Enigma canons in Moscheles' autograph book

Sigismund Neukomm [f71.v]
Gutta cavat lapidem, non vi sed saepe cadendo.
"The drop pierces the stone, not by force, but by constancy" (Ovidio, Ex Ponto)

The Neukomm canon is solved following the order of clefs given at the end, with voice entries at a distance of one bar. What originates is a canon in ascending fifths with successive entries in E-flat, B-flat, F, C, G, D and A. The successive entries will need to adjust the alterations of the modulating melody. The abundance of alterations in the initial melody has a simple explanation: The harmonic rhythm is of one chord per bar and as in each bar we are ascending a fifth, after the prescribed twelve bars (including the essential rest bar at the end) we have given a complete turn to the circle of fifths, reason why we will be able to return to the beginning of infinite form.

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François-Joseph Fétis [f85.v]

Fétis himself provides the solution to his enigmatic canon [f86.r]. It is a triple canon formed by:
1. Two part canon  in unison
2. Four part canon in unison and the lower fourth
3. Four part canon in unison and the fifth

Again the clefs give us the interval of the entries although the rhythmic organization of the entries is more complex to adjust the three canons with each other.

If the previous canon was chromatic, this is completely diatonic and is based on a four-bar chord progression (also by ascending fifths: I-V-II-VI ) that is repeated continuously.

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Bernhard Molique [f100.r]

The case of the canon of Molique is curious. In the first place it has the indications of the keys as in the previous ones. If we look at the key signature, we see that they follow an ascending fifth order (again!). And indeed, the thing works if I start with the canon to the fifth in the third measure (there is a written five), and raising another fifth we reach a ninth in the fifth measure (there is a written nine). So far so good. But the next entry would have to be to the 13th (or what is the same to the 6th), however now there is written ¿15? or ¿i5? And that is not the only problem. If I apply the keys as they are written, there are totally unacceptable dissonances.

The fact is that modifying the keys so that each entry to a fifth is effectively produced (as the succession of key signatures does) the canon does sound in harmony. 

I find it hard to believe that Molique has been confused in such a simple detail (besides the indication of the third entry i5 or 15 I suppose it will mean something). Am I missing something? Does anyone have an idea?

But hopefully, at least for Molique I had some proposed solution, for the following I don't have any. I hope that some perceptive reader can illustrate us with beautiful solutions. I'll tell you at least what I tried.

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Berthold Damcke [f124.r]

Berthold Damcke gives us an indication for his canon:

NB: die zweite Stimme beginnt mit ihrer ersten Note
"NB: The second voice begins on its first note."

In addition, he indicates two clefs. Soprano clef and tenor clef. The question is how to read the latter, which is inverted 180º on both the vertical and horizontal axis. Regarding the horizontal axis, I think it is clear that you have to invert the score and read the notes in tenor clef normally. But as for the vertical axis, I'm not sure. That it is turned to the left means that we have to retrograde the notes of the melody? If that were the case, shouldn't you have put the key at the end? When in doubt I tried all the possibilities but I won't find any in which it makes musical sense…

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Ignaz von Seyfried [f144.v]

Zum Andenken von Ihrem innigen Verehrer
und ewig dankbaren Freunde Seyfried
Wien den 22ten October 1826 
noch berauscht von dem Vergnügen des gestrigen Concertes
"In memory of your admirer
and eternally grateful friend Seyfired
Vienna, 22 October 1826
still intoxicated by the pleasure of yesterday's concert."

The text of the canon says:
Fuori dagli occhi, fuori dal cuore! non sia il proverbio mai vero frà noi
"Out of sight, out of mind!
May the proverb never be true between us."

And to finish Seyfried's canon. Again a succession of clefs seems to be the key to the resolution of the canon. Even a few marks every two bars seem to indicate the distance of the inputs (9 voices, 18 bars, inputs every 2 bars...everything in order).

Now, if I follow the order of the keys there are unassumable dissonances shortly after starting...

I think I have tried all the combinations of entries and I didn't find any in which the voices were perfectly harmonic. But wait, now comes the best part of the story.

Mr. Seyfried has a book entitled "Louis van Beethoven's Studies in thorough-bass, counterpoint and the art of scientific composition". Well, this book has a chapter dedicated to the canon in which the author enumerates the different types of canons affirming the following:

10.  The arithmetical [sic] and enigmatical canons, which like all other kinds of riddles, are easier to invent than to solve, and seldom* repay the time and trouble spent upon them. In former times people considered it meritorious to cudgel their brains with such laborious triffles, but the world is really grown a little wiser now! 

*Never

Reading this after trying countless combinations that look like they're going to work but in the end don't, make you think: has Seyfried been trolling us all this time? Maybe some avid reader can get us out of the doubt.

Ignaz von Seyfried

Dear reader, maybe you can get us out of the doubt. If you can think of something, don't hesitate to send me your solution to these riddles!

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For those who have been left wanting more enigmatic canons, I recommend the website www.puzzlecanon.com. There are some great things to explore out there. 

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