How did the Catholic Masses' kyriales get their names?

Question

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 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?

Answer 1

"The names derive from the tropes that the chants were associated with for some hundreds of years." (M. Jackson Osborn).

Tropes are "musical additions to the preexisting liturgical chants".

The popularity of tropes waned with the centralization of the liturgy wrought to a degree by the introduction of the Tridentine books and the establishment of the Sacred Congregation of Rites, but probably still more by the invention of the printing press. The Missal of the Roman Curia, which essentially became the Tridentine Missal of 1570, had no tropes, which is hardly surprising: Roman curial officials must not have been particularly interested in additions to the liturgy that might prolong the Mass, and indeed their missal was designed for the celebration of low Masses, hardly an environment favourable for troping. As a result, books published to provide the music for liturgical celebrations according to or based on the Tridentine model contained few if any tropes. At no point does it seem that tropes were expressly prohibited, except for one rubric contained in the 1570 Roman Missal (and not in the 1464 Missal) stating Sic dicitur Gloria in excelsis etiam in missis beatæ Mariæ ["The Gloria in excelsis is said even in Masses of the Blessed Virgin."], which might indicate an effort to forbid the popular Marian tropes on the Gloria.

—Notkerus Balbulus, "On Tropes"

Example trope:
Notkerus Balbulus, "Trope of the Week: Kyrie de Angelis":

Latin	English
Kyrie, Rex æterno posse superno, cunticreator, eleison. Kyrie, laudat dignum turba benignum tota polorum, eleison. Kyrie, nunc præsentes respice gentes dona petentes, eleison.	Lord, eternal King of lofty power, creator of all, have mercy. Lord, the entire multitude of the globe praises thee, worthy and merciful, have mercy. Lord, behold now the people here desiring gifts, have mercy.
Christe, prævenias morbis nostris nunc Conditor orbis, eleison. Christe, peste triumphata sumens hæc nostra peccata, eleison. Christe, sanguine qui digno præservas hoste maligno, eleison.	Christ, mayest thou now keep us from our ills, founder of the world, have mercy. Christ, having triumphed over pestilence, taking up these our sins, have mercy. Christ, who by thy worthy blood savest us from the evil enemy, have mercy.
Kyrie, fac tibi clerum psallere verum pectoris hymnum, flamine fultus lumine vultus vivat in ævum, eleison. Kyrie, nunc populorum Rex miserorum cerne precatus, flos pie florum fonsque bonorum terge reatus, eleison. Kyrie, suscipe rursum, dirige cursum, corde rogamus, scandere sursum vivere cursum quo valeamus, eleison.	Lord, make the clergy sing a true hymn of the heart to thee, may they live for aye, borne by the spirit, a brilliant countenance, have mercy. Lord, now, King of the wretched peoples, behold the prayers, O righteous flower of flowers and fount of good things, cleanse our guilt, have mercy. Lord, take us up anew, lead the way, we beseech thee from the heart, by which we might have the strength to climb up and live the way, have mercy.

See Notkerus Balbulus's "Tropes" category blog posts.

^{Notkerus Balbulus sources courtesy MatthewRoth}