Luciane Beduschi

Composer’s opinions about the multiple solutions for their puzzle canons

The first canon composed by Joseph Haydn on the Ten Commandments is a puzzle canon with multiple solutions: all the more numerous because the sources differ with respect to the use of clefs and number of voices. The enigma is two semi-circles that can be read turned up and down, clockwise and anticlockwise. These readings give four different realizations. Changing the order of the realizations, one changes the harmonic progression. Changing from three to four voices, one changes the chords. Changing clefs, one changes the pitches.

Luigi Cherubini solved the 72 enigmatic canons from Padre Martini’s Storia della Musica, with comments like this: “I have no additional comment to make about this canon, unless that its composition is carelessly treated and, if I dare say, faulty even in the last measures, either in the arrangement of the parts, or in the way in which the chords are reverted.”
In 1814 Sigismund Neukomm composed a canon for the gravestone of Joseph Haydn. The solution was sought for 30 years. Neukomm derided one of them: “Your MD appears to have studied counterpoint under Alexander the Great; at least, his so-called resolution is realized in this great art. […] The dissonances in this resolution are absolutely faulty […], true contrapuntic impieties.”
J. G. Albrechtsberger writes: “It happens that a melody able to produce a canon yields several hidden answers.” The number of possible solutions is still higher in the case of puzzle canons because the enigma can be read in different manners. Nevertheless, composers appear to have had their preferred solution, carrying their particular harmonic conception. This paper proposes to raise and discuss these issues through the analysis of different solutions for enigmatic canons composed by J. Haydn, Padre Martini, and S. Neukomm.