Sources for the antiphons and responsories that I've been able to locate are listed below. If you are aware of any alternative sources, please do let me know.
Translations for the responsories can be found by following the link to the feast here.
AM =Antiphonale Monasticum
LH= Liber Hymnarius
LR=Liber Responsorialis NR=Nocturnale Romanum
PM=Processionale Monasticum
CHANT SOURCES FOR THE FEAST OF THE TRANSFIGURATION
Invitatory antiphon: Summum Regem gloria - LR 445/NR 236*/LH (pg 408).
Hymn: Quicumque Christum quaeritis - LR 445/AM 995-6 (Vespers)/NR 237*
Nocturn I
Antiphons and psalms
1: Ant. Paulo minus * ab Angelis minorátus, glória et honóre coronátus est, et constitútus super ópera mánuum Dei - (NR 238*) Tone 1G: Ps 8
2: Revelávit Dóminus * condénsa, et in templo ejus omnes dicent glóriam - (NR 239*) 1G - Ps 28
3: Speciósus forma * præ fíliis hóminum, diffúsa est grátia in lábiis tuis - (NR 240*) 1g: Ps 44

(Codex synopticon)
5. Petrus et qui cum illo praesentes erant, Christo laetificati videre gloriam Dei. - IVe (Ps 46)
For chant see Slovak Early Music Database
6. Respondens Petrus ait ad Iesum: Dominue si vis faciamus hic tria tabernacula - II (Ps 47)

Responsories
1. Surge, illumináre, NR 241*
2. In splendénte nube, NR 242*/PM 173
3. Vidéte qualem caritátem, NR 242*
4. Assumpsit Iesus Petrum

(Regensberg University)
Nocturn II
Psalms and antiphons
Nocturn III
Antiphon
Hodie ad patris vocem, transfigurato Domino, Moyses et Elias affluerunt splendidi, excessum eius, quem completurus erat, loquentes - canticles of Sundays throughout the year.
(Antiphonale synopticon)

Responsories
9. Vocávit nos Deus - NR 253*
10. Deus, qui fecit de ténebris lumen - NR 254*
11. Descendentibus illis de monte

12. Dum orasset Dominus - Cantus transcription.
Translations for the responsories can be found by following the link to the feast here.
AM =Antiphonale Monasticum
LH= Liber Hymnarius
LR=Liber Responsorialis NR=Nocturnale Romanum
PM=Processionale Monasticum
CHANT SOURCES FOR THE FEAST OF THE TRANSFIGURATION
Invitatory antiphon: Summum Regem gloria - LR 445/NR 236*/LH (pg 408).
Hymn: Quicumque Christum quaeritis - LR 445/AM 995-6 (Vespers)/NR 237*
Nocturn I
Antiphons and psalms
1: Ant. Paulo minus * ab Angelis minorátus, glória et honóre coronátus est, et constitútus super ópera mánuum Dei - (NR 238*) Tone 1G: Ps 8
2: Revelávit Dóminus * condénsa, et in templo ejus omnes dicent glóriam - (NR 239*) 1G - Ps 28
3: Speciósus forma * præ fíliis hóminum, diffúsa est grátia in lábiis tuis - (NR 240*) 1g: Ps 44
4. Ecce nubes lucida obumbravit
eos: paterna vos audita est: Hic est filius meus 8G: Ps 45
Antiphonale Synopticum
Antiphonale Synopticum
(Codex synopticon)
5. Petrus et qui cum illo praesentes erant, Christo laetificati videre gloriam Dei. - IVe (Ps 46)
For chant see Slovak Early Music Database
6. Respondens Petrus ait ad Iesum: Dominue si vis faciamus hic tria tabernacula - II (Ps 47)
Responsories
1. Surge, illumináre, NR 241*
2. In splendénte nube, NR 242*/PM 173
3. Vidéte qualem caritátem, NR 242*
4. Assumpsit Iesus Petrum

(Regensberg University)
Nocturn II
Psalms and antiphons
1. Illuminana tu mirabiliter (Ps
75) – NR 243*, IVE - Psalm 75
2. Melior est Mélior est dies una
in átriis tuis, super míllia - NR 244* -
Va : Ps 83
3. Gloriósa dicta sunt de te,
cívitas Dei NR 245* – VIf: Ps 86
4. Thabor et Hermon in nomine tuo
exsultabunt: tuum bracchium cum potentia
NR 248* - VIIa - Ps 88
5. Lux orta est iusto et rectis
corde laetitia – NR 250* - VIIIG - Ps 96
6.
Confessionem et decorem induit amictus lumine sicut vestimento – NR 251* - I d
- Ps 103
Responsories
5. Inebriáti sunt ab ubertáte - NR 245*
6. Præceptor, bonum est nos - NR 246*
7. Si ministrátio mortis - NR 246-7*
8. Assumptis hodie Dominus
Nocturn III
Antiphon
Hodie ad patris vocem, transfigurato Domino, Moyses et Elias affluerunt splendidi, excessum eius, quem completurus erat, loquentes - canticles of Sundays throughout the year.
(Antiphonale synopticon)
Responsories
9. Vocávit nos Deus - NR 253*
10. Deus, qui fecit de ténebris lumen - NR 254*
11. Descendentibus illis de monte
12. Dum orasset Dominus - Cantus transcription.
Britannica: ...It is not known when the festival was first celebrated, but it was kept in Jerusalem as early as the 7th century and in most parts of the Byzantine Empire by the 9th century. It was gradually introduced into the Western Church, and its observance was fixed as August 6 by Pope Calixtus III in 1457 as a thank offering for the victory over the Turks at Belgrade on that day in 1456....
The Gospel is also used on Ember Sat in Lent and Sunday Lent II.