Bayes theorem and the interpretation of the te'amim

I watched several lectures on Bayes theorem - too bad it wasn't this much fun to study when I was in school 56 years ago and taking probability theory.

I wonder if probabilities even apply, but the idea is that one makes a hypothesis and asks what is the probability it is true given some new evidence.

On the subject of the te'amim, there have been several hypotheses. That the te'amim are: 

1. Punctuation.
2. Hierarchic and recursively dividing the phrases in two.
3. Musical signs whose form and meaning have been lost.
4. Musical signs that have a deciphering key that is decidable based on the evidence arising from the results of using it.

Which hypothesis is most likely to be true?

The evidence. 

• For 1. Ask Victor Borge. There are too many symbols (24+) for them to be punctuation. 
• For 2, there are theories over the last 1000 years of writing culminating in Wickes's law of continuous dichotomy - they are all without exception as obscure as the Ptolemaic universe and as full of contradictions. They are counter-intuitive as part of a sequential text. This so-called 'law' should be utterly forgotten. It is crippling.
• For 3. This is undoubtedly partly true. The variety and lack of consistent usage of the signs in Synagogues is evident. 

I vote for 4 since the deciphering key of Suzanne Haïk-Vantoura has considerable supporting evidence in my view. 

1. It is clearly defined in a few pages.
2. It is consistently interpreted in sequence, suitable for sight reading of the music, and supports a predictable musical line.
3. Beauty and expressivity are the result.
4. The theory is an efficient use of the evidence in the signs themselves - agreeing with the principle of Ockham's razor.
5. A musician can develop and arrange a piece based on the derived melodies.
6. It is a different tonality than music of the past 500 years.
7. The music allows variety of modality and is suitable for ancient and modern instrumental accompaniment.
8. It complements and interprets the text, and reveals the tone of voice.

The above are evidentiary support for the theory of SHV's key. Challenge - apply Bayes theorem.

As the application of isospin to the particle zoo revealed the theory of quarks, so the application of statistical and musical inference to the zoo of signs over and under the text in the Tanach reveals the music embedded in them. The system effectively divides the problem space and shows us how to explain the 16,689 distinct sequences of accents. (See my series on 'the ladder'.)

The frequency of syllables per reciting note for the 3 poetry books
plotted for lengths of 4, 5, 6, 7, and 8 syllables.
(The low c only appears in the prose chapters of Job.)

The frequency of syllables per reciting note for the 21 prose books
plotted for lengths of 4, 5, 6, 7, and 8 syllables.

• What is the likelihood that there were musicians in the ancient world like us - designers, singers, aware of tonality, physicists experimenting with string tension and length? (Yes - there were.) 
• What is the reliability of aural transmission of melodies? (It's quite low.) 
• What is the likelihood that the Masoretes would invent a notation? (Not likely.)

Challenge - develop the social statements, theses, and probabilities that would allow the application of Bayes theorem?

For an introduction to the music, see my book, The Song in the Night. See the examples of the music  on this blog here and here.