More metrics for the shape of the music

Shapes abound in music. What rationale is there for their choice. How easy would it be to hear patterns? Various other questions as we think of them.

One that stood out is the shophar motif. You perhaps noticed that Psalm 61 is one of the shophar psalms with several intervals of a fifth 'e B' and 'B e' in it.

Ten psalms have no verses beginning with the opening fifth. The remaining 140 psalms have a range of 1 verse in 14 verses to 3 verses in 4 with an opening fifth (Psalm 149). But the range is widespread so the interval does not define the shape of a psalm by itself.

Many verses end with a descending fifth from B to e.  All the verses in Psalm 136 end with the interval B e. The range here for the 141 psalms with verses ending in B-e is again widespread. 4 psalms have a count greater than 4 verses in 5 ending with the descending interval of the fifth. 15 are between 3 and 4 verses in 5, 41 are between 2 and 3 verses in 5, 68 between 1 and 2 in 5, so that leaves 13 with fewer than 1 in 5 but at least 1 and 9 with none.

To summarize:

Interval	none	fewer than 1/5	more than 1/5	more than 2/5	more than 3/5	more than 4/5
Opening e B	10	36	73	26	5	0
Ending B e	9	13	68	41	15	4

I looked at the sequences of accents under the text, eliminating consecutive duplicates. In the psalms alone there are 660 patterns. 436 of them occur in only one verse. 90 occur in 2 verses. 33 occur in 3 verses, and so on. The pattern e B A f e occurs the most often, 111 verses. g B A f e occurs in 105 verses. e f A f e in 96 verses.

Here's a graph of the top 40 phrases. That leaves 420 more to trail off to the right....

Top 40 sequences of sublinear te'amim in the Psalms

And these are the 298 verses that start and end with the interval of a fifth.

Sublinear te'amim silluq-munah and munah-silluq

Because of the nature of the illuy (above the text), not all fifths are noted using only the accents below the text.

See also here and here.