The latter half of it, from vs. 15 "Hymnum cantemus Domino", is the canticle sung at EF Lauds on Wednesdays. I believe this would have been introduced as part of Pius X's revisions to the psalter.
Slightly off topic, is there an English translation set to the chant melody of Tota pulchra es? Something like the various settings of the Marian Antiphons, and even specifically, those in the Pius X hymnal. The Tota was part of the novena prior to the Immaculate Conception as observed by the Sisters of the Holy Names of Jesus and Mary that I heard at Marylhurst College, in suburban Portland, and now closed.
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