If you are an intermediate or advanced player, and you play the music of Chopin and the other Romantic composers, as well as a great deal of the music since that time, you will have encountered places where the beat consists not of the usual divisions of two (such as eights or sixteenth notes) or three (triplets), but in what I will call "non-standard" divisions. In Chopin, for example, you will find many beautiful passages in the Nocturnes, Ballades, etc. where there is a run (sometimes written in eights, sometimes in sixteenths) with a number such as 5, or 15, or 17, or just about anything, written over the beat (or beats). This means, of course, you must fit all those notes in the beat as shown. Since it is Romantic music, you have the opportunity to have some nuance of timing, and the 15 notes, say, don't have to be exactly metrically equal. There can, and probably should be, some subtle slowing and/or speeding up within it, to enhance the musical line. But they must fit in the beat; you cannot change the length of the beat (except possibly the tiniest amount -- again, a nuance), and therefore the measure, because that would destroy the integrity of the rhythm.
If the number of notes within the beat is say, 15, it will probably be fairly fast. If it is only 5, then it may not be. But regardless what the number, or whether it is fast or slow, you need to learn how to play these. I cannot emphasize this point enough: if you have depended on "counting" to help you with rhythms, you will find it impossible and will be utterly at a loss as to how to approach it. If you try to break them down into smaller units, such as dividing up 15 in 3 groups of 5, it may seem to work but will probably sound stiff and unmusical. Remember, Chopin didn't mean for you to divide it in three groups of five, or he would have notated it that way. The idea is to make the passage sound flowing, and even improvisatory, not metric.
So how do you learn to do these? You learn by giving yourself a unit of time, and then "filling in." Start by playing (probably in your right hand) the note C and then the note G. The time between these is now your unit. Then you fill in the notes (white keys) in between. That's five notes, but the C is the beginning of the beat, and the G is the beginning of the next beat. It is important to remember that whatever number of notes you are filling in, it ends on the next beat. So if you fill in the notes from C to G (C-D-E-F-G) you will have actually played 4 sixteenth notes, again, ending on the G, which is the beginning of the next beat. Four sixteenths should be very simple and of course we do it all the time. You will find it helpful to pick a moderate to fast speed for this. Then, take the same time unit, but go from C to A and fill in. You will now have filled in 5 notes. Remember, don't even think about trying to divide it up into smaller units, which would defeat the whole purpose. Now do from C to B, filling in 6 notes, etc., continuing to make the unit larger each time, with more notes to fill in. Don't worry about perfect fingering, just do anything that works. We are not working on the physical aspect here, but rather, we are training the ear to hear these units and be able to fill them in. It's all about the ear.
Later on, you need to do them randomly. In other words, start with filling in 7, say. Then the next time, start with 10. And so on.
The concept is the same as my approach to learning rhythm from the very beginning. The analogy is that you have a "log" and you learn to "chop" it in equal pieces without the benefit of a measuring tape. With an actual log, you "eyeball" it; with a unit of time, as in music, you "earball" it. See my posts on rhythm for more explantaion.
When you get to filling in really larger numbers, say beyond 12, it is really extremely challenging. But try to be able to get to at least 10 or 12.
You can also fill in using the chromatic scale. If you were trying to fill in 12, for example, you could go from C to C with the chromatic scale.
When you start this, you may not be able to tell if you are doing it correctly. If you start to slow down the time unit (the beat) each time, then you are not actually filling in, you are just changing the length of the beat. And remember, in the actual music we are talking about, you can't do that -- it would be a distortion and not at all what the composer intended. You might be tempted to set a metronome to the time unit, and see if you were able to do it correctly. But what would be even better is to be your own metronome. Slap you left hand on your lap, or tap your foot, and see if you can keep it steady on the time unit while your right hand fills in.
When I do this with my students, I play the "outsides" of the unit, in other words, the beat, along with them as they play. So if they didn't end with me, then they didn't keep to the beat. If they went too slow, then they know they just need to go faster. There is no way to "calculate" how much faster, you just keeping adjusting, trying again, adjusting again, until you get it.
Obviously, it it easier to do this when you are just playing a scale -- notes in sequence. The actual notes in a passage in Chopin will be harder, probably, but at least you now have a foundation.
Another reason why learning to hear these divisions of the beat is critical is so that you can do cross rhythms (also called poly-rhythms). I'm thinking of a Rachmaninoff prelude where the left hand has the beat dividing in 5, and the right hand in either 2 or 3, for the whole piece. Each hand has to be sinuoulsy smooth and silky-sounding. You can't try to "calculate" it out mathematically (like some people might tell you to do with two against three). The only way is to train your ear to hear two different rhythms, or more precisely, two different divisions of the beat.
Rhythm is probably the area that students of music have the most trouble with. Some never actually learn to read the rhythmic notation and instead they just go to YouTube to listen to the piece they are playing and try to copy the rhythm. But obviously, that is not a path to mastery. Rhythm CAN be taught, and CAN be learned, including complex rhythms.
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