The organization of the Temple singers was established through a formal lottery, which determined the exact sequence of their service. Rather than following the chronological birth order of the sons, this lottery dictated the schedule entirely on its own, jumping between different Levite families [מצודת דוד, מלבי״ם]. The very first lot fell to Joseph, the son of Asaph. Immediately following him, the second shift was assigned to Gedaliah, the son of Jeduthun.
The structure of these musical teams is defined as a unit of twelve individuals, consisting of the leader, his sons, and his brothers. Although this specific group size is noted directly alongside Gedaliah, there is a general consensus among commentators that it applies equally to Joseph. Because both leaders are introduced together, the group structure is stated just once to cover both of them. Furthermore, the term "brothers" in this context does not imply biological siblings. Instead, it describes an organized, professional group of singers [רש״י, מלבי״ם].
This foundational setup establishes the rule for the entire musical arrangement in the Temple. Every single shift was composed of a fixed group of exactly twelve Levites. This precise division perfectly completes the overall count of expert singers. With twenty-four shifts operating in total, and twelve men serving in each shift, the system accounts for the grand total of two hundred and eighty-eight Levite musicians [רש״י, מצודת דוד].