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Wednesday 29 January 2020

The ladder, part 2/5, going up to the subdominant

Describing the ladder is long, so I have divided it into five parts. This is part two.
The introductory post did not isolate actual usage of a phrase approaching the subdominant beyond phrases of exactly 2 notes in length.

To climb fully, we need actual usage for phrases to the tonic of all lengths. Looking at them by adding a note at a time will prove to be enlightening.

There are 15 sequences of three notes ending on the atnah that are used in the Scriptures.
SequenceAccentsCount(Ref)
e g A e-sil g-tif A-atn761...
g B A g-tif B-mun A-atn633...
e B A e-sil B-mun A-atn602...
e f A e-sil f-mer A-atn480...
B g A B-mun g-tif A-atn80...
f g A f-mer g-tif A-atn69...
C B A C-mph B-mun A-atn66...
C g A C-mph g-tif A-atn30...
C f A C-mph f-mer A-atn12...
f e A f-mer e-sil A-atn9...
g f A g-tif f-mer A-atn5...
g e A g-tif e-sil A-atn3...
C e A C-mph e-sil A-atn1Proverbs 16:10
e C A e-sil C-mph A-atn1Proverbs 6:27
f B A f-mer B-mun A-atn1Psalms 88:1

If you sing this table, you are already hearing the shape of the music and its potential. Notice the ones that begin on a note other than e, the tonic. These may illustrate connections to something prior to the current verse. It may be a specific connection, like the verses in Job that continue a pairing of speeches, each one of which begins on a g. This shows that the narrator was aware of the construction of the dialogues within the cycles of speeches. Or it may be a phrase that highlights a rationale within the text, Like Psalms 51:18. Or it may show strophic aspects of the passage like the verses with a high C in Psalms 96. Or as below, it may be a part of the logic of the passage which the composer determined to highlight. There are many possible reasons why a verse (or even a book, or a chapter) does not begin on the tonic. 3,131 verses in the Scripture do not begin with the tonic.
Genesis 18:28, an accent showing a connection with the prior verse.
Here are the sequences of four notes leading to the atnah:
SequenceAccentsFreq(Ref)
e f g A e-sil f-mer g-tif A-atn1079...
e g B A e-sil g-tif B-mun A-atn1056...
e B g A e-sil B-mun g-tif A-atn965...
e C g A e-sil C-mph g-tif A-atn259...
B g B A B-mun g-tif B-mun A-atn168...
e g e A e-sil g-tif e-sil A-atn86...
f g B A f-mer g-tif B-mun A-atn80...
C B g A C-mph B-mun g-tif A-atn73...
e f e A e-sil f-mer e-sil A-atn66...
e C B A e-sil C-mph B-mun A-atn50...
d f g A d-gal f-mer g-tif A-atn36...
B f g A B-mun f-mer g-tif A-atn34...
C g B A C-mph g-tif B-mun A-atn28...
e C f A e-sil C-mph f-mer A-atn24...
g B e A g-tif B-mun e-sil A-atn24...
g e B A g-tif e-sil B-mun A-atn24...
B g e A B-mun g-tif e-sil A-atn19...
C f g A C-mph f-mer g-tif A-atn19...
B C g A B-mun C-mph g-tif A-atn18...
e g f A e-sil g-tif f-mer A-atn17...
C e g A C-mph e-sil g-tif A-atn15...
C e f A C-mph e-sil f-mer A-atn12...
B e g A B-mun e-sil g-tif A-atn10...
e f B A e-sil f-mer B-mun A-atn10...
e d f A e-sil d-gal f-mer A-atn9...
f e f A f-mer e-sil f-mer A-atn8...
e B e A e-sil B-mun e-sil A-atn7...
C g e A C-mph g-tif e-sil A-atn6...
c d g A c-dar d-gal g-tif A-atn6...
f e g A f-mer e-sil g-tif A-atn6...
f g e A f-mer g-tif e-sil A-atn5...
C e B A C-mph e-sil B-mun A-atn4...
f B g A f-mer B-mun g-tif A-atn4...
f d g A f-mer d-gal g-tif A-atn4...
B g f A B-mun g-tif f-mer A-atn2...
C d f A C-mph d-gal f-mer A-atn2...
B e B A B-mun e-sil B-mun A-atn1Proverbs 13:8
C B e A C-mph B-mun e-sil A-atn1Proverbs 1:32
C B f A C-mph B-mun f-mer A-atn1Psalms 32:4
C C B A C-mph C-mph B-mun A-atn1Psalms 49:11
C d B A C-mph d-gal B-mun A-atn1Psalms 11:2
C f B A C-mph f-mer B-mun A-atn1Proverbs 3:12
C g f A C-mph g-tif f-mer A-atn1Psalms 44:24
e C e A e-sil C-mph e-sil A-atn12 Kings 5:27
e d B A e-sil d-gal B-mun A-atn1Psalms 13:3
e d g A e-sil d-gal g-tif A-atn1Leviticus 15:8
f C B A f-mer C-mph B-mun A-atn1Psalms 96:4
f d f A f-mer d-gal f-mer A-atn1Psalms 140:12
g e f A g-tif e-sil f-mer A-atn1Psalms 116:1
g f B A g-tif f-mer B-mun A-atn1Psalms 139:7

We will find more complexity in the music of the first section of the verses.
  • Already there are 52 rows for just 4 notes (including the A). 
  • There are 111 sequences for 5 notes from start to the mid-point rest of a verse, 
  • 213 for a 6 note sequence, 
  • 315 for a 7 note sequence, 
  • the count peaks at an 8 note sequence at 358, 
  • then decreases for a 9 note sequence to 318, 
  • 215 for a 10 note sequence, 
  • 105 for an 11 note sequence, 
  • 33 for a 12 note sequence, 
  • 22 for a 13 note sequence, 
  • and an additional 16 for longer sequences.
Imagine the graph: 5 with one note preceding the atnah, 15 with 2 etc. It is more asymptotic to the right, but I have truncated it by collecting all 14 note and longer sequences.

Distribution of sequences from 1 to 19 notes to the atnah according to the key of Haïk-Vantoura
Here are the longest first-'halves'. I will extend the analysis of longer sequences in part 5 of this series. 
SequenceAccentsFreq(Ref)
e B C e B C B C e B g B e A e-sil B-mun C-mph e-sil B-mun C-mph B-mun C-mph e-sil B-mun g-tif B-mun e-sil A-atn1Ezekiel 33:12
e B e B C B C B f d f e g A e-sil B-mun e-sil B-mun C-mph B-mun C-mph B-mun f-mer d-gal f-mer e-sil g-tif A-atn1Jeremiah 36:32
e B e B C e B d e f e g B A e-sil B-mun e-sil B-mun C-mph e-sil B-mun d-gal e-sil f-mer e-sil g-tif B-mun A-atn1Joshua 22:31
e B e B c B e C e B f g B A e-sil B-mun e-sil B-mun c-dar B-mun e-sil C-mph e-sil B-mun f-mer g-tif B-mun A-atn1Ezekiel 13:9
e B e B d e c B d f e g B A e-sil B-mun e-sil B-mun d-gal e-sil c-dar B-mun d-gal f-mer e-sil g-tif B-mun A-atn12 Samuel 4:2
e B e B e B e B C B e B g B A e-sil B-mun e-sil B-mun e-sil B-mun e-sil B-mun C-mph B-mun e-sil B-mun g-tif B-mun A-atn12 Chronicles 13:11
e B e B e B e B C e f g B A e-sil B-mun e-sil B-mun e-sil B-mun e-sil B-mun C-mph e-sil f-mer g-tif B-mun A-atn1Ezekiel 46:12
e B e B e B e B e B C f g A e-sil B-mun e-sil B-mun e-sil B-mun e-sil B-mun e-sil B-mun C-mph f-mer g-tif A-atn1Esther 8:9
e B e B e B e B e B e B e c d f g A e-sil B-mun e-sil B-mun e-sil B-mun e-sil B-mun e-sil B-mun e-sil B-mun e-sil c-dar d-gal f-mer g-tif A-atn1Daniel 5:23
e B e B e B e B e C B g B A e-sil B-mun e-sil B-mun e-sil B-mun e-sil B-mun e-sil C-mph B-mun g-tif B-mun A-atn12 Chronicles 18:7
e B e B e B e C e f d f g A e-sil B-mun e-sil B-mun e-sil B-mun e-sil C-mph e-sil f-mer d-gal f-mer g-tif A-atn1Esther 4:11
e B e B e c B C B f d g B A e-sil B-mun e-sil B-mun e-sil c-dar B-mun C-mph B-mun f-mer d-gal g-tif B-mun A-atn12 Kings 16:15
e B e f B e B e c d f g B A e-sil B-mun e-sil f-mer B-mun e-sil B-mun e-sil c-dar d-gal f-mer g-tif B-mun A-atn1Deuteronomy 13:6
e c B e B c B C c d e f g A e-sil c-dar B-mun e-sil B-mun c-dar B-mun C-mph c-dar d-gal e-sil f-mer g-tif A-atn1Jeremiah 40:4

Next installment coming soon: Going down from the subdominant

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