The Ubiquitous Silluq, Ga'ya, and Metheg

Just what is this little half-length mark, this 'short perpendicular stroke' (Lambdin), this tittle under a consonant and to the left of the vowel sign (if any)?

Is it an indication of the tonic (Haïk-Vantoura), the silluq that occurs almost without fail at the end of every verse? Or is it an indication of a long /a/ vowel rather than a short /o/ vowel? Or both?

There are many occurrences sometimes even on a word that would be otherwise without accent since it is joined by a maqaf to the next word. 

E.g. Zechariah 14:2, וְאָסַפְתִּ֨י אֶת־כָּל־הַגּוֹיִ֥ם ׀ אֶֽל־יְרוּשָׁלִַם֮ לַמִּלְחָמָה֒, 

Zech 14:2 one of 7762 instances where silluq is the lone musical sign prior to a maqaf

This is a clue that the sign may not be playing a musical role here. It is certainly not an accented syllable. It is redundant since the reciting note is already /e/. It is not an indication of a short or long vowel. It does not appear to fit any of Lambdin's usage notes.

There are only 186 of these 7762 instances where the musical sign is not the silluq, and of these, 54 are on the first word where an opening accent can indicate a connection to the prior verse. 

This music may be heard
as 'Bribery at rest'.

Incidentally, 1 Samuel 8:3, וַיִּ֨קְחוּ־שֹׁ֔חַד וַיַּטּ֖וּ מִשְׁפָּֽט  is an example of a significant musical sign in a word that might otherwise have none, given its attachment via maqaf to the next word.

But it turns out that the music paints a simple ironic picture and does not conflict with the flow of the verse or seeing the first two words as a single unit. Again Haïk-Vantoura's key fits the lock without difficulty.

Does the great Grammarian, Gesenius, make any explanation of this sign easier? He defines several classes of silluq/metheg/ga'ya: 

... i.e. a bridle, indicates most frequently the secondary stress or counter-tone, as opposed to the principal tone marked by the accents. It serves, however, in other cases to point out that the vowel should not be hastily passed over in pronunciation, but should be allowed its full sound. Hence the other names of Metheg are Ma'arikh, i.e. lengthener, and Ga'ya, i.e. raising of the voice, which is Great Ga'ya with long vowels, otherwise Little Ga'ya.

This is the easiest part of his dissertation. He goes on for two pages to describe the light metheg, and when it is omitted, and the firm or indispensable metheg, the grave metheg, the euphonic ga'ya, and for the first two of these, there are lists and sublists of examples and exceptions. 

It's so much easier to sing it. How many times does this sign really appear and can we tell anything from its placement that might help distinguish its multiple possible uses?

It occurs 41,305 times in the Tanakh. Of these, 2,223 are in the first word of the verse, and 20,880 are in the last word of a verse. 

So 18,202 are in the middle words somewhere. The first and last ones will resolve using the Haïk-Vantoura deciphering key to recitation beginning and ending on the tonic /e/. So will the middle ones unless one has some fuzzy logic to bypass them. 

Gen 2:7

I tested some of Gesenius' examples. He cites הָֽאָדָ֗ם as a light metheg. It is frequent in Genesis 2. My music program ignores these (see 2:7 on the left) so as not to pull the melody down to the tonic without better cause. Haïk-Vantoura did not ignore them. They can be lightly passed over by a singer whether on the current reciting note or a drop to the tonic in cases such as these. They do seem unnecessary. Given that the first syllable is open, it does not seem required for pronunciation either.

Gen 4:25

Gesenius cites Genesis 4:25 as a firm or indispensable Metheg. My music program does not ignore this one. 

You can see that it impacts the musical line and emphasizes this word to some extent. He also cites Psalms 138:2 but in the WLC, this metheg does not occur, so it can't be very indispensable.

That's my beef with the long and complex paragraphs. They are unreadable and they do not all stand up to the data when they are read in detail. His example stands up for Job 41:26 (34) but is inconsequential since it is the first word of the verse and so signifies the default tonic as the start point in any case. 

In the following example from Joshua, one might think that the music is depleted by this signal. Perhaps I should ignore more of the inner verse methegs, if only I could distinguish them from a real silluq. Each composer can consider if the pulling down of the vocal line is suitable. It depends I suppose of what you think about Caleb's daughter and nephew inciting Caleb to give them a blessing. 

Joshua 15:18 where the metheg maybe is not a silluq.

"Every kind of light metheg" (of which he cites 6 subtypes), says Gesenius, "can be changed into a conjunctive accent." Unbelievable sentence. But he cites 2 Chronicles 34:11 as an instance. וּלְקָרוֹת֙ אֶת־הַבָּ֣תִּ֔ים אֲשֶׁ֥ר הִשְׁחִ֖יתוּ מַלְכֵ֥י יְהוּדָֽה

2 Chr 34:11b - definitely not a morphing of a metheg into a conjunctive accent!

For the grave metheg (ga'ya in the more limited sense) he cites an example from Psalms 1:3. But at the beginning of the word it has little impact. The word is very frequent without a metheg. That would be one way of distinguishing metheg from silluq: compare it to the other uses of the stem and its word-form. This could be done programmatically.

For the euphonic metheg, Gesenius says very little. And he concludes his details with Lambdin's general comment that distinguishing an /a/ from an /o/ is a dominant usage of the metheg. Having seen just how prevalent the qamats may be as an /o/, however, I doubt that the metheg is adequate to the task. In this, of course, it violates my sense that the music and the vowels are separate magisteria. So one is left with the ambiguity unresolved.

Who will explain this little vertical jot well? Gesenius is certainly exhausting in his hierarchic approach.