Double Crab Canon

Hi

The crab canon (cancrizans in Latin, cangrejo in Spanish) is  know (wiipedia) as well as "retrograde canon, canon per recte et retro or canon per rectus et inversus)... is an arrangement of two musical lines that are complementary and backward. If the two lines were placed next to each other (as opposed to stacked), the lines would form something conceptually similar to a pallindrome. The name 'crab' refers to the fact that crabs are known to walk backward (although they can also walk forward and sideways).

The most famous crab canon is the one Bach wrote for the Musical Offering. There are no many canon of this type, because it is more an exercise.

It has its difficulty. The crab canon harmonizes one melodic line with itself in retrograde. So, you have to write a double (invertible) counterpoint, taking care of the fifth interval, because once inverted it becomes a dissonant fourth. So, fifths should be treated as dissonances.

I have written, with time, some crab canon, just for fun and as a counterpoint exercise.

But I had a concern with the possibility of writing a double crab canon. That is to say: two crab canon which can sound together.

I have not seen any methods to to this. But I developed my own.

I wrote a simple cancrizans 6 + 6 measures. Afterwards I wrote. second one in a lower register, having in mind the first. Third, I put both canon together. Fourth, I wrote the result with all the lines in retrograde. I think more combinations are possible, but taking care of the intervals.

At least, it was fun. I'll keep this piece... Perhaps I use it in a larger format as a part of an orchestral work.

It's so hard to write a crab canon, let alone a double crab canon.... Really amazed by your skill!

I do find some little flaws though, e.g. b.4 of the lower parts crab canon when both get on an E, b.6 and 7 with the harmony, b.10 with a parallel octaves from Bb to D, b.12 with parallel octaces from A to D.

In the combined crab canon, there's a parallel octave btw first violin and viola fr. b.2 to 3, A to Bb. B.6 has a clash of Bb in first violin and B natural in cello, b.9 F sharp in first violin and F in cello.

But of course I am way too nitpicky. We all know how hard it is to write a crab canon, let alone a double one!! Thank you so much for displaying your skill here and sharing this wonderful counterpoint studying piece!! I am very appreciated on this!!

Henry

Thanks for listening.

Let's see...... with 4 voices, or more, it's quite difficult to avoid all those parallels. What I have in mind is avoiding that between the soprano and bass voice. ut with middle voices, I am more permissive.

Doubling the third is not impossible, either. An in this case, on of the thirds jumps immediately to the 5th. But it has an easy solution, I take it.

The clash is, of course, a mistake, I'll mend it soon. 

Luis.

@Henry Ng Tsz Kiu

Fine!, I made those corrections, it's better.

Very nice work, Luis! I'm quite impressed by this. 

Regarding parallels: One thing to keep in mind is that parallels themselves aren't necessarily bad when the individual lines retain their independence. You don't want the parallels to harmonize with each other -this 'independence' is why that rule exists. Many composers find that difficult. Thus, many composers avoid parallels like the plague. In this instance though, you have enough independence within the lines that I don't think the parallels really would've detracted from it. Just my two cents.

Enjoyable work! 

1 hour ago, jawoodruff said:

Very nice work, Luis! I'm quite impressed by this. 

Regarding parallels: One thing to keep in mind is that parallels themselves aren't necessarily bad when the individual lines retain their independence. You don't want the parallels to harmonize with each other -this 'independence' is why that rule exists.

 

I totally agree. When the texture becomes complex with 4 or more voices trying o avoid some parallel here and there can lead to unnatural melodies with leaps, etc...

I the crab canon, besides, there are more limitations since fifths must be taken carefully because when inverted, they become fourths.

In all, it's just an exercise.

I'm learning so much from your music lol

This is admittedly an era of music that I've neglected solely because I don't enjoy most of it aurally, but I'm learning new things here and there from each compositional exercise you post. Thanks so much for sharing your studies in an applicable way, I'm sure you're having loads of fun with it. 

I'm very curious where this leads your musical voice, as although I'm finding loads of interesting things from these types of pieces you post, I'm even more eager to what your style becomes once you've exhausted your studies in this realm. 

As always, I really enjoy your clear markings of chords and color coding for what you're portraying. Wonderful work, Luis

5 hours ago, Thatguy v2.0 said:

 

 

I'm very curious where this leads your musical voice, as although I'm finding loads of interesting things from these types of pieces you post, I'm even more eager to what your style becomes once you've exhausted your studies in this realm. 

 

 

Yes, many times Ive use tool I learn and explain in my blogs.

In my opinion, the more resources a composer knows, the better compositions he/she can produce.

I make a distinction between writing short or very short exercises just to show how the tools work, and other larger compositions. The problem is I don't have time enough to do everything. 

As I said in another post, some day I'll have to stop and write something I want to.