All this led me to a careful look at something that West had to say about the grave accent:
The reference is to West's Review of Allen's Accent and Rhythm. On page 5:Oxytone words, be it noted, did not at this period (or indeed in the classical period) lose their acute within the phrase.
Footnote: See Gnomon xlviii (1976) 5.
Here is Cratylus from Perseus:And in classical Greek, indeed down to the beginning of our era, the evidence indicates that oxytone words retained their accent within the sentence as well as at the end of it.
Footnote: Plato Crat. 399ab; Demetrius Byz. ap. Philod. de poem. (JbPhil Suppl. 17, 1889, 247 fr. 18); Dion Hal. comp. 63; and the musical inscriptions.
He is talking about Διὶ φίλος -> Δίφιλος. Socrates mentions one of the iotas going away from Διὶ (notice that he doesn't appear to distinguish between them). And Plato says that the high-pitched middle syllable becomes low-pitched. Does West take his silence about the accent of Διὶ as evidence that it was high-pitched in both Διὶ and Δί-?πρῶτον μὲν γὰρ τὸ τοιόνδε δεῖ ἐννοῆσαι περὶ ὀνομάτων, ὅτι πολλάκις ἐπεμβάλλομεν γράμματα, τὰ δ’ ἐξαιροῦμεν, παρ’ ὃ βουλόμεθα ὀνομάζοντες, καὶ τὰς ὀξύτητας μεταβάλλομεν. οἷον “Διὶ φίλος” —τοῦτο ἵνα ἀντὶ ῥήματος ὄνομα ἡμῖν γένηται, τό τε ἕτερον αὐτόθεν ἰῶτα ἐξείλομεν καὶ ἀντὶ ὀξείας τῆς μέσης συλλαβῆς βαρεῖαν ἐφθεγξάμεθα. ἄλλων δὲ τοὐναντίον ἐμβάλλομεν γράμματα, τὰ δὲ βαρύτερα <ὀξύτερα> φθεγγόμεθα.
339c is the only other mention of pitch, and there Socrates says that ἀναθρῶν ἃ ὄπωπε becomes ἄνθρωπος through "ἑνὸς γράμματος τοῦ ἄλφα ἐξαιρεθέντος καὶ βαρυτέρας τῆς τελευτῆς γενομένης."
In this example Socrates doesn't mention which syllable takes the high pitch either.
I don't have access to the Demetrius of Byzantium fragment. Maybe someone else does?
Dionysius of Halicarnassus is on Perseus:
http://www.perseus.tufts.edu/hopper/tex ... apter%3D11
West has lengthier discussion of the Dionysius passage in his Documents of Ancient Greek Music pg. 10, though it doesn't touch on the grave directly. Certainly the statement about λευκὸν not being monotone is suggestive of a differently pitched grave.ἐν γὰρ δὴ τούτοις τὸ ‘σίγα σίγα λευκὸν’ ἐφ᾽ ἑνὸς φθόγγου μελῳδεῖται, καίτοι τῶν τριῶν λέξεων ἑκάστη βαρείας τε τάσεις ἔχει καὶ ὀξείας.
For musical evidence, I've looked through DoAGM, noting the pieces where music follows accent, and I can't make a convincing case either way about the grave. The Delphic Paeans come closest to proving. But even there, the musical notation often seems to ignore the grave. Seiklos' music seems to contradict the grave while following other accents.
Allen has a discussion about the grave accent in VG 124ff and A&R 244ff, which covers the standard graphical and linguistic arguments that I'm familiar with.
Sommerstein (160f) had an argument that I hadn't seen before:
The strongest evidence for believing that the grave accent-mark means precisely what it seems to say is that it is regularly put on proclitics where these appear graphically as separate words. There is overwhelming evidence that proclitics were unaccented; and especially seeing that most prepositions were not oxytone when they were accented independently, the ancient grammarians would never have regarded proclitics as oxytone if there had not been something in the behaviour of real oxytones to mislead them. The only thing likely to do that would be for the real oxytones also to be sometimes unaccented. The principle on which the traditional graphic practice was based is a reasonable one. A mark is put on the structurally accented syllable, as usual; but it is the grave and not the acute, to show that the accent has in this case no phonetic value.
Footnote: Another language with a system of tonal accent, Japanese, also has, according to McCawley (1968, 134), 'a number of environments in which a final-accented noun is made unaccented' (emphasis mine: AHS), e.g., under certain conditions, before the enclitic no. (See further McCawley 1968, 140-1 and 177-9). The syllable which would have been accented is in such cases pronounced exactly as if it had never been accented. This shows that we need not be afraid of concluding that in Greek oxytone words frequently had no accent, phonetically speaking, at all.