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How did fugue and variation appear in concerto grosso movements?

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caricature of Antonio Vivaldi — concerto Caricature of Antonio Vivaldi, pen and ink on paper by Pier Leone Ghezzi, 1723; in the Codex Ottoboni, Vatican Library, Rome. The inscription below the drawing reads, “Il Prete rosso Compositore di Musica che fece L'opera a Capranica del 1723” (“The red priest, composer of music who made the opera at Capranica [College in Rome] of 1723”).

In the Baroque concerto grosso, fugue and variation served as recurring structural principles that provided musical continuity alongside the rondo principle.1

Fugue

The fugue is based on the polyphonic treatment of a recurring subject through melodic imitation. In a concerto grosso, fugal sections typically appear in fast movements. During these sections, the tutti (full orchestra) and soli (soloists) groups either unite or alternate between expositions—where the subject is stated—and episodes, where the subject appears only fragmentarily or not at all. These applications range from loose, as often seen in Italian works, to strict, as frequently found in German compositions.1

Variation

The variation process relies on the continual development of a constant factor, such as a group of harmonies or a simple, freely recurring bass line known as an ostinato. This technique occurs primarily in slow movements. The ostinato often serves as a foundation for the soli parts, which may enter on long tones and unfold into expressive, decorative passages. When the bass line and treble melody are sufficiently distinct, the movement can evoke the effect of an aria, highlighting the influence of opera on the concerto grosso.1