herbert eimert described what he called the "eight modes" of the twelve-tone series, all mirror forms of one another. the inverse is obtained through a horizontal mirror, the retrograde through a vertical mirror, the retrograde-inverse through both a horizontal and a vertical mirror, and the "cycle-of-fourths-transform" or "quartverwandlung" and "cycle-of-fifths-transform" or "quintverwandlung" obtained through a slanting mirror . with the retrogrades of these transforms and the prime, there are eight permutations.