A: The Traditional Latin Rite!
They are the first syllables of the stanzas of the Vespers hymn of the feast of the Nativity of St. John the Baptist (June 24th).
Ut queant laxis
resonare fibris
Mira gestorum
famuli tuorum
Solve polluti
labii reatum
Sancte Ioannes.
Later, Do was exchanged for Ut and Ti was added as the named of the 7th tone. Guido of Arezzo (990-1050) chose the hymn to name the musical notes.