AUGMENT, DIMINISH AND IMAGINE

Finding inspiration when composing can seem tricky. Most of us will have techniques that expedite the creative process, especially when a deadline looms and there is no time to waste. One very helpful technique I have stumbled upon is the archaic musical device known as mensuration canon. Also known as prolation canon or canon by augmentation/diminution, mensuration canon can be a very powerful tool in a composers artistic-arsenal. The experience I have gained from doing my own experiments with mensuration canon has been of great importance to my development as a composer and if you want to know more about this musical supplement then please let me share my findings on the recent rhythmic resurgence.

Mensuration canon is nothing new and early examples can be found throughout history, with documented pieces dating back to the Renaissance. In my opinion mensuration canons feel like they predate the word music and from my experiments I have had some great epiphanies and formulated some unsubstantiated theories. Who doesn’t love an unsubstantiated theory, right? Beside my own personal beliefs that are nothing more than an observance and lay in the imaginary realm of possibility, mensuration canon has an inherently artificial quality to it. Artificial because it is quite a cognitive process to make one. By describing the canons as artificial, I am not implying that they are unmusical, in fact some of them seem so perfect that it is hard to imagine a series of notes in any other way. So what is a mensuration canon? Let’s take a look!

Mensuration canon’s fundamental principle is the notion of multiplying or dividing the rhythmic duration of a melody or phrase. It is true that mensuration canons do not need pitch and can be played in a purely percussive manner, but in the interest of sharing my experience I would like to demonstrate them using pitch. It is up to the composer to decide how the divisions will occur and there are no real rules governing this – the only rule being that the subdivisions divide evenly or the additions are perfect multiples of the original. By adding to the duration, we achieve augmentation and by subtracting we have diminution. I have found that I use both of these techniques at the same time, probably because I have composed short motives that fit somewhere in the middle. I don’t lock into the fact that I will use all addition or all subtraction, I just experiment with the material by expanding and contracting the rhythmic values. Remember that besides being a largely cognitive process, the result still needs to sound musical.

An initial example could be shown as such.

Example 1

Notice in Example 1 that the original is quarter notes, the diminished is eighths and the augmented is half notes. All of the lines contain the exact amount of melodic information. I generally use modes or limited pitch sets when I am creating these canons, as I have found they lend themselves incredibly well to this style of music creation. I think this is from thinking in a minimalist way, where diatonic clustering is utilised and adored.

Making musical passages from such a crude method of composition is helped by using a Resultant Melody. Resultant melodies are a melodies or phrases built from the information supplied in the canon. By systematically working through the material, a melody can be developed that in essence was always there – we just articulate certain beats to make it more pronounced.

Example 2

Example 2 shows the resultant melody with highlights indicating where it was taken from. Notice that the length of the melody may change, as long as the initial pulse is synchronised with the material. Of course, these rules are more like guidelines to make early experiments work and like anything, rules can bend or be broken.

The time it takes for a mensuration to complete its cycle is dependant on the rhythms used. In Example 2, we see that the length of the cycle is two bars. If we were to augment the original by 1.5 (turning the quarter notes into dotted-quarter notes) then we notice that the cycle takes 3 bars to complete.

Example 3

You can see from the picture of Example 3 that it now takes three measures for the cycle to complete. I have also dropped the augmented voice down two octaves and dropped the original voice down one octave. A reason behind dropping the voices is that it frees up space and less clusters are heard – this is a double edged sword because diatonic clustering works best in registers above middle C, so take caution when dropping parts. Too many notes in the bass registers will sound muddy and won’t have the same effect as when they are played in higher registers, this is because human hearing responds better dissonances at higher pitches. By making a resultant melody (Example 4) with the new material, we now have another phrase to the canon.

Notice that the resultant melody in Example 4 borrows the material from any register and assigns it wherever it works to make a convincing melodic idea.

As you would have noticed, I have only used an original phrase with uniform note values. An experiment that I still have to try is using unequal note lengths in the original but for now, I’ve found that using equal note values is a quick way to make some convincing minimal or post minimal music. Using mensuration canon is also a great way to create accompaniments that have a motor and become the engine room of the music. Try using your favourite chord progression in a mensuration canon and you will be amazed at how the music begins to write itself – which gives way to all sorts of philosophical ideas. Use this technique as part of your compositional practice but don’t feel restricted to stay in the confines of the rules, use it whenever and wherever your artistic judgement calls for something of this nature.

So the above examples worked as a quick demonstration and introduction to mensuration canon, but how does it sound in a piece of music. Can this technique be used to create a compelling listening experience for the listener, unaware of the cognitive puzzle-play of the composer? I have written a piece for String Quartet to let you be the judge. Mensuration canon is everywhere in this piece and is the foundation for the entire work (for the most clear example of it, take note of bar 53).

Thanks for reading and stay creative! 😀

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