Hello Bruce,
As I understand, the Odes, preserved in the book of Hours, the Horologion, are the original psalmic verses recited at Matins, prior to the development of hymnography during and after the Hagiopolite contribution. Eventually, when canons were introduced in the 8th C, they were interleaved in each psalmic verse of the Odes (1, 3-9). I have seen this ancient practice in monastic communities on Mount Athos, where instead of the euphemiae, "Glory to thee o God, glory to thee", and, "All-holy Mother of God intercede for us", "Glory... Now..." etc., the odal psalmic verses from the Odes were sung.
Here is an example below that could be applicable for today's Matins service, April 26. If the number of hymns in each Ode in the daily canons from the Parakleteki, Pentecostarion, and Menaiae is not enough, then they are repeated as many times as there are psalm verses in each Ode in the Horologion. It is a long process but their services last for hours and are not lacking in resources.
ODE ONE
Canon Hymns from the Pentecostarion (Psalmic verses in red from Ode One)
Τῷ Κυρίῳ ᾄσωμεν· ἐνδόξως γὰρ δεδόξασται.
«ᾌσωμεν πάντες λαοί, τῷ ἐκ πικρᾶς δουλείας, Φαραὼ τὸν Ἰσραὴλ ἀπαλλάξαντι, καὶ ἐν βυθῷ θαλάσσης, ποδὶ ἀβρόχως ὁδηγήσαντι, ᾠδὴν ἐπινίκιον, ὅτι δεδόξασται».
ᾌσωμεν τῷ Κυρίῳ· ἐνδόξως γὰρ δεδόξασται, ἵππον καὶ ἀναβάτην ἔρριψεν εἰς θάλασσαν.
Σήμερον ἔαρ ψυχῶν, ὅτι Χριστὸς ἐκ τάφου, ὥσπερ ἥλιος ἐκλάμψας τριήμερος, τὸν ζοφερὸν χειμῶνα ἀπήλασε τῆς ἁμαρτίας ἡμῶν, αὐτὸν ἀνυμνήσωμεν, ὅτι δεδόξασται.
Βοηθὸς καὶ σκεπαστὴς ἐγένετό μοι εἰς σωτηρίαν, οὗτός μου Θεός, καὶ δοξάσω αὐτόν, Θεὸς τοῦ Πατρός μου, καὶ ὑψώσω αὐτόν.
Ἡ βασιλὶς τῶν ὡρῶν, τῇ λαμπροφόρῳ ἡμέρᾳ, ἡμερῶν τε βασιλίδι φανότατα, δορυφοροῦσα τέρπει, τὸν ἔγκριτον τῆς Ἐκκλησίας λαόν, ἀπαύστως ἀνυμνοῦσα, τὸν ἀναστάντα Χριστόν.
Κύριος συντρίβων πολέμους, Κύριος ὄνομα αὐτῷ.
Πύλαι θανάτου Χριστέ, οὐδὲ τοῦ τάφου σφραγῖδες, οὐδὲ κλεῖθρα τῶν θυρῶν σοι ἀντέστησαν, ἀλλ' ἐξαναστὰς ἐπέστης, τοῖς φίλοις σου εἰρήνην Δέσποτα δωρούμενος, τὴν πάντα νοῦν ὑπερέχουσαν.
Canon hymns from the Menaion (Psalmic verses in red from Ode One)
Ἅρματα Φαραὼ καὶ τὴν δύναμιν αὐτοῦ ἔρριψεν εἰς θάλασσαν, ἐπιλέκτους ἀναβάτας τριστάτας κατεπόντισεν ἐν Ἐρυθρᾷ, θαλάσσῃ.
Ἱερεύσας, σεαυτὸν ὡς ἀρνίον πανάμωμον, τυθεὶς Παμμακάριστε, καὶ ταῖς ῥοαῖς τῶν αἱμάτων σου, θάλασσαν ἐξήρανας, τῆς πονηρᾶς ἀθεΐας θείᾳ χάριτι.
Πόντῳ ἐκάλυψεν αὐτοὺς, κατέδυσαν εἰς βυθὸν ὡσεὶ λίθος.
Βασίλειον, ἐπιχρώσας ἐσθῆτα τοῖς αἵμασι, καὶ νίκης διάδημα, τῇ κεφαλῇ περιθέμενος, χαίρων προσεχώρησας, εἰς τὰ βασίλεια Πάτερ τὰ οὐράνια.
Ἡ δεξιά σου, Κύριε, δεδόξασται ἐν ἰσχύϊ, ἡ δεξιά σου χείρ, Κύριε, ἔθραυσεν ἐχθρούς. Καὶ τῷ πλήθει τῆς δόξης σου συνέτριψας τοὺς ὑπεναντίους.
Ὁσίως σου, καὶ δικαίως ποιμάνας τὸ ποίμνιον, εἰς μάνδραν εἰσήλασας, τὴν ἐπουράνιον Ὅσιε, ἔνθα τῆς ἀθλήσεως, περικοσμούμενος στέφει προσεχώρησας.
Ἀπέστειλας τὴν ὀργήν σου, κατέφαγεν αὐτοὺς ὡσεὶ καλάμην.
Πανύμνητε, τῶν ἀνθρώπων ἑτοίμη βοήθεια, τὰ ἄγρια κύματα, τῶν πειρασμῶν καταπράϋνον, σῴζουσα τοὺς δούλους σου, τῆς τῶν ἐχθρῶν ἐπηρείας προστασίαις σου.
......
How were they sung? They were not. The psalmic verses of the Odes in the Horologion were not melismatic or rhythmic. They were read like everything else, by the Canonarchs (whence the term) who stood in the middle of the naive, in intonation on a given pitch matching the tone of the canons.
Coincidentally, the Egkomia of the Matins of Holy Saturday (i.e. Friday night epitaphios service) were done in the same way. The canonarchs would read on a pitch the Άμωμο (Psalm 118) before every verse of the egkomia.