Most of William Billings’s compositions were "plain tunes," but later collections included pieces that open with a syllabic and homophonic section, feature a passage in free imitation, and close with voices again in homophony. These are known as:

Fuging tunes    

Explanation:

Fuging tune is one of the type of choral music in the Anglo-america and this tune is basically placing in tenor voice section that basically integrating and coordinating the chords. The fuging tunes is initial flourished in the middle of the 18th century.

 According to the given question, the composition of the William billings's worked in the plain tunes but now there is huge collection which include the homo-phonic sections and this is known as the fuging tunes.  

 Therefore, Fuging tune is the correct answer.

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