Golden ratio
The concluding "Fuga concertante" exactly doubles the proportions of the finale of J. S. Bach’s "Fourth Brandenburg Concerto" (BWV 1049), as well as literally doubling its contrapuntal premise into a double fugue on two Lithuanian folk songs. As in the Bach, the fugal ritornelli are interspersed with elaborate cadenzas for the instrumental soloists, in one place in the form of the actual tracing on the guitar and ‘cello fingerboards of the Chinese brushstrokes for the ideographs for ‘broken string’. Where the movement divides at the Golden ratio, the string players stand and slash the air with their bows, to announce a structural demarcation usually left concealed by composers. During the fifth ritornello, the soprano’s first movement solo recurs in fragmentary guise as a wordless vocalise, so that in this movement the Spanish as well as Chinese presence survives only in allusive form. On the other hand, the Afro-Brazilian elements come into their own as a candomblé ceremony in miniature, the ethnomusicologically documented drumming, cowbell, and clapping effects all mimicked by the string orchestra and solo guitar without any actual percussion. The concerto ends with the dense Baroque counterpoint of solo guitar and ‘cello unwinding into silence like a rundown motor, by means of well-coordinated coups de grâce administered to the soloists’ tuning pegs by three players from the orchestra.