (上拍子, "upper beat"), builds on this rhythmical foundation with unique and typically improvised rhythms. While there are specific types of underlying rhythms, the accompanying player is free to express an original musical beat. Kumaoji-daiko also features an unusual positioning for taiko: the drums are sometimes suspended from ropes, and historically, sometimes drums were suspended from trees.The contemporary style of Hachijō-daiko is called shin-daiko (新太鼓, "new taiko"), which differs from Kumaoji-daiko in multiple ways.  For instance, while the lead and accompanying roles are still present, shin-daiko performances use larger drums exclusively on stands. Shin-daiko emphasizes a more powerful sound, and consequently, performers use larger bachi made out of stronger wood. Looser clothing is worn by shin-daiko performers compared to kimono worn by Kumaoji-daiko performers; the looser clothing in shin-daiko allow performers to adopt more open stances and larger movements with the legs and arms. Rhythms used for the accompanying shita-byōshi role can also differ.  One type of rhythm, called yūkichi, consists of the following: 
This rhythm is found in both styles, but is always played faster in shin-daiko. Another type of rhythm, called honbadaki, is unique to shin-daiko and also contains a song which is performed in standard Japanese.
shita-byōshi