Introduction by Bruce Berr, Editor 
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hen I started thinking about my introduction to the fine articles
you are about to read, some lyrics came to mind from Stephen Sondheim's
haunting Children Will Listen:
A little later on in the song . . .
Although the lyrics refer to parenthood, I believe they also apply to teachers as well, and on many levels. When a piece has a pervasive problem that might impede the student's learning, of course we pounce on it right away and try to make sure that the student will master it so that it doesn't get in the way of an artistic performance down the road. Sometimes, we do this by introducing the challenging element before the student ever sees the score to the new piece. We isolate the element-we drill it, we vary it, we emphasize to the student the importance of its being rendered accurately. All of this is called preparation, and it can be good pedagogy.
But sometimes the student confuses the means for the end. When so much emphasis is placed on just one element (even for a good reason), the student is tempted to believe that once that element has been mastered, the job is done! The more challenging it is (and thus the more time and energy the teacher devotes to it), the more likely that this kind of musical myopia will occur. The end result might be a performance that sports perfect executions of the now-mastered element but one that still lacks the poetry of the piece. Surprisingly, the groundwork for this to happen can insidiously be laid in our studios throughout the teaching process just by the sheer amount of time and attention lavished on one single element or skill.
To discuss the teaching of the rhythm of the subtle and charming Grieg Nocturne, one cannot avoid examining how to teach two-against-three, because that element is so prevalent. But as you read what Camille Witos and Robyn Gibson have to say, you will see that both authors harp on the importance of going beyond the accuracy of the rhythm-that the rhythm pattern is just a building block in creating a lyrical and mysterious performance. It is what happens after dealing with two-against-three that can make this Nocturne a nocturne.
Camille has recorded several audio clips that demonstrate
points made in her article, as well as a segment from an actual lesson with
a student. We have also recorded her performance of the entire piece. All
of these are posted here on this website. Just about every home computer
can now easily play audio, so we encourage you to listen to them.
Look for the green button in the article for places that refer to audio
on our website.
For those of you with a keyboard synthesizer hooked up to your computer, we have also included the MIDI file of the performance of the entire piece. The advantage of downloading this is that the file is much smaller than its audio counterpart. Also, you can hear the playing in perfect fidelity since your own keyboard will be realizing the performance! Look for the dark blue button for places that refer to MIDI files on our website.
(However, don't bother using your computer's built-in synthesizer to play the MIDI file-the pedaling and nuances will most likely NOT be present due to limitations in current technology. If you don't have a keyboard synthesizer, listen instead to the audio clips).
While you are logged on here, be sure to visit the Rhythm Department articles from a recent back issue of Keyboard Companion (Spring 1997), where Marvin Blickenstaff asked Naomi Oliphant and Constance Kotis the question, "How do you teach two-against-three?" These articles, coupled with the current ones and our website offerings, provide an in-depth exploration of an important rhythm pattern and its teaching application in a wondrous piece of music.
ecently, I judged a competition in which one of the required
pieces was the one we are discussing here, Grieg's Nocturne from
Op. 54. Of course, I wondered how the participants would handle
the inevitable challenge of two-against-three. Some students played it with
ease, while others struggled to make it work. I believe that what makes
it easy for some and more difficult for others is how they are taught to
listen.
All teachers know how difficult it can be to play two notes of any value against three notes of the same value. To achieve mastery of the rhythm, there are some basic principles and skills that every student needs - the intellectual understanding, the physical coordination, and the aural refinement.
First, I teach the intellectual understanding of what I call the basic math lesson. Take this measure from the Nocturne:

Students easily see that the right hand has the twos and the left hand has the threes. To figure out how the rhythms connect, they need to find the common denominator, which in this case is six. Next, I ask them to subdivide the two different rhythms and figure out where the main pulses occur in each hand. This helps them notice where the beats come and where the two hands play alternately and play together.

As they will discover-both hands play together on some beats, play separately on others, and that there are beats where neither hand plays. I think it is important for students to see visually how the voices relate and how to count them.
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