Kagai' written in kanji as '嬥歌' is a dialect for 'utagaki' spoken in the Togoku region (eastern part of Japan, especially the Kanto region,) which is also considered to have originated from 'kakeai' ('calling each other in rhythmic dialogue').
また、東国方言の「かがい（嬥歌）」も「懸け合い」に由来すると考えられている。