A “virtuous” stacked canon

I’m pleased to report on a recent attempt to solve a canon found on the title page of a music anthology, Odae suavissimae (1601/1602?). Philipp Schöndorff (sometimes Schöndorpp) (1558–after 1617) dedicated this collection, including two eponymous odes, to his Liégeois compatriot Jacob Chimarrhaeus (1542–1614). Both men were at that date employed at the Imperial court of Rudolf II, Chimarrhaeus as almoner (previously as a singer and very good viol player) and Schöndorff as a chapel singer and trumpeter. Indeed, the Schöndorff had gained employment at Rudolf’s court following Chimarrhaeus’s recommendation in 1590, and the younger man’s esteem for his older co-worker may have stemmed in part from that gesture.

As so often happens among researchers these days on social media, musicologist Erika Supria Honisch reached out to colleagues for help to solve the canon that appears towards the top of the ornately engraved title page,  indicated by “CAN 4. VOC”, that is a canon in four parts (4 ex 1). [Edit: I’ve modified the previous sentence, so it does not sound like it is just Dr Honisch reaching out! JS] The canon sets the text “DOMAT OMNIA VIRTUS”, which seems to have been Chimarrhaeus’s motto: “Virtue conquers everything”. I’m grateful to Dr Honisch for the opportunity to exercise my mind on this canonic puzzle and sharing the following image.

Odae suavissimae detail
Detail of title page of Odae Suavissimae (1601/1602?) showing a canon on “Domat omnia virtus”.

Determined not to be conquered by this canon, I set out in the early morning of the 6 March 2019 to find a solution, also providing a few updates on my progress on social media. My first hurried comment suggests that at first I was flummoxed but had started assembling some information:

A tough one. First instinct is to read in C1 clef. Certainly not canon at the unison. Signa placement below notes may be significant. Will return to this later this week. Source?

Well, clearly I decided soon after this post that I could not put it down. Still without a solution, my next update addressed questions around the use of s-shaped signa congruentiae (signs of congruence) to indicate entries of each canonic voice in imitation of the first.

I am beginning to suspect that the last signum indicates a parallel entry, i.e. a third or tenth, and that the other voices enter on the fourth and fifth below (or one above). Possibly multiple solutions.

The penny had almost dropped. I knew of examples of canons from the early 17th century that duplicated a subject at the interval of an imperfect consonance (at third or sixth, and their compound intervals), so the last signum made some sense. I also took a cue from the fact that all signa were placed below the written subject (the dux or guida) and decided that other canonic voices (the comites or conseguentes) must sound beneath it. The dots above the last signum suggested that I try the last entry at the third, although the tenth turned out to be better.

So then there were the first two signa. From about 1500, entries at the fifth and then fourth are the non-unison intervals of imitation most commonly found in canons, so those seemed like good starting points for testing entries on the 1st and 2nd signa. I had wondered if the signa themselves below the notes might indicate the interval of imitation as is sometimes done, but the fourth seemed just right for the first signum. I wasn’t so sure about the second entry, so I tried a fifth, not really convinced with the orthodoxy of this solution. So a first attempt, using a classic technique for composing and teaching canons by a condensed score was hastily posted to the discussion. (This technique is similar  to the synchronic method for composing canons with a “harmoniola” described by Joachim Burmeister in his Musica Poetica [1606], especially apt for canons with subjects moving in similar motion.)

Failed virtue
Screenshot (FinaleTM) of first attempt (fail!) at solving Domat omnia virtus (before breakfast!). Written part is shown as the Soprano voice, with entries of canonic voices every two measures. To perform from this score, the first time round the Alto would not sing the first two measures, the Tenor not sing the first four measures and the Bass only join on the first repeat. Note the many parallel perfect consonances and horrible counterpoint in m. 4. Wrong, wrong, wrong!

After a day of lecturing and administration, I looked at my transcription again and realised its many errors – I obviously had been lacking in virtue before breakfast. It immediately dawned on me that second entry of the subject needed to be at the double fourth (i.e. seventh) below the subject. I should have recognised this possibility quicker. The descending musical sequence C-G-?-A should have suggested to me a D entry straight away! That the solution turned out to be a stacked canon immediately made a lot of sense. A stacked canon is where each voice enter at the same interval in relation to the immediately prior voice, in this case at fourths below. Here it produces successive entries at the fourth, seventh and tenth in relation to the notated voice. What also made sense was the simple underlying structure of interlocking descent though a melodic third.

Domat omnia virtus stacked and condensed
Screenshot (FinaleTM) of condensed score of Domat omnia virtus as a stacked canon.

And so here is a performing score of Domat omnia virtus.

By 1601/02 stacked canon was an established canonic technique in the toolbox of European contrapuntists. The first known example of stacked canon in three parts, Jean Ockeghem (or Okeghem)’s Prenez sur moy, comes from the last decades of the fifteenth century. The first known example of a four-part stacked canon is Jean Mouton’s En venant de Lyon, which was composed in the first decade of the 1500s; see my earlier post on this canon and some of the literature on stacked canons. Stacked canon is an ingenious compositional technique that nonetheless raises interesting questions about whether canonic imitation should be interpreted strictly, that is the relative positions of semitones in the original subject be maintained in transposed versions, or not. Stacked canons in general defy strict imitation; as in Domat omnia virtus, the tetrachordal or hexachordal segment, in which each transposition of the subject falls due to the different interval of imitation, cannot take on the same characteristics of the pitch structure of the original subject, lest the original subject is altered by additional accidentals. For other types of canons, however, this restriction may not come into play.

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