How did the Catholic Masses' kyriales get their names?

There are eighteen plainchant settings of the ordinary of the Mass (kyriales ), sixteen of which have specific names. 1961 *Liber Usualis* : **Ordinary Chants** | | Name | Season | Mode | Century | |----|----------------------------|-----------------------------------------------------------------------------------------|------|------------| | 1 | _Lux et origo_ | In Paschal Time | 8 | 10 | | 2 | _Kyrie fons bonitatis_ | For feasts of the I class. 1. | 3 | 10 | | 3 | _Kyrie Deus sempiterne_ | For feasts of the I class. 2. | 4 | 11 | | 4 | _Cunctipotens Genitor Deus_| For feasts of the II class. 1. | 1 | 10 | | 5 | _Kyrie magnæ Deus potentiæ_| For feasts of the II class. 2. | 8 | 13 | | 6 | _Kyrie Rex Genitor_ | For feasts of the II class. 3. | 7 | 10 | | 7 | _Kyrie Rex splendens_ | For feasts of the II class. 4. | 8 | 10 | | 8 | _De Angelis_ | For feasts of the II class. 5. | 5 | 15-16 | | 9 | _Cum jubilo_ | For feasts of the Blessed Virgin. 1. | 1 | 12 | | 10 | _Alme Pater_ | For feasts of the Blessed Virgin. 2. | 1 | 11 | | 11 | _Orbis factor_ | For Sundays throughout the Year. | 1 | (10) 14-16 | | 12 | _Pater cuncta_ | For feasts of the III class. 1. | 8 | 12 | | 13 | _Stelliferi Conditor orbis_| For feasts of the III class. 2. | 1 | 11 | | 14 | _Jesu Redemptor_ | For feasts of the III class. 3. | 8 | 10 | | 15 | _Dominator Deus_ | For commemorations and ferias of the Christmas season. | 4 | 11-13 | | 16 | — | For ferias throughout the Year. | 3 | 11-13 | | 17 | — | For the Sundays of Advent and Lent. | 1 | (10) 15-17 | | 18 | _Deus Genitor alme_ | For the ferias of Advent and Lent as well as for Vigils, Ember Days, and Rogation Days. | 1 | (10) 15-17 | **Chants “*Ad Libitum*”** | | Name | Mode | Century | |----|------------------------------|------|---------| | 1 | _Clemens Rector_ | 1 | 10 | | 2 | _Summe Deus_ | 1 | 11 | | 3 | _Rector cosmi pie_ | 2 | 11 | | 4 | _Kyrie altissime_ | 5 | 11 | | 5 | _Conditor Kyrie omnium_ | 7 | 10 | | 6 | _Te Christe Rex supplices_ | 8 | 10 | | 7 | _Splendor æterne_ | 1 | 11 | | 8 | _Firmator sancte_ | 6 | 13 | | 9 | _O Pater excelse_ | 8 | 11 | | 10 | _Orbis factor*_ | 1 | (10) | | 11 | _Pater cuncta†_ | 1 | 10 | *For Sundays throughout the year.
†For the Sundays of Advent and Lent. Perhaps the most well-known name is *Missa de Angelis,* which is Mass VIII; the most used setting is probably the “Missa Simplex” which is assembled from parts of Masses XVI, XV and XVIII. Mass XVIII has the name *Deus Genitor alme.* I’m aware that polyphonic settings of the Mass texts can be based on other tunes and inherit their names, for example the *Western Wynde* Mass of John Taverner or the Missa *Salve Regina* of Victoria . I haven’t been able to find a source for the names of the plainchant Masses. [Wikipedia](https://en.wikipedia.org/wiki/Kyriale) mentions that the names are inherited from the “opening of the *prosula* formerly sung to each respective Kyrie melody,” but the page has the incipit of Kyrie XI and it’s difficult to see how the words “Orbis factor” fit. And there is no information about what these *prosulae* actually are and where to find them. Is there any light to be shed here, or is it all shrouded in the mists of time?