I have been wrestling with some problems with notating rhythms recently. Perhaps I should say I have been exploring rhythmic possibilties? In my String Quartet No. 2, I decided that I wanted a particular effect in the first movement where the last beat of the measure would be slowly expanded to give a sort of limping meter. At first I wanted to do this with just a text instruction: "Repeating the chordal passage sixteen times, expand the last beat of the measure from a quarter note value to a half note value incrementally." My violinist suggested notating this precisely so I ended up with this:
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That is just part of the passage. Each measure is repeated four times. The last beat of the measure grows from a quarter note, to a quarter tied to a sixteenth, to a quarter tied to an eighth and so on, until the last beat becomes a half note. The latter part of this process is shown above. Now there is no doubt that this is notationally ugly! I soon realized that the composer that had really explored this technique, known as "additive rhythm" was Olivier Messiaen. What inevitably happens if you use additive rhythms is that you destroy the meter; this kind of music is "ametric." I discovered this looking at Messiaen scores and seeing that he simply omits meter entirely. Here is an excerpt from his
Catalogue d'oiseaux, "Le Chocard des Alpes."
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Even where, as in the beginning of the piece, the meter is clearly 2/4, he shows no meter and there are many passages like this where there is no regular meter. Unfortunately, not showing or more importantly, not having a regular meter, is not an option in my music software, so for my most recent piece, I simply notate everything in 4/4, but the bar lines are actually irrelevant. In this passage the violin is doing a "subtractative" rhythm while the guitar does an additive one:
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Deal with that, copyright bots!
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