As the Royal Library homepage wrote absolutely nothing about this being a puzzle canon, or that a third voice was required to perform the completed composition, this author contacted a librarian there who reported that they had not thought about this at all. He then agreed that both the hypothesis about the missing third voice, and this author's preliminary solution seemed correct. They suggested contacting the Mendelssohn Archives in Berlin in order to find the answer.

Meanwhile, as a part of the H.C. Andersen celebration held by the Schiller Institute in Denmark , we performed this author's preliminary solution with a flute, violin and piano.

There was only one problem – certain measures sounded terrible, and this author became convinced that her solution was wrong.

Finally, the answer came from the Mendelssohn Archive. Mendelssohn had written the original canon in 1838. He had not only sent it to H.C. Andersen, but to four others between 1839-46, including a Carl Kuhlau. (See box about Carl Kuhlau.) 

Here is a copy of the same canon by Mendelssohn as it was written in Carl Kuhlau's album

(From an article in the magazine published by the Gewandthaus Orchestra in Leipzig. There was also no indication that there was a missing voice in this article.)

They also provided a scanned picture of the first few measures of Mendelssohn’s 1838 version.

Eureka ! This was the proof that the hypothesis was correct! Here, in Mendelssohn’s own handwriting, was the canon, complete with the third, missing voice, and how it should be played![3]

Now I will give you two hints:

The correct solution is found by using two transformation principles:

time displacement

musical space displacement (The third voice begins on a different note, at an interval from the first note which is not an octave.)

Now, see if you can solve the puzzle. It is still quite a challenge. Do not proceed until you have at least tried to solve the mystery.

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