Data points and the application of Bayes theorem to the Music of the Hebrew Bible

We have the formula for Bayes theorem. It is easily applied if we can agree on the hypotheses and the probabilities of whatever background knowledge we are in possession of. 

A second approach was suggested in the last lecture called 'Inference to the Best Explanation'. The shape of the argument is in this one frame I have borrowed from the lecture by Matthew Joss given March 31 from Australia (7 am), Victoria BC time 1 pm, but organized by Christoph Heilig from Berlin time - 10 pm

IBE - Matthew Joss 2022

D is a collection of data - in this case the Hebrew Bible - all 23,197 verses. 

It will be agreed that a verse is a set of 1, 2, or 3 cola. A colon is a set of words. I define a colon as ending with a rest point, either an atnah, an ole-veyored, or the silluq at the close of each verse. It is possible to extend the definition with some other pausal accents, but only these three are reliable. E.g. a revia or a zaqef-qatan may be used but not all such accents are rest points (disjunctive).

A word consists of letters, vowels, at least one accent, and 0 or more maqaf (hyphens). Two Hebrew words connected by a maqaf is one 'word' (from the point of view of the music). 

So somewhat at random, here is a datapoint:

אִֽם־תִּשְׁכְּבוּן֮ בֵּ֪ין שְׁפַ֫תָּ֥יִם
כַּנְפֵ֣י י֭וֹנָה נֶחְפָּ֣ה בַכֶּ֑סֶף
וְ֝אֶבְרוֹתֶ֗יהָ בִּֽירַקְרַ֥ק חָרֽוּץ

So here we have a verse (Psalms 68:14) consisting of three cola. The first ends with an ole-veyored. These occur only in the poetry books. The second ends with an atnah. Atnah occurs in 21,559 of the verses in D. Atnah never occurs more than once per verse. Similarly the ole-veyored only occurs once in a verse, and if it occurs in a verse with an atnah such as the above, it is always before the atnah. [These are not hypotheses. They are measurements of D and repeatable by anyone.]

For the list of accents, see e.g. this post among others. In the above example:

• Colon 1 has three words, 5 accents, three below the text and 2 above.
• Colon 2 has 4 words, 4 accents, all below the text.
• Colon 3 has three words, 5 accents, three below the text and 2 above.

Notice that some cola have no accents above the text at all. All cola have accents below the text. Those accents below the text number 8 in total for all verses of the 21 prose books and 7 for the poetry verses in the three books. (Job has prose sections - chapters 1, 2, and 42 and the narrator's parts - these use the accents of the 21 books.)

The music for this verse is as follows:

Psalms 68:14

For an explanation as to how I arrived at this, please refer to my book or the many posts on this blog that explain the deciphering key. This is my chief hypothesis H. It is not a data point. It makes use of musical background knowledge and the design of coding systems that are meta-data to the notation. 

It is my thesis that H explains D and explains it better than any other hypothesis.

There are other hypotheses which I have noted in the first post arising from these lectures. One (call it H1) is that current tropes represent some vestiges of the meaning of the accents. Another (H2) is that the accents are a recursive division of a verse into two sections. With both of these it is assumed that the accents are confined in their impact to the current verse. It is H2 that states this rule.

Problems: H1: Current tropes have many variations from place to place and tradition to tradition. Deciding which is original is difficult - in effect there is no place to stand to determine which 'zarqa table' is the most reliable. 

H2: The so called law-of-continuous-dichotomy is simply useless and confusing. Music does not behave this way. Musical lines in a song are related by form a-b-a or a-b-chorus c-d-chorus etc. If the psalms are to be sung, and the accents are musical notation, then such forms should be observed.

In contrast, (H) the deciphering key approach demonstrates repeatedly that the accents do have cross-verse impact and even cross-chapter and multi-book impacts. They form psalms into melodies that show repetition, form, and choruses and define stanzas. Also the deciphering of Psalms 114 In Exitu Israel has a melody that is a variation on one that is still in use today for the same psalm. The tone called tonus peregrinus as used in both the plainsong and the Anglican chant versions is a vestige from the tone that arises naturally from the deciphering key.

The idea of a varying reciting note is the principle that makes the connection. The variation in reciting note is determined simply from the 7 or 8 accents that are used below the text. This provides a place to stand for the analysis of the songs and prophecies throughout the Scripture.

The final post in the ladder series has a summary of the 'best explanation'. The principle of Ockham's razor can be applied: it is futile to do with more what can be done with fewer symbols, and the best explanation is one that explains more of the usage of the patterns of the symbols. 

Comparing H and H1 with discussion of each of the background data issues would be a useful exercise. Let each hypothesis start at 50%, then consider each of the analyzed points, assign likelihoods, and see if Bayes factors prefer one over the other. I have no doubt that they will. For a basic intro to the music with aural examples see this popular post.