Sunday, September 13, 2015

Returning to the tonic, an analysis

Here is an analysis of the ways in which the accents in the Hebrew text of the Psalms manage the first and second parts of each verse, given that the verse is divided into two parts by a rest on the subdominant A.

It is to be noted that although every verse does not have a rest on the subdominant (atnach) or even a secondary cadence on the supertonic (ole-veyored), every verse returns to the tonic at the end of the verse. Some verses in the text at tanach.us have no final silluq, but this sign is a redundant marker if you have already distinguished the verses. In what follows, I have not considered the secondary cadence here which may also occur. In particular this will exclude the 45 verses where the secondary cadence (ole veyored) is the only inner-verse cadence. I have reexecuted this query after discovering that I had left out the galgal.

We could count and list them all - the shape of the notes that get the reader/singer to the rest on A and returning from there to the tonic E. But there are 836 combinations (just in the 2335 of a total 2527 verses of the Psalms which have a rest on the A) - too many - so here's a limited list of the most common. There are also 236 unique combinations - i.e. the shape of the line in the psalms considering only changes in the reciting note, is unique in the Psalter.  You can see why explaining this music in terms of diacritics is a problem. Who would ever understand it? I assure you - no human being.

But - sing these to yourself to la-la-la or play them on a piano (free rhythm). Use, for example, the key of E minor. You will quickly see how musical all these sequences are. I am surprised at the result.

This is what Haik-Vantoura did in her confinement. She studied the statistics related to the usage of the accents and decided on the basis of their usage what the best mapping of accents to music would be. A musician would expect to come to a rest and a musician would expect to return to the tonic - both in musical ways. Hear for yourself. Which notes might you change related to the use of signs under the letters of the Hebrew? It's quite a job that she did, is it not?

Approach
Rest on A
Number
of times
Return
to e
Number of times
for this approach
e B B ^A310A f# e79
e B B ^A310A g B e57
e B B ^A310A e43
e B B ^A310A B e34
e B B ^A310A e f# e27
e B B ^A310A f# f# e15
e B B ^A310A e e12
e B B ^A310A e g B e9
e B B ^A310A f# B e8
e B B ^A310A f# e e6
e B B ^A310A e B e5
e B B ^A310A g e B e2
e B B ^A310A g B2
e B B ^A310A f#1
e B B ^A310A B e e1
e B B ^A310A e e g B e1
e B B ^A310A f# e f# e1
e B B ^A310A e B e e1
e B B ^A310A f# e f# e e1
e B B ^A310A e f# B e1
e B B ^A310A f# f# f# e1
e B B ^A310A C g B e1
e B B ^A310A C e1
e B B ^A310A e e e1
g B ^A264A f# e75
g B ^A264A g B e53
g B ^A264A e40
g B ^A264A B e20
g B ^A264A e f# e16
g B ^A264A e e14
g B ^A264A f# f# e8
g B ^A264A f# B e7
g B ^A264A f# e e5
g B ^A264A g e B e5
g B ^A264A e g B e4
g B ^A264A B e e4
g B ^A264A e f# B e3
g B ^A264A e f# f# e2
g B ^A264A e B e2
g B ^A264A g B e e2
g B ^A264A e e e1
g B ^A264A f# f# B e1
g B ^A264A B f# e1
g B ^A264A f# e f# e1
e f# ^A247A f# e66
e f# ^A247A e37
e f# ^A247A g B e36
e f# ^A247A e f# e21
e f# ^A247A f# B e15
e f# ^A247A f# f# e12
e f# ^A247A B e12
e f# ^A247A e e7
e f# ^A247A C e6
e f# ^A247A e g B e5
e f# ^A247A f# e e3
e f# ^A247A e e f# e3
e f# ^A247A e B e3
e f# ^A247A C g B e3
e f# ^A247A f# e f# e3
e f# ^A247A f# f# B e2
e f# ^A247A e f# B e2
e f# ^A247A e e e2
e f# ^A247A g f# f# e1
e f# ^A247A g B1
e f# ^A247A f# g B e1
e f# ^A247A e f# e f# e1
e f# ^A247A e f# f# e1
e f# ^A247A e g B e e1
e f# ^A247A C e f# e1
e f# ^A247A g B e e1
e f# ^A247A B e e1
e B g B ^A199A f# e41
e B g B ^A199A g B e35
e B g B ^A199A f# f# e31
e B g B ^A199A e f# e15
e B g B ^A199A B e15
e B g B ^A199A f# B e14
e B g B ^A199A e e8
e B g B ^A199A e8
e B g B ^A199A f# e e5
e B g B ^A199A f# e f# e3
e B g B ^A199A e g B e3
e B g B ^A199A e e e3
e B g B ^A199A f# f# f# e3
e B g B ^A199A e f# f# e2
e B g B ^A199A C e2
e B g B ^A199A C g B e2
e B g B ^A199A e e f# e1
e B g B ^A199A f# g B e1
e B g B ^A199A f# f#1
e B g B ^A199A f# B e e1
e B g B ^A199A g f# e B e1
e B g B ^A199A B e e1
e B g B ^A199A f# e g B e1
e B g B ^A199A e f# B e1
e B g B ^A199A C e g B e1
e B g ^A177A f# e46
e B g ^A177A e33
e B g ^A177A g B e25
e B g ^A177A B e11
e B g ^A177A e e10
e B g ^A177A e f# e10
e B g ^A177A f# f# e7
e B g ^A177A e g B e7
e B g ^A177A f# B e5
e B g ^A177A f# e e4
e B g ^A177A e f# f# e3
e B g ^A177A C e g B e3
e B g ^A177A g e B e2
e B g ^A177A e B e2
e B g ^A177A e f# e e1
e B g ^A177A 1
e B g ^A177A g B e e1
e B g ^A177A C e1
e B g ^A177A C g B e1
e B g ^A177A f# B e e1
e B g ^A177A f# e f# e1
e B g ^A177A f# e e e1
e B g ^A177A f# f# e B e1
e g B ^A175A f# e47
e g B ^A175A g B e43
e g B ^A175A e19
e g B ^A175A f# f# e11
e g B ^A175A e f# e11
e g B ^A175A B e9
e g B ^A175A e e7
e g B ^A175A f# B e6
e g B ^A175A f# e e4
e g B ^A175A C e3
e g B ^A175A f# e f# e2
e g B ^A175A g B2
e g B ^A175A f# f# f# e1
e g B ^A175A C f# g B e1
e g B ^A175A e f# e e1
e g B ^A175A C g B e1
e g B ^A175A B e e1
e g B ^A175A f# e f# e f# e1
e g B ^A175A e g e B e1
e g B ^A175A e g B e1
e g B ^A175A e B e1
e g B ^A175A g e B e1
e g B ^A175A C e g B e1
B g B ^A38A g B e11
B g B ^A38A f# f# e8
B g B ^A38A f# e8
B g B ^A38A e6
B g B ^A38A e f# f# e1
B g B ^A38A f# e f# e1
B g B ^A38A f# f# e e1
B g B ^A38A e f# B e1
B g B ^A38A B e1
e f# e ^A36A f# e9
e f# e ^A36A g B e8
e f# e ^A36A e f# e5
e f# e ^A36A B e3
e f# e ^A36A e3
e f# e ^A36A C f# g B e2
e f# e ^A36A C g B e2
e f# e ^A36A f# f# e1
e f# e ^A36A e f# e B ^A //f# e1
e f# e ^A36A f# B e1
e f# e ^A36A e g B e1
C B B ^A31A g B e7
C B B ^A31A B e6
C B B ^A31A f# e5
C B B ^A31A e f# e2
C B B ^A31A f# f# e2
C B B ^A31A e g B e2
C B B ^A31A e e1
C B B ^A31A e e e1
C B B ^A31A e1
C B B ^A31A B e e1
C B B ^A31A g B e e1
C B B ^A31A e f# B e1
C B B ^A31A e f# f# e1
e C B B ^A31A f# e10
e C B B ^A31A g B e5
e C B B ^A31A f# f# e4
e C B B ^A31A e f# e4
e C B B ^A31A e g B e1
e C B B ^A31A g f# e1
e C B B ^A31A f# B e1
e C B B ^A31A C g B e1
e C B B ^A31A e1
e C B B ^A31A B e1
e C B B ^A31A f# f# f# e1
e C B B ^A31A e e1


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