Broken time is an accompaniment concept in bass playing that evolved in jazz music at the turn of the 1950s and 1960s. The phenomenon grew out of the diversification and rhythmic variation of the bass line, the development of the double bass as a solo instrument, and a conceptual change in the level of interaction between the accompaniment and the soloist in the late 1950s. In the broken time bass line, regular and repeating rhythmic patterns were abandoned and replaced with varying rhythmic patterns or a constantly changing improvised rhythm. My dissertation deals with the development of broken time through three significant double bassists: Scott LaFaro, Jimmy Garrison, and Ron Carter. The transcriptions I made from recordings by the Bill Evans Trio, the John Coltrane Quartet, and the Miles Davis Quintet from 1959 to 1967 are the main focus of the thesis. The expressive approaches of these groups formed a strong model for generations to come. The groups' intense expression also shaped the bassists' melodic language, who started to play rhythmically more freely than before without compromising their accompaniment role. With selected examples from my transcriptions, I present the rhythmic ideas and means of forming a bass line that these bassists employed. The interaction became increasingly the focus of attention through the liberated rhythmic role of the double bass. Broken time became a new way to control the tension of the bass line and, consequently, the overall shape of the song. I will present a new perspective on how rhythmic improvisation in accompaniment became a significant part of the living jazz tradition to which these bassists have left their strong personal contribution.