Composer Karim Haddad’s Motets present a complex rhythmic language based on the medieval concept of prolation taken to a modern extreme. The notation is beautiful and evocative, but tremendously difficult to realize as a performer.

The original, complex notation for Haddad's motets

Conceptually lucid, impossible to perform (currently)

Realizing this (thanks Karim!), the composer has also presented a ‘quantized’ version of the score, translating the many layers of tuplets into their duration in milliseconds, then mapping this information onto the closest approximation afforded by 2-8 subdivisions per quarter note. The result can be extremely variegated series of tuplet subdivisions of a regular beat, requiring accurate placement of say, the final septuplet of one beat, and the final triplet of the following beat, as in the below example.

The human-readable quantized notation for Haddad's motets

Eminently readable and aurally identical

This notation, while immensely more familiar and readable, poses a unique challenge. It requires of the musicians the ability to switch subdivisions in some cases, every beat. This is not something that musicians are normally trained for; we are usually very good with duple and triple subdivisions of the beat and can fake our way through fives, and switching between them involves some grinding of gears. I wanted to train myself to instantly hear these higher-prime subdivisions in the same immediate way we hear duple and triple divisions.

I began by practicing each division on its own, putting on the metronome and simply subdividing, for example, an even five, ensuring that each attack was of equal length and unaccented. Of course 5s and 7s end up in groupings of 2 and 3, but I found it most useful to keep the subdivisions flexible, later improvising groupings with the metronome, exploring aspects of the subdivision. Then I would move between several subdivisions, alternating fives and fours, feeling the even pulse of each, and how they relate. After I felt more comfortable in each subdivision, I wanted a way to practice long strands of changing subdivisions like I knew I would find in the Motets. Using a favorite tool of practice and composition,, I created a string of hundreds of random numbers between 2 and 8, presented in 4 columns. I put my trusty Dr. Beat on 4/4 and dove in, reading each number as a subdivision. It’s tedious work, but even a few sessions found me more confident in dealing with simple subdivisions of the beat. In a way, there’s no difference between triplets, sixteenth notes, and septuplets; they’re all periodic subdivisions, evenly filling the space between two pulses. There’s no special secret to learning them, only the familiarity that we have from years of duple/triple based music that has led us into rhythmic complacency and fear of the higher primes!

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  1. is there an indicated tempo? I ask this because I’d say this really plays a large role in understanding the ‘interpretive breadth’ for such a work. If its just a regular old ___ note = _ , then the 5/4, 3/4 bar example is a necessary step. But it’s my opinion (and I’m not much of a performer, so for what it’s worth), that if the tempo is in words, or left out, then I’d say that the most important element is the proportions inside each smallest tuplet, and the tempo relations: slowest, slower, slow, fast, faster, fastest, etc.

    What do others think? My thoughts definitely apply to other works, but maybe it’s not clear exactly which ones. The main thing about this material is the idea that there is an operation upon rhythmic values that are being halved, thereby taking what was boxy and making it lean in different ways.

    whouf, too early to be succinct..

  2. There is an indicated metronome marking for the piece. I don’t think there’s _too_ much ‘interpretive breadth’ in rhythmic interpretation, although that’s a heady general issue when dealing with complex notation! The difference between a septuplet and a 32nd note attack at quarter=40 is about .02 seconds (if my math is right), so the specificity is quite important, I think.

    Of course, the transcription of the work into this new notation is another step in composing, really, and could have been done in many different ways.

  3. right on. which score do you see yourself using leading up to the performance?

  4. Absolutely the second version – the piece is for up to 5 voices, often with different irrational time signatures occurring simultaneously in each part – so there would be no practical way to perform it from the original score except to use it graphically (which I think is antithetical to the idea of the piece, and the reason why he gives a quantified version).

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