In the wonderful The Triune God, Fred Sanders praises the work of a medieval theologian who composed a Trinitarian response to each of the psalms. Fred writes:
The Carolingian theologian Gerhohus the Great (1093-1169) [AKA Gerhoch of Reichersberg] concluded his
commentary on each of the psalms with a customised trinitarian Gloria Patri keyed
to the vocabulary and themes of each psalm. It is a very sophisticated
manoeuvre. Gerhohus is not finding the Trinity revealed in each psalm, but is
making use of the psalm’s discrete witness, its distinctive way of speaking, in
a canonical celebration of the full counsel of the Bible…
Gerhoch’s Trinitarian psalm doxologies are models of Trinitarian interpretation of the Old Testament. They are rereadings in light of the later developments of the story of salvation told in the canon. They negotiate the canonical hinge expertly, letting the Old Testament maintain its discrete witness rather than ignoring the unrevealedness of the Trinity under the old covenant. The rich vocabulary of the psalms infuses and enriches the Trinitarian theology in such a way that the Old Testament actually influences trinitarian theology. While they include many fanciful leaps of association, they are fundamentally grounded in Jesus' own appropriation of the Psalms as his personal voice. They point forward to the events of the incarnation and Pentecost, permitting us to distinguish adumbration from revelation. They are uniquely creative, yet grounded in a widespread tradition of Christian use of the psalms. (pp235-37)
I'm not sure of the extent to which Gerhoch is dependent on Christian tradition. Certainly some of the gloria reflect quite ancient interpretations - for example, the gloria for Psalm 3 is essentially a distillation of Augustine's exposition. Whatever the balance of tradition and creativity, though, they are such a stimulating example of theological interpretation and a model of the instinct to ascribe glory to the God we now name as Father, Son, and Holy Spirit.
I'm also not sure that they are readily available anywhere in a collection, so I've started gathering them from J. N. Neale and R. F. Littledale's A Commentary on the Psalms: From Primitive and Mediaeval Writers. 4 vols. London: Joseph Masters, 1868.
Below are the gloria for Book 1 of the psalms. More to follow...
UPDATE: You can also download the full set here
BOOK 1
Psalm 1
Glory be to the Father, who knoweth the way of the righteous; glory
be to the Son, who is the way of the righteous, the man who is blessed, and
prosperous in whatsoever he doeth; glory be to the Holy Ghost, who is the wind
that scattereth the ungodly;
As it was in the beginning, is now, and ever shall be: world
without end. Amen.
Psalm 2
Glory be to the Father, who hath begotten the Son today, that
is, eternally, and hath set him as king, and heard his desire as that of a
Priest; glory be to the Son, who desireth the Father for us, and possesseth the
nations for an inheritance unto the utmost parts of the earth; glory to the
Holy Ghost, who is the blessedness wherewith blessed are all they that put
their trust in him;
As it was in the beginning, is now, and ever shall be: world
without end. Amen.
Psalm 3
Glory be to the Father, who, lifting up my head, which is
Christ, is glorified in Him; glory be to the Son, who laid him down, and slept,
and rose up again; glory be to the Holy Ghost, who is the salvation and blessing
of which is said, Salvation is of the Lord, and thy blessing is upon thy people;
As it was in the beginning, is now, and ever shall be: world
without end. Amen.
Psalm 4
Glory be to the Father, who is the Lord; glory be to the Son,
who is his countenance; glory to the Holy Ghost, who is the light of that
countenance;
As it was in the beginning, is now, and ever shall be: world
without end. Amen.
Psalm 5
Glory be to the Father, unto whom is said, Ponder my words,
O Lord; glory be to the Son, unto whom is said Consider my meditation;
glory be to the Holy Ghost, unto whom is said Hearken thou unto the voice of
my calling;
As it was in the beginning, is now, and ever shall be: world
without end. Amen.
Psalm 6
Glory be to the Father, the Lord who hath heard the voice of my
weeping; glory be to the Son, the Lord who hath heard my petition; glory be to
the Holy Ghost, the Lord who will receive my prayer;
As it was in the beginning, is now, and ever shall be: world
without end. Amen.
Psalm 7
Glory be to the Father, the Lord my God, in whom I have put my
trust; glory be to the Son, the Lord who shall judge the people; glory be to
the Holy Ghost, the righteous God, who preserveth them that are true of heart;
As it was in the beginning, is now, and ever shall be: world
without end. Amen.
Psalm 8
Glory be to the Father, who hath put all things under the feet
of the Son of Man; glory be to the Son, who, though Son of God, vouchsafed to
become Son of Man, and to be made lower than the angels, and now is crowned
with glory and honour as priest and king; glory be to the Holy Ghost, the finger
of God, by whom the heavens were made;
As it was in the beginning, is now, and ever shall be: world
without end. Amen.
Psalms 9 and 10
Glory be to the Father, who lifteth up his hand and forgetteth
not the poor; and to the Son, the poor King who shall one day be helped to his
right; and to the Holy Ghost, the desire of the poor, who is always heard;
As it was in the beginning, is now, and ever shall be: world
without end. Amen.
Psalm 11
Glory be to the Father, the Lord who is in his holy temple; and
to the Son, the righteous Lord, who loveth righteousness; and to the Holy
Ghost, the countenance by whom all the just and the saints are illuminated;
As it was in the beginning, is now, and ever shall be: world
without end. Amen.
Psalm 12
Glory be to the Father, who is our help when godly men fail;
and to the Son, of whom it is written, “‘I will up’ saith the Lord;” and to
the Holy Ghost, whose words are pure words;
As it was in the beginning, is now, and ever shall be: world
without end. Amen.
Psalm 13
Glory be to the Father, who will not forget his servants for
ever; and to the Son, the angel of the Great Counsel (v2) and to the Holy Ghost, who
lighteneth our eyes that we sleep not in death;
As it was in the beginning, is now, and ever shall be: world
without end. Amen.
Psalm 14
Glory be to the Father, who looked down from heaven upon the
children of men; and to the Son, Who is in the generation of the righteous: and
to the Holy Ghost, from whom and by whom that generation receives its righteousness;
As it was in the beginning, is now, and ever shall be: world
without end. Amen.
Psalm 15
Glory be to the Father, whose is the holy hill; and to the Son,
who shall abide in it for ever; and to the Holy Ghost, by whom only we are to
reach it;
As it was in the beginning, is now, and ever shall be: world
without end. Amen.
Psalm 16
Glory be to the Father, who restores our lot to us; and to the
Son, who is the portion of our inheritance; and to the Holy Ghost, who is on
our right hand, that we should not fall;
As it was in the beginning, is now, and ever shall be: world
without end. Amen.
Psalm 17
Glory be to the Father, whose presence we shall behold in righteousness;
and to the Son, who awoke up after His likeness; and to the Holy Ghost, who is
himself that satisfaction, communicated in this world partly, that in heaven he
may be bestowed fully and everlastingly;
As it was in the beginning, is now, and ever shall be: world
without end. Amen.
Psalm 18
Glory be to the Father, who showeth loving-kindness unto David
his anointed, and to his seed; and to the Son, Christ the King, the true David,
who goeth forth to sow his seed; and to the Holy Ghost, Who is that loving-
kindness itself;
As it was in the beginning, is now, and ever shall be: world
without end. Amen.
Psalm 19
Glory be to the Father, from whom was the going forth of the
Sun; and to the Son, which cometh forth as a bridegroom out of his chamber; and
to the Holy Ghost, the spiritual heat, from which not anything is hid;
As it was in the beginning, is now, and ever shall be: world
without end. Amen.
Psalm 20
Glory be to the Father, who hears us in the day of trouble; and
to the Son, whose name defends us; and to the Holy Ghost, in whose salvation we
will rejoice;
As it was in the beginning, is now, and ever shall be: world
without end. Amen.
Psalm 21
Glory be to the Father, who preventeth [in the archaic sense of "goes before"] the Son with the blessings
of goodness; and to the Son, on whose head a crown of pure gold is set; and to
the Holy Ghost, the joy of the countenance of God;
As it was in the beginning, is now, and ever shall be: world
without end. Amen.
Psalm 22
Glory be to the Father, to whom all the ends of the world, when
they remember themselves, shall turn; and to the Son, who hath made the people
that shall be born; and to the Holy Ghost, the governor among the people;
As it was in the beginning, is now, and ever shall be: world
without end. Amen.
Psalm 23
Glory be to the Father, who anoints our head with oil; and to
the Son, the shepherd of his people; and to the Holy Ghost, who provides for us
that inebriating chalice which is so excellent.
As it was in the beginning, is now, and ever shall be: world
without end. Amen.
Psalm 24
Glory be to the Father, whose is the earth and all that therein
is; and to the Son, the king of glory; and to the Holy Ghost, the righteousness
of the God of our salvation;
As it was in the beginning, is now, and ever shall be: world
without end. Amen.
Psalm 25
Glory be to the Father, who is gracious and righteous; and to
the Son, the way in whom sinners are taught; and to the Holy Ghost, the secret
of the Lord;
As it was in the beginning, is now, and ever shall be: world
without end. Amen.
Psalm 26
Glory be to the Father, to whom we seek for judgment, and to
the Son, the truth in which we walk; and to the Holy Ghost, who is merciful
unto us;
As it was in the beginning, is now, and ever shall be: world
without end. Amen.
Psalm 27
Glory be to the Father, in whose house we desire to dwell all
the days of our life; and to the Son, the right way in which we are led; and to
the Holy Ghost, in whose tabernacle we are hid;
As it was in the beginning, is now, and ever shall be: world
without end. Amen.
Psalm 28
Glory be to the Father, the Lord our strength; and to the Son,
in whom our heart hath trusted and we are helped; and to the Holy Ghost, who is
the wholesome defence of his anointed;
As it was in the beginning, is now, and ever shall be: world
without end. Amen.
Psalm 29
Glory be to the Father, that commandeth the waters; and to the
Son, who is mighty in operation; and to the Holy Ghost, who shall give his
people the blessing of peace;
As it was in the beginning, is now, and ever shall be: world
without end. Amen.
Psalm 30
Glory be to the Father, to whom the Son cried and was heard, in
that he feared; and to the Son, whose life was kept from them that go down into
the pit; and to the Holy Ghost, to whom we cry, “Lord, be thou my helper”;
As it was in the beginning of the dedication of the Lord’s
temple on the cross, is now, that the true Son of David it sat down on the
throne, and ever shall be, when his people shall behold the glory which he had
before the world was: world without end. Amen.
Psalm 31
Glory be to the Father, to whom the Son saith, "Into thy
hands, O Lord, I commend my spirit;" and to the Son, of whom it is
written, “Thou art my strong rock and my castle;” and to the Holy Ghost,
through whom they that are his saints love the Lord;
As it was in the beginning, is now, and ever shall be: world
without end. Amen.
Psalm 32
Glory be to the Father, the Lord to whom we confess our sins;
and to the Son, “the way wherein we shall go”; and to the Holy Ghost, who
informs us and teaches us;
As it was in the beginning, is now, and ever shall be: world
without end. Amen.
Psalm 33
Glory be to the Father, whose counsel shall endure for ever;
and to the Son, the Word of the Lord, by whom the heavens were made; and to the
Holy Ghost, the breath of his mouth;
As it was in the beginning, is now, and ever shall be: world
without end. Amen.
Psalm 34
Glory be to the Father, the Lord in whom we make our boast; and
to the Son, the angel that tarrieth round about them that fear him; and to the
Holy Ghost, who is near unto them that are of a contrite heart;
As it was in the beginning, is now, and ever shall be: world
without end. Amen.
Psalm 35
Glory be to the Father, who hath pleasure in the prosperity of
his servant; and to the Son, against whom false witnesses did rise up, laying
to his charge things that he knew not; and to the Holy Ghost, who pleadeth our
cause;
As it was in the beginning, is now, and ever shall be: world
without end. Amen.
Psalm 36
Glory be to the Father, with whom is the well of life; and to
the Son, in whose light we shall see light; and to the Holy Ghost, whose
righteousness standeth like the strong mountain;
As it was in the beginning, is now, and ever shall be: world
without end. Amen.
Psalm 37
Glory be to the Father, who ordereth a good man's going; and to
the Son, who forsaketh not his that be godly; and to the Holy Ghost, who is
also their strength in the time of trouble;
As it was in the beginning, is
now, and ever shall be: world without end. Amen.
Psalm 38
Glory be to the Father, the Lord
God of our salvation; and to the Son, who shall answer for us; and to the Holy
Ghost, who will not be far from us;
As it was in the beginning, is
now, and ever shall be: world without end. Amen.
Psalm 39
Glory be to the Father, in whose image
we are created; and to the Son, who was chastened with rebukes; and to the Holy
Ghost, of whom it is said “My hope is ever in thee”;
As it was in the beginning, is
now, and ever shall be: world without end. Amen.
Psalm 40
Glory be to the Father, in whose
book it is written that the only-begotten should do his will; and to the Son,
who saith, “Lo, I come”; and to the Holy Ghost, who openeth our ears;
As it was in the beginning, is
now, and ever shall be: world without end. Amen.
Psalm 41
Glory be to the Father, who
raiseth up the Son again that he may reward his enemies; and to the Son, who
considereth me poor and needy; and to the Holy Ghost, who upholdeth us when we are
in our health;
As it was in the beginning, is
now, and ever shall be: world without end. Amen.