Saturday 1 February 2020

The ladder, part 5/5, further subdivisions of long verses

Describing the ladder is long, so I have divided it into five parts.
In the earlier posts we traced the broad shape of verses and their major internal cadences. In this post, we will look at ornaments that allow for pauses in long vocal lines, phrases that are common to many of the musical lines, and at intervals as descriptive of them.

Attitudes against the Haïk-Vantoura solution
Once one is given the mapping of accents below the text to notes, one must then consider beauty, the ancient knowledge of music, and tonal relationships, the coding efficiency of designers of a sol-fa type of notation, among other things.

But some people have said, You are only imposing your musical knowledge onto the graphemes that we see in the text.

The trouble is, I could not imagine for a moment that such an imposition would produce anything except confusion. The fact is that it removes confusion, and produces
  • clarity, 
  • tone of voice, 
  • meaning (if you like that sort of thing), 
  • character in the text, and
  • connections across verses. 
It is, in a word, spell-binding. It works so well that it must be the right step towards a solution. Can you imagine the alien playing the golden record and hearing the Goldberg variations for the first time? Would that ear hear punctuation? Would that eye see only sequences? Would they not also hear the implicit vibration of a moving tonal centre?

And others say (if the cantor is good) that beauty is there already, and skill, and knowledge. And what is efficiency when it comes to music? Yes there is beauty in some canting traditions when well-sung, because a well-produced voice is beautiful for its own reason. Imagine the beauty of the voice of God. (To those who disdain from putting God in a sentence, I apologize.)

But hang on, musical notation must be both efficient and carefully designed. It is futile to do with many symbols what can be done with fewer. And the corollary, an explanation of a system that uses more of the information implicit in the system is to be preferred over one that uses less. Thinking only in sequences does not use some information that is evident on the surface of the text. And the information, the placement of the accents below the text, fits the proposed key perfectly and turns the lock and opens the door. I do not think our ancestors were any poorer at design than we are.

Pauses in a long line
So how did they manage long lines where they knew they were heading toward a mid-point of the verse? There are several possible accents which may correspond sometimes with a break in the vocal line that is mediated by the words. Any of the mordents (either zaqen or revia), turns or horns, and not impossibly, even just a change in reciting note. But notice I have never had to say that this or that accent always demands a pause. Sometimes they may. And this is how it is with attempts to define hierarchy and disjunction. The traditional rules just do not work consistently. The deciphering key does not need such rules. The music and sense, the vocal line of one who recites the word of God, all these depend on the underlying text and the spirit who breathes it to the cantor and listener. It is not a matter of rules.

Common phrases
It is fair to ask, however, if there are common phrases in the text. The endless variety is hard to search, but there are some sequences in the first half of verses that are relatively common. I picked Daniel 5:23 almost at random.
Daniel 5:23 
And against the Lord of the heavens you have exalted yourself, (paz) and the vessels (pas) of his house (ger) they have brought before you, (rev) and you (pas) and your overlords, (ger) your consorts and your choristers, (zar) red wine (zar) have imbibed from them, (seg) and the gods of silver and gold, (t-g) brass, (pas) iron, (ger) wood and stone, (pas) that (t-g) perceive not and hear not and know not, you have commended,
and the God (tar) in whose hand is your breath, and whose are all your paths, you have not honoured.
The note sequence above, ignoring ornaments, is: e B e B e B e B e B e B e c d f g ^A e f d f g f e.

With ornaments it is:
e B e B paz,e pas,e ger,B e rev,pas,ger,e B zar,zar,B seg,e B e t-g,pas,ger,B rev,t-g,e c d f g# ^A
e tar,e f d f g# f e.

The string, like all complex sequences, is difficult to decompose. (It also may include metheg since my abbreviations do not eliminate these spurious returns to the tonic.)

The final approach to the atnah from c: c d f g A is quite common. The table shows this and the counts of similar phrases.

c d f g B A
d f g B A
f g B A
c d f g A
d f g A
The 21 books
271
950
3,059
228
1,120
The 3 books
1 (Job prose)
32
87
2 (Job prose)
1

Consider all the verses of Daniel containing c d f g, a rising phrase which in the default mode includes a diminished triad (tuning and mode are other questions entirely). Every one of these is a unique sequence. Every accent plays its own role. They are similar phrases but although the last two omit the B, it was a musical decision. It is not a rule that sometimes the first accent in a pair is omitted. And there are no cases of one accent replacing another. Idiosyncratic rules such as these play no part in the design of the notation. They would all be bad design decisions for a music notation. Why should the ancients do a bad design?

SequenceAccentsFreq(Ref)
C e B c d f g ^A f e g f e C-mph e-sil B-mun c-dar d-gal f-mer g-tif ^A-atn f-mer e-sil g-tif f-mer e-sil1Daniel 6:6
e B C B c d g B ^A c d f g e e-sil B-mun C-mph B-mun c-dar d-gal g-tif B-mun ^A-atn c-dar d-gal f-mer g-tif e-sil1Daniel 11:24
e B c d f g B ^A B g f e e-sil B-mun c-dar d-gal f-mer g-tif B-mun ^A-atn B-mun g-tif f-mer e-sil1Daniel 2:47
e B c d f g B ^A C e c B e g f e e-sil B-mun c-dar d-gal f-mer g-tif B-mun ^A-atn C-mph e-sil c-dar B-mun e-sil g-tif f-mer e-sil1Daniel 5:11
e B c d f g ^A C B f g f e e-sil B-mun c-dar d-gal f-mer g-tif ^A-atn C-mph B-mun f-mer g-tif f-mer e-sil1Daniel 11:17
e B c e d c d f g B ^A g e e-sil B-mun c-dar e-sil d-gal c-dar d-gal f-mer g-tif B-mun ^A-atn g-tif e-sil1Daniel 10:12
e B d f g ^A c d f g f e e-sil B-mun d-gal f-mer g-tif ^A-atn c-dar d-gal f-mer g-tif f-mer e-sil1Daniel 5:14
e B e B e B e B e B e B e c d f g ^A e f d f g f e 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 e-sil f-mer d-gal f-mer g-tif f-mer e-sil1Daniel 5:23
e B e C B f g B ^A B e C e B c d f g f e e-sil B-mun e-sil C-mph B-mun f-mer g-tif B-mun ^A-atn B-mun e-sil C-mph e-sil B-mun c-dar d-gal f-mer g-tif f-mer e-sil1Daniel 3:12
e B e c d f g B ^A f g f e e-sil B-mun e-sil c-dar d-gal f-mer g-tif B-mun ^A-atn f-mer g-tif f-mer e-sil1Daniel 12:4
e B f g B ^A B c d f g f e e-sil B-mun f-mer g-tif B-mun ^A-atn B-mun c-dar d-gal f-mer g-tif f-mer e-sil1Daniel 6:9
e B f g ^A C e B e c d f g f e e-sil B-mun f-mer g-tif ^A-atn C-mph e-sil B-mun e-sil c-dar d-gal f-mer g-tif f-mer e-sil1Daniel 3:18
e B g B ^A c d f g e e-sil B-mun g-tif B-mun ^A-atn c-dar d-gal f-mer g-tif e-sil1Daniel 1:3
e B g e ^A c d f g e e-sil B-mun g-tif e-sil ^A-atn c-dar d-gal f-mer g-tif e-sil1Daniel 11:33
e C e B f g B ^A e C e c d f g f e e-sil C-mph e-sil B-mun f-mer g-tif B-mun ^A-atn e-sil C-mph e-sil c-dar d-gal f-mer g-tif f-mer e-sil1Daniel 3:14
e c B c d f g ^A e B f g e e-sil c-dar B-mun c-dar d-gal f-mer g-tif ^A-atn e-sil B-mun f-mer g-tif e-sil1Daniel 6:15
e c d f g B ^A B e B f g e e-sil c-dar d-gal f-mer g-tif B-mun ^A-atn B-mun e-sil B-mun f-mer g-tif e-sil1Daniel 6:5
e c d f g B ^A B e g f e e-sil c-dar d-gal f-mer g-tif B-mun ^A-atn B-mun e-sil g-tif f-mer e-sil1Daniel 8:26
e c d f g B ^A C f g f e e-sil c-dar d-gal f-mer g-tif B-mun ^A-atn C-mph f-mer g-tif f-mer e-sil1Daniel 11:20
e c d f g B ^A e C e d f g f e e-sil c-dar d-gal f-mer g-tif B-mun ^A-atn e-sil C-mph e-sil d-gal f-mer g-tif f-mer e-sil1Daniel 10:19
e c d f g ^A e B c B e g e f e e-sil c-dar d-gal f-mer g-tif ^A-atn e-sil B-mun c-dar B-mun e-sil g-tif e-sil f-mer e-sil1Daniel 2:27
e c d f g ^A e B e B g f e e-sil c-dar d-gal f-mer g-tif ^A-atn e-sil B-mun e-sil B-mun g-tif f-mer e-sil1Daniel 1:7
e c d f g e e-sil c-dar d-gal f-mer g-tif e-sil1Daniel 10:18
e f g ^A c d f g f e e-sil f-mer g-tif ^A-atn c-dar d-gal f-mer g-tif f-mer e-sil1Daniel 8:22
e f g e ^A c d f g f e e-sil f-mer g-tif e-sil ^A-atn c-dar d-gal f-mer g-tif f-mer e-sil1Daniel 4:26
e g ^A c d f g f e e-sil g-tif ^A-atn c-dar d-gal f-mer g-tif f-mer e-sil1Daniel 7:12
e g ^A e c d f g f e e-sil g-tif ^A-atn e-sil c-dar d-gal f-mer g-tif f-mer e-sil1Daniel 5:4
f B c B e B g ^A c d f g f e f-mer B-mun c-dar B-mun e-sil B-mun g-tif ^A-atn c-dar d-gal f-mer g-tif f-mer e-sil1Daniel 6:13

This sequence containing the c could not be in the poetry sections of the three books, but d f g is used in the three books. Here are the distinct melodies for all the Psalms containing that sequence.

SequenceAccentsFreq(Ref)
e d f g B ^A g B e e-sil d-gal f-mer g-tif B-mun ^A-atn g-tif B-mun e-sil3...
C d f g B ^A g B e C-mph d-gal f-mer g-tif B-mun ^A-atn g-tif B-mun e-sil2...
e C d f g f e e-sil C-mph d-gal f-mer g-tif f-mer e-sil2...
e d f g B ^A B e e-sil d-gal f-mer g-tif B-mun ^A-atn B-mun e-sil2...
e d f g B ^A e e-sil d-gal f-mer g-tif B-mun ^A-atn e-sil2...
e d f g B ^A f e e-sil d-gal f-mer g-tif B-mun ^A-atn f-mer e-sil2...
C B d f g B ^A g B e C-mph B-mun d-gal f-mer g-tif B-mun ^A-atn g-tif B-mun e-sil1Psalms 78:20
C d d f g B ^A f e C-mph d-gal d-gal f-mer g-tif B-mun ^A-atn f-mer e-sil1Psalms 126:2
C d e C f d f g B ^A e C-mph d-gal e-sil C-mph f-mer d-gal f-mer g-tif B-mun ^A-atn e-sil1Psalms 75:9
C d f g B ^A e C-mph d-gal f-mer g-tif B-mun ^A-atn e-sil1Psalms 27:5
C d f g B ^A f e C-mph d-gal f-mer g-tif B-mun ^A-atn f-mer e-sil1Psalms 37:7
C d f g e B ^A e C-mph d-gal f-mer g-tif e-sil B-mun ^A-atn e-sil1Psalms 56:14
C d f g f e C-mph d-gal f-mer g-tif f-mer e-sil1Psalms 30:6
C e B d f g B ^A e C-mph e-sil B-mun d-gal f-mer g-tif B-mun ^A-atn e-sil1Psalms 37:14
e C d f g B ^A C e e-sil C-mph d-gal f-mer g-tif B-mun ^A-atn C-mph e-sil1Psalms 10:14
e C d f g B ^A g B e e-sil C-mph d-gal f-mer g-tif B-mun ^A-atn g-tif B-mun e-sil1Psalms 78:8
e C e B d f g B ^A e e-sil C-mph e-sil B-mun d-gal f-mer g-tif B-mun ^A-atn e-sil1Psalms 65:5
e C e d f g B ^A e e-sil C-mph e-sil d-gal f-mer g-tif B-mun ^A-atn e-sil1Psalms 101:6
e C f d f g B ^A e e-sil C-mph f-mer d-gal f-mer g-tif B-mun ^A-atn e-sil1Psalms 128:3
e C f d f g B ^A e f e e-sil C-mph f-mer d-gal f-mer g-tif B-mun ^A-atn e-sil f-mer e-sil1Psalms 21:10
e C f d f g f e e-sil C-mph f-mer d-gal f-mer g-tif f-mer e-sil1Psalms 40:3
e d f g B ^A e f e e-sil d-gal f-mer g-tif B-mun ^A-atn e-sil f-mer e-sil1Psalms 11:5
e d f g B ^A f B e e-sil d-gal f-mer g-tif B-mun ^A-atn f-mer B-mun e-sil1Psalms 63:12
e d f g f B e e-sil d-gal f-mer g-tif f-mer B-mun e-sil1Psalms 31:6
e f d f g B ^A B e e-sil f-mer d-gal f-mer g-tif B-mun ^A-atn B-mun e-sil1Psalms 48:3
e f d f g B ^A f C e e-sil f-mer d-gal f-mer g-tif B-mun ^A-atn f-mer C-mph e-sil1Psalms 99:4
Psalms 40:3 expresses what the Lord has done for me with the music of this deciphering key.
Psalms 40:3
He brought me up from a noisy pit, from wine-soaked muck, [ole veyored cadence on the f#]
and placed my feet on a cliff, establishing my steps.

Intervals
Music is by its nature not entirely subject to sequential rules, though some sequences are common: ascending by step, by thirds, fourths and fifths, or even sixths and sevenths, or octaves and descending likewise including octaves.

Intervals are essentially two note sequences and they will test the subdivisions of the longer passages from a musical point of view. The frequency of intervals in  adjacent reciting notes subdivided by interval type is in the following tables.

For octaves and sevenths there are 6 possibilities, one of which never occurs.
c to C        
C to c
c to B
B to c
d to C
C to d
0
114
259
844
18
254
C to c is a striking interval. Singers will remember the bass line from the Sanctus of the B Minor Mass. How surprising it was to find this interval on the Holy of Isaiah 6.

For fourths there are 10 possibilities. I have subdivided this by book just for example. The others could be as well but it would make this post too long! It does point out the location of some rare uses.
c to f
f to c
d to g
g to d
e to A
A to e
f to B
B to f
g to C
C to g
Book
0
0
218
0
76
189
14
419
0
125
GENESIS
0
0
192
0
45
128
20
288
0
99
EXODUS
0
1
162
0
39
72
15
219
0
73
LEVITICUS
0
0
211
0
45
164
19
263
0
95
NUMBERS
0
0
140
0
30
132
33
321
0
80
DEUTERONOMY
0
0
81
0
51
83
13
150
0
67
JOSHUA
0
0
90
0
39
76
13
205
0
50
JUDGES
0
0
135
0
29
115
25
272
0
87
1 SAMUEL
0
2
130
0
42
69
9
210
0
67
2 SAMUEL
0
0
120
0
44
86
11
245
1
80
1 KINGS
0
0
101
0
67
84
19
226
0
77
2 KINGS
0
0
139
0
87
139
17
345
0
203
ISAIAH
1
1
177
0
114
206
16
419
1
172
JEREMIAH
0
0
154
0
131
127
18
405
0
143
EZEKIEL
0
0
17
0
27
21
5
40
0
38
HOSEA
0
0
6
0
11
14
1
15
0
9
JOEL
0
0
12
0
12
21
2
29
0
27
AMOS
0
0
2
0
1
5
0
7
0
0
OBADIAH
0
0
8
0
9
6
2
13
0
6
JONAH
0
0
10
0
11
15
2
28
0
10
MICAH
0
0
7
0
6
5
0
11
0
5
NAHUM
0
0
4
0
2
4
0
12
0
13
HABAKKUK
0
0
8
0
4
8
0
14
0
7
ZEPHANIAH
0
0
11
0
2
5
1
11
0
4
HAGGAI
0
1
20
0
32
20
4
67
0
16
ZECHARIAH
0
0
5
0
10
9
0
14
0
15
MALACHI
0
0
2
0
109
718
249
6
0
78
PSALMS
0
0
0
0
56
180
84
1
3
7
PROVERBS
0
0
13
0
56
229
76
12
0
25
JOB
0
0
4
0
4
10
2
18
0
26
SONG
0
1
12
0
4
5
2
29
0
12
RUTH
0
0
21
0
0
11
0
24
0
41
LAMENTATIONS
0
0
20
0
11
25
5
72
0
11
QOHELET
0
1
23
0
15
14
2
51
0
20
ESTHER
0
0
32
0
26
49
4
115
0
30
DANIEL
0
0
23
0
21
27
6
83
0
21
EZRA
0
0
37
0
24
50
8
93
0
27
NEHEMIAH
0
0
105
0
40
73
8
179
0
75
1 CHRONICLES
0
0
127
0
40
106
14
218
0
70
2 CHRONICLES

For thirds, there are 12 possibilities:
 Interval
c-e
d-f
e-g
f-A
g-B
A-C
C-A
B-g
A-f
g-e
f-d
e-c
The 3
0
191
657
704
2,978
90
6
1,368
1,709
189
46
8
The 21
341
4,866
4,973
5
7,671
3,228
1
6,814
3,322
11,418
1,900
1,371
Total
341
5,057
5,630
709
10,649
3,318
7
8,182
5,031
11,607
1,946
1,379

For seconds, (ascending or descending by step) there are 14 possibilities, all of which are used.
c to d
d to c
d to e
e to d
e to f
f to e
f to g
g to f
g to A
A to g
A to B
B to A
B to C
C to B
2669
8
402
1332
6866
11850
17137
8269
9256
3479
4759
10221
3546
6326

It is interesting to compare thirds with two consecutive seconds by step. The following table shows that every possible group of consecutive seconds is used in the music.
c d e
d e f
e f g
 f g A
 g A B
 A B C
 C B A
  B A g
   A g f
  g f e
   f e d
   e d c
109
293
4,189
4,683
2,246
775
137
1,723
1,219
8,203
11
4

For triads and fifths, there are 8 possibilities.
Triad
c e g
g e c
d f A
A f d
e g B
B g e
f A C
C A f
freq
0
0
38
461
1922
1845
17
4
Fifth
c to g
g to c
d to A
A to d
e to B
B to e
f to C
C to f
freq
1
0
0
820
11263
5987
88
1774
Some intervals are not used.

 Concluding notes
I have not come to the end of my explorations, but more to the mid-point. Now, however, I can return to the individual pieces of music and explore the land, rather than do hard labour in the pit.

Again and again, in every part of the Scripture I work with, there are obvious aspects in the song about the text that are made by the music. Therefore since the music and accents are isomorphic to each other, these connections are made by the accents, but they cannot be heard without singing.

So I must remain with the conclusion that Suzanne Haïk-Vantoura has determined, for these reasons:
  • efficiency of the notation, 
  • clarity of recitation, 
  • preservation of tone of voice, 
  • highlighting of structure and allusion, 
  • and beauty. 
I know when I decipher these texts musically, that I am communicating via sound with an ancient musical and knowledgeable mind.

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