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Thursday, 23 January 2020

Splitting statistics between the 21 books and the 3 books

To discover sequences, it is, of course, necessary to split the 21 from the three books. Because the three books have a slightly different set of te'amim (or accents). They lack the low c and they have a few variations in ornaments.

Here's some of the ways in the three books to the mid-point rest considering notes only (ignoring ornaments). The full set is 345 variations on the sequence, so a partial set illustrates, three notes prior to the atnah, 40 distinct sequences two or fewer notes approaching the atnah.

notes to the Atnah - corresponding accent names to the Atnah      Frequency
g B A g-tif B-mun A-atn 1294...
e B A e-sil B-mun A-atn 602...
g B A g-tif B-mun A-atn 595...
e f A e-sil f-mer A-atn 480...
B g A B-mun g-tif A-atn 417...
e B A e-sil B-mun A-atn 88...
e f A e-sil f-mer A-atn 83...
f e A f-mer e-sil A-atn 83...
g e A g-tif e-sil A-atn 75...
C B A C-mph B-mun A-atn 71...
C B A C-mph B-mun A-atn 66...
B g A B-mun g-tif A-atn 50...
B e A B-mun e-sil A-atn 46...
e g A e-sil g-tif A-atn 43...
f B A f-mer B-mun A-atn 42...
C f A C-mph f-mer A-atn 37...
d f A d-gal f-mer A-atn 37...
g f A g-tif f-mer A-atn 34...
B A B-mun A-atn 20...
f A f-mer A-atn 14...
f g A f-mer g-tif A-atn 14...
C f A C-mph f-mer A-atn 12...
e g A e-sil g-tif A-atn 9...
f e A f-mer e-sil A-atn 9...
g A g-tif A-atn 7...
g f A g-tif f-mer A-atn 5...
C e A C-mph e-sil A-atn 4...
d B A d-gal B-mun A-atn 3...
d g A d-gal g-tif A-atn 3...
B f A B-mun f-mer A-atn 2...
C g A C-mph g-tif A-atn 2...
g C A g-tif C-mph A-atn 2...
g e A g-tif e-sil A-atn 2...
B C A B-mun C-mph A-atn 1Psalms 137:7
C A C-mph A-atn 1Proverbs 1:9
C e A C-mph e-sil A-atn 1Proverbs 16:10
e A e-sil A-atn 1Psalms 102:28
e C A e-sil C-mph A-atn 1Proverbs 6:27
e C A e-sil C-mph A-atn 1Proverbs 6:3
f B A f-mer B-mun A-atn 1Psalms 88:1

Here's the full set for the three books of getting from the mid point rest to the tonic. The sequence is by notes.

notes from A to e   Accent names from the atnah to the end of the verse
^A ^A-atn 1Psalms 37:32
^A B ^A-atn B-mun 1Psalms 31:20
^A B C B c d f g f e ^A-atn B-mun C-mph B-mun c-dar d-gal f-mer g-tif f-mer e-sil 1Job 1:8
^A B c d f g f e ^A-atn B-mun c-dar d-gal f-mer g-tif f-mer e-sil 1Job 1:1
^A B e ^A-atn B-mun e-sil 388...
^A B e C B f d g f e ^A-atn B-mun e-sil C-mph B-mun f-mer d-gal g-tif f-mer e-sil 1Job 42:7
^A B e f g e ^A-atn B-mun e-sil f-mer g-tif e-sil 1Job 1:4
^A B e g f e ^A-atn B-mun e-sil g-tif f-mer e-sil 1Job 1:14
^A B f e ^A-atn B-mun f-mer e-sil 1Psalms 60:3
^A B f e g e ^A-atn B-mun f-mer e-sil g-tif e-sil 1Job 2:11
^A B f g f e ^A-atn B-mun f-mer g-tif f-mer e-sil 1Job 2:3
^A B g e ^A-atn B-mun g-tif e-sil 2...
^A B g f e ^A-atn B-mun g-tif f-mer e-sil 1Job 2:4
^A C B e f g e ^A-atn C-mph B-mun e-sil f-mer g-tif e-sil 1Job 2:13
^A C B e g e ^A-atn C-mph B-mun e-sil g-tif e-sil 1Job 1:7
^A C B f g e ^A-atn C-mph B-mun f-mer g-tif e-sil 1Job 42:11
^A C B f g f e ^A-atn C-mph B-mun f-mer g-tif f-mer e-sil 1Job 2:7
^A C B g e ^A-atn C-mph B-mun g-tif e-sil 1Job 2:2
^A C e ^A-atn C-mph e-sil 25...
^A C e B g f e ^A-atn C-mph e-sil B-mun g-tif f-mer e-sil 2...
^A C e f e ^A-atn C-mph e-sil f-mer e-sil 2...
^A C e g B e ^A-atn C-mph e-sil g-tif B-mun e-sil 11...
^A C e g e ^A-atn C-mph e-sil g-tif e-sil 1Job 2:1
^A C f e ^A-atn C-mph f-mer e-sil 1Proverbs 27:1
^A C f g B e ^A-atn C-mph f-mer g-tif B-mun e-sil 4...
^A C g B e ^A-atn C-mph g-tif B-mun e-sil 37...
^A C g e B e ^A-atn C-mph g-tif e-sil B-mun e-sil 1Psalms 127:2
^A C g f e ^A-atn C-mph g-tif f-mer e-sil 1Job 1:10
^A c B C B f d g f e ^A-atn c-dar B-mun C-mph B-mun f-mer d-gal g-tif f-mer e-sil 1Job 42:8
^A c d f g e ^A-atn c-dar d-gal f-mer g-tif e-sil 1Job 42:10
^A c d g f e ^A-atn c-dar d-gal g-tif f-mer e-sil 4...
^A d f g e ^A-atn d-gal f-mer g-tif e-sil 3...
^A e ^A-atn e-sil 617...
^A e B e ^A-atn e-sil B-mun e-sil 46...
^A e B f d g e ^A-atn e-sil B-mun f-mer d-gal g-tif e-sil 1Job 2:12
^A e C e ^A-atn e-sil C-mph e-sil 1Proverbs 19:10
^A e C e f g f e ^A-atn e-sil C-mph e-sil f-mer g-tif f-mer e-sil 1Job 42:12
^A e c d g f e ^A-atn e-sil c-dar d-gal g-tif f-mer e-sil 1Job 1:15
^A e f ^A-atn e-sil f-mer 1Proverbs 24:15
^A e f B e ^A-atn e-sil f-mer B-mun e-sil 26...
^A e f e ^A-atn e-sil f-mer e-sil 339...
^A e f e B ^A f e ^A-atn e-sil f-mer e-sil B-mun ^A-atn f-mer e-sil 1Psalms 145:13
^A e f e B e ^A-atn e-sil f-mer e-sil B-mun e-sil 1Psalms 94:9
^A e f e f e ^A-atn e-sil f-mer e-sil f-mer e-sil 3...
^A e f g e ^A-atn e-sil f-mer g-tif e-sil 1Job 1:9
^A e g B e ^A-atn e-sil g-tif B-mun e-sil 86...
^A e g e ^A-atn e-sil g-tif e-sil 1Job 12:15
^A e g e B e ^A-atn e-sil g-tif e-sil B-mun e-sil 1Psalms 83:5
^A f ^A-atn f-mer 4...
^A f B e ^A-atn f-mer B-mun e-sil 225...
^A f C e ^A-atn f-mer C-mph e-sil 4...
^A f e ^A-atn f-mer e-sil 1427...
^A f e B e ^A-atn f-mer e-sil B-mun e-sil 7...
^A f e C e ^A-atn f-mer e-sil C-mph e-sil 1Psalms 127:1
^A f e f B e ^A-atn f-mer e-sil f-mer B-mun e-sil 1Proverbs 26:2
^A f e f e ^A-atn f-mer e-sil f-mer e-sil 26...
^A f e f e f e ^A-atn f-mer e-sil f-mer e-sil f-mer e-sil 1Psalms 27:12
^A f e g B e ^A-atn f-mer e-sil g-tif B-mun e-sil 2...
^A f e g e ^A-atn f-mer e-sil g-tif e-sil 1Job 1:6
^A f g B e ^A-atn f-mer g-tif B-mun e-sil 2...
^A f g e ^A-atn f-mer g-tif e-sil 5...
^A f g f e ^A-atn f-mer g-tif f-mer e-sil 2...
^A g B ^A-atn g-tif B-mun 6...
^A g B e ^A-atn g-tif B-mun e-sil 893...
^A g e B e ^A-atn g-tif e-sil B-mun e-sil 15...
^A g f e ^A-atn g-tif f-mer e-sil 6...
^A g f e B e ^A-atn g-tif f-mer e-sil B-mun e-sil 1Psalms 52:11
^A g f e g B e ^A-atn g-tif f-mer e-sil g-tif B-mun e-sil 1Job 32:6
^A g f g B e ^A-atn g-tif f-mer g-tif B-mun e-sil 1Job 37:12

Now for the 21 books, we can do three preceding notes and find 74 approaches

f g B A f-mer g-tif B-mun A-atn 2984...
B g B A B-mun g-tif B-mun A-atn 1769...
B f g A B-mun f-mer g-tif A-atn 1381...
e f g A e-sil f-mer g-tif A-atn 1079...
d f g A d-gal f-mer g-tif A-atn 1071...
e g A e-sil g-tif A-atn 718...
e g B A e-sil g-tif B-mun A-atn 696...
d g B A d-gal g-tif B-mun A-atn 650...
e B g A e-sil B-mun g-tif A-atn 642...
e g B A e-sil g-tif B-mun A-atn 633...
C B g A C-mph B-mun g-tif A-atn 522...
C f g A C-mph f-mer g-tif A-atn 495...
C g B A C-mph g-tif B-mun A-atn 483...
e f g A e-sil f-mer g-tif A-atn 482...
f e g A f-mer e-sil g-tif A-atn 342...
f g e A f-mer g-tif e-sil A-atn 342...
c d g A c-dar d-gal g-tif A-atn 329...
g B e A g-tif B-mun e-sil A-atn 270...
e C g A e-sil C-mph g-tif A-atn 257...
B e g A B-mun e-sil g-tif A-atn 254...
f d g A f-mer d-gal g-tif A-atn 206...
B g e A B-mun g-tif e-sil A-atn 204...
e B g A e-sil B-mun g-tif A-atn 171...
C e g A C-mph e-sil g-tif A-atn 169...
B C g A B-mun C-mph g-tif A-atn 116...
e g e A e-sil g-tif e-sil A-atn 80...
e g e A e-sil g-tif e-sil A-atn 76...
f g B A f-mer g-tif B-mun A-atn 75...
f g A f-mer g-tif A-atn 69...
d g e A d-gal g-tif e-sil A-atn 68...
g e B A g-tif e-sil B-mun A-atn 51...
C B g A C-mph B-mun g-tif A-atn 47...
e A e-sil A-atn 47...
C g e A C-mph g-tif e-sil A-atn 40...
B g B A B-mun g-tif B-mun A-atn 38...
g B A g-tif B-mun A-atn 38...
e d g A e-sil d-gal g-tif A-atn 37...
d f g A d-gal f-mer g-tif A-atn 36...
B f g A B-mun f-mer g-tif A-atn 34...
B g A B-mun g-tif A-atn 30...
C g A C-mph g-tif A-atn 30...
g A g-tif A-atn 27...
f B g A f-mer B-mun g-tif A-atn 25...
d e g A d-gal e-sil g-tif A-atn 22...
e C g A e-sil C-mph g-tif A-atn 22...
C f g A C-mph f-mer g-tif A-atn 19...
C g B A C-mph g-tif B-mun A-atn 19...
B C g A B-mun C-mph g-tif A-atn 18...
C e g A C-mph e-sil g-tif A-atn 15...
B e g A B-mun e-sil g-tif A-atn 9...
c B g A c-dar B-mun g-tif A-atn 7...
C g e A C-mph g-tif e-sil A-atn 6...
c d g A c-dar d-gal g-tif A-atn 6...
f e g A f-mer e-sil g-tif A-atn 6...
B g e A B-mun g-tif e-sil A-atn 5...
f g e A f-mer g-tif e-sil A-atn 5...
g B e A g-tif B-mun e-sil A-atn 5...
f d g A f-mer d-gal g-tif A-atn 4...
B d g A B-mun d-gal g-tif A-atn 3...
f C g A f-mer C-mph g-tif A-atn 3...
B d f A B-mun d-gal f-mer A-atn 1Exodus 4:10
B g g A B-mun g-tif g-tif A-atn 1Jeremiah 31:32
C e B A C-mph e-sil B-mun A-atn 1Nehemiah 6:7
c c g A c-dar c-dar g-tif A-atn 1Deuteronomy 13:15
e C e A e-sil C-mph e-sil A-atn 12 Kings 5:27
e d g A e-sil d-gal g-tif A-atn 1Leviticus 15:8
e g f A e-sil g-tif f-mer A-atn 1Jeremiah 46:4
f B g A f-mer B-mun g-tif A-atn 1Joshua 23:16
f e B A f-mer e-sil B-mun A-atn 1Deuteronomy 24:10
f g C A f-mer g-tif C-mph A-atn 11 Kings 6:2
f g f A f-mer g-tif f-mer A-atn 1Judges 11:24
g B f A g-tif B-mun f-mer A-atn 1Deuteronomy 5:6
g e A g-tif e-sil A-atn 1Hosea 8:12
g f e A g-tif f-mer e-sil A-atn 11 Kings 8:11

For the 21 books, we can comfortably look at the 42 distinct patterns of notes that return from the atnah to the silluq where there are 1, 2 or 3 notes prior.
f g e f-mer g-tif e-sil 1574...
g e g-tif e-sil 1306...
g f e g-tif f-mer e-sil 1209...
f g f e f-mer g-tif f-mer e-sil 1010...
B g f e B-mun g-tif f-mer e-sil 758...
B g e B-mun g-tif e-sil 734...
B f g e B-mun f-mer g-tif e-sil 554...
d f g e d-gal f-mer g-tif e-sil 425...
C g f e C-mph g-tif f-mer e-sil 296...
C f g e C-mph f-mer g-tif e-sil 281...
C B g e C-mph B-mun g-tif e-sil 274...
C g e C-mph g-tif e-sil 246...
e f g e e-sil f-mer g-tif e-sil 241...
e g e e-sil g-tif e-sil 210...
e g f e e-sil g-tif f-mer e-sil 182...
c d g e c-dar d-gal g-tif e-sil 162...
f e g e f-mer e-sil g-tif e-sil 126...
B e g e B-mun e-sil g-tif e-sil 108...
C e g e C-mph e-sil g-tif e-sil 99...
f d g e f-mer d-gal g-tif e-sil 95...
e B g e e-sil B-mun g-tif e-sil 92...
B C g e B-mun C-mph g-tif e-sil 56...
e e-sil 53...
g e f e g-tif e-sil f-mer e-sil 39...
e C g e e-sil C-mph g-tif e-sil 34...
f B g e f-mer B-mun g-tif e-sil 8...
d g e d-gal g-tif e-sil 4...
d g f e d-gal g-tif f-mer e-sil 4...
B d g e B-mun d-gal g-tif e-sil 3...
B f e B-mun f-mer e-sil 2...
c B g e c-dar B-mun g-tif e-sil 2...
e g e-sil g-tif 2...
f e f-mer e-sil 2...
f g f-mer g-tif 2...
1Numbers 25:19
B d g f B-mun d-gal g-tif f-mer 1Deuteronomy 10:15
C e g f C-mph e-sil g-tif f-mer 1Deuteronomy 12:2
C g C-mph g-tif 1Leviticus 26:28
d d-gal 1Judges 13:18
e d g e e-sil d-gal g-tif e-sil 11 Chronicles 10:9
e f g f e-sil f-mer g-tif f-mer 1Deuteronomy 23:18
g f g-tif f-mer 1Hosea 11:7

When I look at even this subset of accent sequences, it is to me like trying to analyse music without being able to hear it. The note sequences that Haïk-Vantoura has mapped, on the other hand, do not need any analysis any more than one would approach Bach by enumerating the sequences of notes and intervals that he used.

I have also put my entire musicstats table into an XML form that could be imported into a database system that supports XML. These are the data that I have generated the statistics from.

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