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The solution to 'Sol post vesperas declinat'

March 13, 2018

Back in January, I posted a puzzle that looked something like this.

 

 

Below, as promised, is a solution. But the question may arise to the reader: "How does one arrive at a solution?" 

 

Some of the questions one asks in solving a canon such as this are these: 

  1. are there any textual clues that might help with categorize the canonic techniques: interval of imitation, inversion, retrograde, etc.?

  2. how long is the canon melody?

  3. are the entries equidistant in time?

  4. if the entries are equidistant in time, is the time between the last entry and first voice's repeat the same as the distance between entries?

  5. if the entries are equal in time, does the pitch interval when compounded cause a clash?

  6. are the entries above or below?

  7. if the entries are not equidistant in time, is there ever a recurring time interval?  

Of course the process is eventually trial and error, and the error consists in finding unidiomatic results, especially those unacceptable to the style of the piece's milieu and to the technique of the skilled composers contemporary and proximate to the composer of the canon.

 

First, it is clear that the canon modulates, because the direct symbol after the repeat sign is not at the same pitch as the first note.

 

The Latin epigram suggests church style, so the typical sixteenth-century counterpoint training should suffice for a student to be able to separate the wheat of a good solution from the chaff of errant hypotheses. 

 

To solve for the bass's entry, one needs to find a first note that is consonant with the tenor's D. It is difficult to imagine a lower first note than the D itself, since the melody is to descend a fifth from its first note. The choices are D, F, A and B-flat, though the last of these would be quite odd, as the sixth would sound somewhat contradictory to the goal note D in the tenor. 

 

B-flat as first bass note

Aside from the previously mentioned objection, this leads to a dissonance as the tenor skips upward to F, forming a fourth between the voices only to be followed by another fourth on the final half note of the bar, and things do not improve.

 

Alto or soprano (canto) as second entry

After considering the above options, one can see that only D would work as the first note of the second entry. However, if either the soprano or alto voice entered with D, a (dissonant) fourth rather than a fifth would occur on the downbeat of measure 4, and this would be sour.

 

A as first bass note

This note is certainly consonant, but a dissonance is formed on the downbeat of measure four as the tenor changes direction.

 

F as the first bass note

This forms parallel unisons with the tenor, F to E, during measure 3.

 

D as the first bass note

This solution does work, as shown in the solution, above.

 

The other entries must also form consonances on beats, with passing tones, etc.

 

 

One may continue with the other entries using the same trial and error to find the composer's intent.

 

The types of errors exemplified above are sufficient to dismiss the hypothesis that a competent composer would choose them. These are parallel perfect unisons, fifths or octaves or dissonances on beats (unless they are suspensions), such as seconds, fourths, sevenths, ninths and so on or augmented or diminished intervals.

 

 

 

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