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.

• Introduction, 
• Going up to the subdominant, 
• Going down from the subdominant, 
• Verses without a rest on the subdominant,
• and further subdivisions for long verses. 

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.

Sequence	Accents	Count	(Ref)
e g A	e-sil g-tif A-atn	761	...
g B A	g-tif B-mun A-atn	633	...
e B A	e-sil B-mun A-atn	602	...
e f A	e-sil f-mer A-atn	480	...
B g A	B-mun g-tif A-atn	80	...
f g A	f-mer g-tif A-atn	69	...
C B A	C-mph B-mun A-atn	66	...
C g A	C-mph g-tif A-atn	30	...
C f A	C-mph f-mer A-atn	12	...
f e A	f-mer e-sil A-atn	9	...
g f A	g-tif f-mer A-atn	5	...
g e A	g-tif e-sil A-atn	3	...
C e A	C-mph e-sil A-atn	1	Proverbs 16:10
e C A	e-sil C-mph A-atn	1	Proverbs 6:27
f B A	f-mer B-mun A-atn	1	Psalms 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:

Sequence	Accents	Freq	(Ref)
e f g A	e-sil f-mer g-tif A-atn	1079	...
e g B A	e-sil g-tif B-mun A-atn	1056	...
e B g A	e-sil B-mun g-tif A-atn	965	...
e C g A	e-sil C-mph g-tif A-atn	259	...
B g B A	B-mun g-tif B-mun A-atn	168	...
e g e A	e-sil g-tif e-sil A-atn	86	...
f g B A	f-mer g-tif B-mun A-atn	80	...
C B g A	C-mph B-mun g-tif A-atn	73	...
e f e A	e-sil f-mer e-sil A-atn	66	...
e C B A	e-sil C-mph B-mun A-atn	50	...
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	...
C g B A	C-mph g-tif B-mun A-atn	28	...
e C f A	e-sil C-mph f-mer A-atn	24	...
g B e A	g-tif B-mun e-sil A-atn	24	...
g e B A	g-tif e-sil B-mun A-atn	24	...
B g e A	B-mun g-tif e-sil A-atn	19	...
C f g A	C-mph f-mer g-tif A-atn	19	...
B C g A	B-mun C-mph g-tif A-atn	18	...
e g f A	e-sil g-tif f-mer A-atn	17	...
C e g A	C-mph e-sil g-tif A-atn	15	...
C e f A	C-mph e-sil f-mer A-atn	12	...
B e g A	B-mun e-sil g-tif A-atn	10	...
e f B A	e-sil f-mer B-mun A-atn	10	...
e d f A	e-sil d-gal f-mer A-atn	9	...
f e f A	f-mer e-sil f-mer A-atn	8	...
e B e A	e-sil B-mun e-sil 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	...
f g e A	f-mer g-tif e-sil A-atn	5	...
C e B A	C-mph e-sil B-mun A-atn	4	...
f B g A	f-mer B-mun g-tif A-atn	4	...
f d g A	f-mer d-gal g-tif A-atn	4	...
B g f A	B-mun g-tif f-mer A-atn	2	...
C d f A	C-mph d-gal f-mer A-atn	2	...
B e B A	B-mun e-sil B-mun A-atn	1	Proverbs 13:8
C B e A	C-mph B-mun e-sil A-atn	1	Proverbs 1:32
C B f A	C-mph B-mun f-mer A-atn	1	Psalms 32:4
C C B A	C-mph C-mph B-mun A-atn	1	Psalms 49:11
C d B A	C-mph d-gal B-mun A-atn	1	Psalms 11:2
C f B A	C-mph f-mer B-mun A-atn	1	Proverbs 3:12
C g f A	C-mph g-tif f-mer A-atn	1	Psalms 44:24
e C e A	e-sil C-mph e-sil A-atn	1	2 Kings 5:27
e d B A	e-sil d-gal B-mun A-atn	1	Psalms 13:3
e d g A	e-sil d-gal g-tif A-atn	1	Leviticus 15:8
f C B A	f-mer C-mph B-mun A-atn	1	Psalms 96:4
f d f A	f-mer d-gal f-mer A-atn	1	Psalms 140:12
g e f A	g-tif e-sil f-mer A-atn	1	Psalms 116:1
g f B A	g-tif f-mer B-mun A-atn	1	Psalms 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. 

Sequence	Accents	Freq	(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-atn	1	Ezekiel 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-atn	1	Jeremiah 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-atn	1	Joshua 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-atn	1	Ezekiel 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-atn	1	2 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-atn	1	2 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-atn	1	Ezekiel 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-atn	1	Esther 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-atn	1	Daniel 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-atn	1	2 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-atn	1	Esther 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-atn	1	2 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-atn	1	Deuteronomy 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-atn	1	Jeremiah 40:4

Next installment coming soon: Going down from the subdominant