From Neil W. Levin's Introduction to Volume 14:
Kaminsky’s setting of modim [anaḥnu lakh], which occurs toward the end of the amida, was intended specifically for the Sabbath mussaf service—even though it could be performed within other services as well. It is similar to Lind’s style in its melodic approach. Indeed, it was one of the few compositions by others that Lind himself sang with his choir when he officiated at Sabbath services (as did his three cantorial sons, whose repertoire almost exclusively otherwise comprised their father’s settings); and the Milken Archive recording is based on Lind’s edited version. The prayer occurs in the cantor’s repetition of the silently recited amida.
During the cantor’s intonation of modim, however, the congregation must simultaneously recite a text that begins with the same phrase; but after the first nine words, the two texts diverge. Kaminsky cleverly addressed this duality by having the cantor sing the same text as he would in the absence of the choir, while the choir sings the congregational text such that the two are intermeshed as a single composition. His is not the only setting so constructed; another more elaborate one well known to cantors is attributed to a hazzan by the name of Vladovsky who served pulpits in Canada as well as the United States. There are no known cantorial-choral compositions for this text emanating from Europe, and the very practice of emphasizing it with cantorial-choral interpretation appears to be an American innovation. The same is true of all the texts following the k’dusha in the cantor’s repetition of mussaf on Sabbaths.
Sung in Hebrew
[We gratefully thank You], our God and the God of our fathers, for having been for all eternity the Rock of our lives, the shield of our salvation – from generation to generation. We are grateful to You and praise You for our lives which are entrusted to Your hands, and for our souls given over to Your care, and for all the miracles and favors which are with us everyday—evening, morning, and afternoon. You are all goodness; Your love never fails us. You are merciful, Your kindness never ceases. Our hopes are with You forever.
We gratefully acknowledge that You are the Lord, Adonai, our God and the God of our fathers, the God of every living thing, our Creator and the Creator of the universe. We worship and offer thanks to Your great and holy name, because You have kept us in life and sustained us; so may You continue to do. Gather our exiles unto Your holy sanctuary, so that we may fulfill all Your commandments according to Your will and serve You wholeheartedly. For all this, we thank You. Worshipped is God, the source of blessings, to Whom we are forever thankful and to Whom all gratitude is due.
Translation: Rabbi Morton M. Leifman