@Bob MacDonald as you point out there seem to be (at least) two roles to the vertical mark known in Unicode as METEG, other than the role of silluq. We might call these two roles the musical and the phonetic. I believe that is what Yeivin calls them. The musical is "merely" about marking a secondary stress whereas the phonetic changes something about the pronunciation other than stress (for example, modulating sheva quality, the topic here). I would caution against distinguishing these roles using the words meteg vs. gaʿya, as you seem to be suggesting.

As tempting as that may be (pointless to have two words for the same thing, so why not assign one word to each of the two roles), this is, as far as I am aware, unprecedented and will confuse many readers. I think following Yeivin's lead and using the adjectives "musical" and "phonetic" is a better idea, applying those adjectives to either meteg or gaʿya (but not to both, i.e. always use meteg or always use gaʿya).

Regarding distinctions of sheva quality, here are some great resources to be aware of (if you're not already).

• Paper editions like Koren and Simanim make these distinctions.

• The online edition of MAM at alhatorah.org makes these distinctions.

E.g. here's a screen snip of Ps 150:1 from Tehillim 150 – תהלים קנ‏ – Mikraot Gedolot – AlHaTorah.org:

There are many cases of disputed sheva quality, and also even where in theory people agree, practice may vary according to context, e.g. chanting in an elevated style vs. informally studying in a group. But it is useful to have these editions as a reference point.

Relatedly: I am working on a phonetic transcription of all of Tanakh based on the Al-Hatorah edition of MAM. I am currently lacking stress indication, but here's a "teaser" for Psalm 150:1, temporarily using an ASCII version of Jacobson's transcription style, is as follows:

ha-l^-lu yah ha-l^-lu-'El b^-kod-shO ha-l^-lu-hu bir-kI-a` `uz-zO

Bob

Further to our discussion of this elsewhere, bear in mind that halleyu is the plural of hallel—hence the shva is נע (mobile), rather than naḥ (quiescent).

That is a good question. If we were to rephrase it in the way that the medieval grammarians tended to discuss these sorts of issues, they might say:

In the case of the Tiberian tradition, it all depends on whether or not a gaʕya is present under the ה: i.e,. הֽ.

If a gaʕya is present, then shewa is pronounced mobile. As such, the preceding pataḥ is lengthened being in an open syllable:

Ps. 150.6: הַֽלְלוּ־ [haːlaluː]

Theoretically, if a gaʕya is not present, then the shewa would be pronounced silent. As a result, there would be a geminated lamed and the preceding pataḥ would also remain a short vowel, since it would be in a closed syllable:

eg: הַלְלוּ [halˈluː]

It seems to be the case, however, that gaʕya was not always marked in such situations and yet readers of the Tiberian tradition still tended to pronounce it as [haːlaluː] as if it had gaʕya, even when it did not.

You can read more about this in Geoffrey Khan's book in section §I.2.5.8.3.